WO2022064445A1

WO2022064445A1 - Automated method for identifying and indicating to an operator pathological risk regions in at least one part of a patient's cardiovascular system by means of the reconstruction of an augmented reality of morphology and hemodynamics

Info

Publication number: WO2022064445A1
Application number: PCT/IB2021/058738
Authority: WO
Inventors: Luca BIFERALE; Roberto VERZICCO; Francesco Viola
Original assignee: Universita' Degli Studi Di Roma "Tor Vergata"; Gran Sasso Science Institute
Priority date: 2020-09-24
Filing date: 2021-09-24
Publication date: 2022-03-31
Also published as: IT202000022528A1

Abstract

A method for identifying and indicating pathological risk regions in at least one part of a patient's cardiovascular system to a healthcare operator, by means of a quantitative and validated reconstruction of augmented reality of morphology and hemodynamics of at least one part of the cardiovascular system, the method comprising the stages of - providing, as input data, position data over time X_meas(t), previously acquired, of the morphology of the at least one part of the cardiovascular system, obtained from two-dimensional and/or three-dimensional images of said at least one part of the cardiovascular system on one or more subsequent cardiac phases; - processing said position data and performing a simulation of the fluid-structure interaction (FSI) of said at least one part of the cardiovascular system guided by the acquired data. The simulation produced allows constructing an augmented representation of the morphology and hemodynamics of said at least one part of the cardiovascular system which allows the software, by means of known calculations, to identify and indicate pathological risk regions to a healthcare operator to carry out a more effective prognosis also in positions not examined by the initial ultrasound data.

Description

AUTOMATED METHOD FOR IDENTIFYING AND INDICATING TO AN OPERATOR PATHOLOGICAL RISK REGIONS IN AT LEAST ONE PART OF A PATIENT’S CARDIOVASCULAR SYSTEM BY MEANS OF THE RECONSTRUCTION OF AN AUGMENTED REALITY OF MORPHOLOGY AND HEMODYNAMICS ***********

Field of the invention

The present invention relates to an automated method for identifying and indicating pathological risk regions in at least one part of a patient's cardiovascular system to an operator by means of a quantitative reconstruction of an augmented reality of morphology and hemodynamics of said at least one part of the cardiovascular system. The invention further relates to a related device for identifying and indicating said pathological risk regions to an operator, and to a machine for acquiring cardiographic images and data comprising said device. Background art

The shape and dynamics of at least one part of the cardiovascular system, the direction and intensity of the blood flows therein, and the intensity of the blood pressure on the walls thereof must be monitored for the diagnosis and prognosis of cardiovascular diseases.

Two-dimensional ultrasound is a widely used non-invasive imaging technique which allows studying the heart in action by highlighting the cardiac structure, the real dimensions and thicknesses of the myocardium, in all the sections thereof, and of the valve apparatuses. Such a measurement technique is based on the use of ultrasounds which are completely harmless and the examination can be performed on any patient countless times, even during pregnancy. Ultrasound has a considerable value both in the diagnostic and prognostic field, but the measurement space is limited to a two-dimensional range the axes of which form an angle which can vary between 30 and 90 degrees. In some specialized centers it is possible (with higher costs with respect to a two-dimensional ultrasound) to analyze a series of 2D scans to reconstruct three-dimensional images which are still (three-dimensional ultrasound) or in motion (four-dimensional ultrasound), without however quantitatively reconstructing all the details of the morphology and hemodynamics within at least one part of the organ over time.

The morphology of the blood vessels and heart chambers is also observable by means of more precise but much more expensive monitoring techniques (CT and MRI) or, in the case of CT, also harmful because they involve a considerable dose of ionizing radiation. Furthermore, in the CT scan, the blood flow measurement also requires the patient to be injected with a toxic substance used as a contrast medium.

Finally, in the case of color Doppler it is possible to detect the blood flow velocity. However, the low accuracy of the instrument generally only allows determining whether the flow is approaching or moving away from the probe, with great uncertainty on the velocity components orthogonal to the probe.

The 4D-MRI technique allows the three-dimensional reconstruction of the velocity field but, despite the great potential, has limited application in the clinical setting, not only due to the high cost but also due to the fact that the use of 4D-MRI in clinical routine is still hampered by long acquisition times: 10-20 minutes for the scan of the thoracic aorta alone with a limited spatial resolution of 2-3 mm in each dimension (often acquired anisotropically) and a temporal resolution of 30-40 ms. Therefore, hemodynamic data are acquired and averaged over multiple cardiac cycles, and hemodynamic changes between heartbeats cannot be considered. A greater spatial-temporal resolution further extends the acquisition times. Furthermore, the hemodynamic results are affected by the patient's breathing pattern and heart rate.

As for the pressure inside the arteries and heart chambers, this can be measured with the Swan-Ganz catheter (pulmonary arterial catheter, PAG) provided with an inflatable balloon at the end thereof. By means of an introducer, inserted in a large-caliber central vein (e.g., jugular vein), the catheter can be pushed into the right atrium, then into the ventricle and into the pulmonary artery. The PAG is disadvantageously an invasive hemodynamic monitoring device used in anesthesia and especially in intensive care.

Finally, as regards the (normal and shear) hydrodynamic loads acting on the tissues, these are difficult to measure in-vivo and are typically extrapolated in a semi-empirical and semi-quantitative manner from pressure measurements. The need is therefore felt to provide a quantitative and validated method to construct an augmented reality of morphology and hemodynamics of at least one part of the cardiovascular system which, based on characteristic data of the individual patient, allows identifying and indicating to an operator, in an automated manner, pathological risk regions in said at least one part of the patient's cardiovascular system.

Currently some computational methods are known but these disadvantageously require 4D images of the whole part of the cardiovascular system under examination, to be imposed as a boundary condition. One of these methods is disclosed in document US2012/022843A1 . However, such images are hardly available and also particularly expensive. Furthermore, these known methods do not allow identifying and indicating possible pathological risk regions to an operator in an automated manner.

Summary of the invention

It is an object of the present invention to provide an automated method for identifying and indicating pathological risk regions in at least one part of a patient’s cardiovascular system to an operator by carrying out a quantitative reconstruction, even starting only from partial data of the position over time of the tissues of the part under examination, of an augmented reality of morphology and hemodynamics of at least one part of the cardiovascular system, useful for an objective evaluation of clinical quantities of the patient which cannot be measured in vivo with non-invasive techniques, such as instantaneous three-dimensional blood velocity field, instantaneous three-dimensional pressure field, mechanical hemolysis, hemodynamic loads generated by blood flow on tissues and/or others.

It is another object of the present invention to provide a device for identifying and indicating pathological risk regions to an operator using the display of such an augmented reality of the morphology and hemodynamics of said at least one part of the cardiovascular system, preferably during data acquisition in the presence of the patient or in a step following the data acquisition.

It is a further object of the present invention to provide a machine for acquiring cardiographic images comprising said device.

The present invention achieves at least one of such objects, and other objects which will become apparent in light of the present description, by an automated method for identifying and indicating pathological risk regions, in at least one part of the cardiovascular system of a patient, to an operator, the method comprising the following stages:

- providing, as input data, position data over time Xmeas(t), acquired by means of imaging techniques, related to at least one subset of the morphology of the at least one part of the patient’s cardiovascular system on a plurality of subsequent cardiac phases;

- processing said position data over time Xmeas(t) and performing a simulation of the fluid-structure interaction (FSI) of said at least one part of the cardiovascular system; wherein processing said position data over time Xmeas(t) and performing said simulation comprises the following stages: a) reconstructing the three-dimensional geometry of the morphology of said at least one part of the cardiovascular system, by means of a shape reconstructor of the morphology; b) producing a three-dimensional calculation grid Xo for the morphology of said at least one part of the cardiovascular system, by means of a segmentor, dividing the three-dimensional geometry into a plurality of geometric elements; c) quantitatively reconstructing the instantaneous three-dimensional configuration X(t) of the morphology of said at least one part of the cardiovascular system by means of a structural solver which receives as input the three-dimensional calculation grid Xo and a position guidance force fNx(t) for guiding said geometric elements during the tracking of said position data Xmeas(t) over time, said position guidance force fNx(t) being determined by a position guidance algorithm; d) quantitatively reconstructing the vector field of the instantaneous blood velocity u(t) and the field of instantaneous blood pressure p(t), by means of a blood velocity and pressure solver which receives as input the instantaneous configuration X(t) from the structural solver; and, given said vector field of the instantaneous blood velocity u(t) and said field of the instantaneous blood pressure p(t), the blood velocity and pressure solver determines the instantaneous hydrodynamic force fn(t) acting on the morphology of said at least one part of the cardiovascular system, sending said instantaneous hydrodynamic force fn(t) as input to the structural solver which, taking into account both the three-dimensional calculation grid Xo and the position guidance force fNx(t), reconstructs the instantaneous configuration X(t); e) constructing by means of a post-processor a representation of augmented reality of morphology and hemodynamics of said at least one part of the cardiovascular system using both the instantaneous configurations X(t) and the vector field of the instantaneous blood velocity u(t) and the field of the instantaneous blood pressure p(t) within said at least one part of the cardiovascular system; wherein an output device displays said representation of augmented reality to an operator; f) identifying, by means of the post-processor, one or more pathological risk regions in said at least one part of the cardiovascular system, and indicating said one or more pathological risk regions to an operator by means of the output device.

In a first variant of the method after stage f) there are provided the stages of: g) acquiring further position data over time X'meas(t), measured by means of imaging techniques, related to said one or more pathological risk regions on said plurality of cardiac phases; h) entering as input data the position data over time Xmeas(t) and said further position data over time X' meas (t); i) processing said position data over time Xmeas(t) and said further position data over time X'meas(t), and performing a simulation of the fluid-structure interaction (FSI) of said at least one part of the cardiovascular system by repeating stages a) to f).

In a second variant, the stages g) to i) are carried out iteratively until the representation of augmented reality of morphology and hemodynamics of said at least one part of the cardiovascular system remains unchanged.

Preferably said at least one subset of the morphology is represented by at least a two-dimensional section of the at least one part of the cardiovascular system on a plurality of subsequent cardiac phases, preferably at least 20 cardiac phases per cardiac period, for example from 20 to 30 cardiac phases. The at least one part of the cardiovascular system can be at least one heart chamber and/or at least one heart valve and/or aorta and/or a pulmonary artery and/or other.

By way of example, the aforesaid pathological risk regions can be regions with high viscous loads and/or regions of blood stagnation and/or regions with high potential for activating platelets and/or regions of hemolysis risk and/or regions of risk of thrombus formation and/or regions with high normal hydrodynamic stress on biological tissues and/or regions with high hydrodynamic shear stress on biological tissues.

Another aspect of the invention relates to a device for identifying and indicating pathological risk regions in at least one part of the cardiovascular system to an operator, said device comprising a computer program configured to perform the above method.

A further aspect of the invention relates to a machine for acquiring cardiographic images comprising the aforementioned device.

The input data, i.e. , the position data over time Xmeas(t), can be previously acquired through imaging techniques, and can be obtained from two-dimensional and/or three-dimensional images of said at least one part of the cardiovascular system.

The method of the invention can be carried out during the data acquisition in the presence of the patient or in a step following the data acquisition.

In a first variant, only two-dimensional ultrasound data acquired on a plurality of subsequent cardiac phases are used to reconstruct the patient's cardiovascular system. For example, it has been found that, to obtain a reconstruction of the augmented reality of morphology and hemodynamics of the part of the cardiovascular system under examination, at least one two-dimensional section of said part of the cardiovascular system on at least 20 cardiac phases per cardiac period is sufficient. This can be achieved by using at least the position guidance force fNx(t).

Instead in another variant, a combination of two-dimensional ultrasound images and/or three-dimensional images acquired by ultrasound and/or MRI and/or CT can be used. The proposed method, which is based on the combination of a computational model of the cardiovascular system coupled with a data assimilation technique, for example a nudging or machine learning or Kalman filter technique, allows reconstructing the three-dimensional structure and dynamics of the blood vessels and heart chambers from two-dimensional ultrasound data only, and both qualitatively and quantitatively improving the ability to reconstruct blood flows even in three-dimensional or four-dimensional ultrasound scans, giving access to new information regarding the hemodynamic properties even of non-measurable observables in a non-intrusive manner and/or in regions not observed by Doppler ultrasound and/or with better resolution, with the consequent improvement of the prognostic abilities on the patient.

Since the computational model of the cardiovascular system comprises a structural solver and a fluid dynamics solver, or blood velocity and pressure solver, the solution of the invention also allows the accurate reconstruction of three- dimensional hemodynamics in the entire volume of interest (e.g., ventricular and atrial chambers of the human heart) and, therefore, the measurement of the pressure field and of the tensions exerted by the blood flow on the cardiac and vascular tissues.

In particular, the proposed method is based on a fluid dynamics solver which calculates the patient’s vector and three-dimensional blood flow from the partial measurements extracted, for example, by Doppler ultrasound and providing a personalized and quantitatively reliable augmented reality for the entire blood circulation inside said part of the organ and/or of the main vessels.

Implemented through the use of software for the analysis and production of data, this method allows the measurement of these quantities non-invasively for the patient and at low cost.

The ultrasound and/or MRI and/or CT and/or other data of the patient are used, through an algorithm of assimilation of empirical data, for example a nudging algorithm, to instruct the virtual model which thus becomes patient-specific.

Guided by the acquired data, the computational model allows estimating the instantaneous three-dimensional geometry of biological tissues (e.g., the heart chambers) and reconstructing the hemodynamics with excellent spatial and temporal resolution. It is also possible to measure other quantities of clinical interest generally not measurable in-vivo with non-invasive techniques, such as: the instantaneous pressure field, mechanical hemolysis and the shear tension generated by the blood flow on the tissues. In fact, since the method predicts the vectorial and three-dimensional velocity field in the entire volume of interest, the hydrodynamic loads on the wall can be calculated directly in the velocity field postprocessing step.

For an adequate diagnostic framework and a consequent therapeutic approach of cardiovascular diseases, it is important to examine the instant morphology of the cardiac structures (walls, valves, cavities) and to detect the blood flows and determine the damage of the biological tissues subjected to pressure and shear loads. The proposed method allows improving the measurement of these quantities with respect to the current technologies of clinical use.

A summary of the main advantages of the method of the invention is below:

1 . The method allows generating a patient-specific computational cardiovascular model starting from ultrasound data (less harmful, rapidly acquired, more accurate and less expensive with respect to other clinical measurement techniques); however, the method can also work starting from MRI and/or CT and/or other data;

2. Our idea of data assimilation and data reconstruction coupled to a computational cardiovascular model, guided by clinical data by means of an algorithm which generates one or more guidance forces, reconstructs the three- dimensional morphology of blood vessels and heart chambers, reproduces the three-dimensional hemodynamic flows, the three-dimensional pressure field and the related loads on the tissues;

3. The model can be used in a complementary manner to the ultrasound systems currently used without the need to modify/replace the machines already in use;

4. The method allows, starting from said reconstruction of augmented reality, identifying and indicating any areas of pathological risk to the operator.

Further features and advantages of the invention will become more apparent in light of the detailed description of non-exclusive embodiments.

The dependent claims describe particular embodiments of the invention.

Brief description of the drawings The description of the invention refers to the accompanying drawings, which are provided by way of non-limiting example, in which:

Figure 1 depicts a diagram of a processing system, with a biophysical simulator and an imaging system;

Figure 2 depicts a diagram of a biophysical simulator;

Figure 3 depicts a diagram of a tissue shape reconstructor with a database of 3D geometries of the cardiovascular system;

Figure 4 depicts a 3D reconstruction example of the geometry of a patient's heart from 2D MRI data;

Figure 5 depicts an example of a 3D calculation grid of a patient's heart from the 3D geometry;

Figure 6 depicts a diagram of a fluid-structure solver with guidance algorithms;

Figure 7 depicts a diagram of a position guidance algorithm for guiding the instantaneous position of the tissues in the computational model;

Figure 8 depicts an example of a position guidance force acting on the tissues, where in a) the positions of the control points of the endocardium of the left ventricle are indicated by the green dots; in b) the direction of a first component of the position guidance force is indicated; in c) and d) the direction of a second component of the position guidance force for respectively reducing or increasing the volume of the left ventricle is indicated;

Figure 9 depicts a diagram of the blood velocity guidance algorithm for guiding the blood flow in the computational model;

Figure 10 depicts an operating diagram of the structural solver;

Figure 11 depicts an operating diagram of the blood velocity and pressure solver;

Figure 12 depicts an example of an application sequence of the method of the invention;

Figure 13 depicts an application example of the method in which ultrasound data are used to reconstruct the geometry of the patient and guide a computational model;

Figure 14 depicts a diagram of a processing system, with a biophysical simulator, an imaging system and a reconstruction system based on a computational model guided by clinical data. The same reference numbers and letters in the figures refer to the same elements or components.

Description of exemplary embodiments of the invention

With reference to the Figures, a method of the present invention is described below for identifying and indicating in an automated manner to an operator, preferably the doctor, pathological risk regions in at least one part of a patient’s cardiovascular system, exploiting an efficient reconstruction of an augmented reality of morphology and hemodynamics of said at least one part of the cardiovascular system, such as heart chambers and/or heart valves and/or aorta and/or pulmonary artery.

Such a method, in all the embodiments thereof, comprises the following stages:

- providing, as input data, position data over time Xmeas(t), acquired, possibly previously, by means of imaging techniques, related to subsets of the morphology, for example related to two-dimensional sections, of at least one part of the cardiovascular system on a plurality of subsequent cardiac phases;

- processing said position data over time Xmeas(t) and performing a simulation of the fluid-structure interaction (FSI) of said at least one part of the cardiovascular system; wherein processing said position data over time Xmeas(t) and performing said simulation comprises the following stages: a) reconstructing the three-dimensional geometry of the morphology of said at least one part of the cardiovascular system, by means of a shape reconstructor 202 of the morphology; b) producing a three-dimensional calculation grid Xo for the morphology of said at least one part of the cardiovascular system, by means of a segmenter 204, dividing the three-dimensional geometry into a plurality of geometric elements; c) quantitatively reconstructing the instantaneous three-dimensional configuration X(t) of the morphology of said at least one part of the cardiovascular system by means of a structural solver 606 which receives as input the three-dimensional calculation grid Xo and a position guidance force fNx(t) for guiding said geometric elements during the tracking of said position data Xmeas(t) over time, said position guidance force fNx(t) being determined by a position guidance algorithm 604; d) reconstructing the vector field of the instantaneous blood velocity u(t) and the field of the instantaneous blood pressure p(t) within the entire volume of said at least one part of the cardiovascular system, by means of a blood velocity and pressure solver 612 which receives as input the instantaneous configuration X(t) from the structural solver 606; and, given said vector field of the instantaneous blood velocity u(t) and the field of the instantaneous blood pressure p(t), the blood velocity and pressure solver 612 determines the instantaneous hydrodynamic force fu(t) acting on the morphology of said at least one part of the cardiovascular system, sending said instantaneous hydrodynamic force fn(t) as input to the structural solver 606 which, taking into account both the three-dimensional calculation grid Xo and the position guidance force fNx(t), reconstructs the instantaneous configuration X(t); e) constructing by means of a post-processor 208 a representation of augmented reality of morphology and hemodynamics of said at least one part of the cardiovascular system using the instantaneous configurations X(t), the vector field of the instantaneous blood velocity u(t) and the field of the instantaneous blood pressure p(t) within the entire volume of said at least one part of the cardiovascular system; wherein said representation of augmented reality is viewed by an operator by means of an output device 124; f) identifying, by means of the post-processor 208, one or more pathological risk regions in said at least one part of the cardiovascular system, and indicating said one or more pathological risk regions to an operator by means of the output device 124.

The indication to the operator of these pathological risk regions can be obtained, by means of software, by the application on the display of the output device, for example, of a highlighted outline of the region, or a specific coloring of the region, or of an appropriate pointer, or by showing on the display the coordinates of the region of pathological risk, preferably near said region.

Therefore, by virtue of an efficient and satisfactory augmented reality reconstruction of morphology and hemodynamics which, by virtue of the algorithm which generates the position guidance force, does not necessarily require 4D images of the entire part of the cardiovascular system under examination as input data, it is advantageously possible, by means of calculations known to those skilled in the art and performed by means of software, to obtain parameters which allow the software to identify and thus indicate one or more pathological risk regions on the display of the output device. Viewing the indicated risk region on the display, the operator can then further investigate this region. In other words, the post-processor 208, by means of the output device 124, communicates for example to the operator where to position the probe to examine, by means of the imaging device 106, for example an ultrasound system, the patient’s pathological risk region, which could be a different region than the one where the position data over time Xmeas(t) was initially acquired.

Advantageously, said at least one subset of the morphology is at least one two- dimensional section, even only one two-dimensional section, of the morphology of the at least one part of the cardiovascular system on a plurality of subsequent cardiac phases, preferably at least 20 cardiac phases per cardiac period, for example 20 to 30 cardiac phases.

However, the accuracy of the reconstruction of the 3D blood and pressure field and of augmented reality improves with the increase in the number of two- dimensional sections provided in input as Xmeas(t).

Alternatively, the method can be performed using input data related also, or exclusively, to 3D position data and/or 4D position data.

The at least one part of the cardiovascular system can be at least one heart chamber and/or at least one heart valve and/or the aorta and/or a pulmonary artery.

In a first variant of the method, after step f) there are provided the stages of: g) acquiring further position data over time X'meas(t), measured by means of the aforesaid imaging techniques, related to said one or more pathological risk regions on said plurality of cardiac phases; h) entering as input data the position data over time Xmeas(t) and said further position data over time X' meas (t); i) processing said position data over time Xmeas(t) and said further position data over time X'meas(t), and performing a simulation of the fluid-structure interaction (FSI) of said at least one part of the cardiovascular system by repeating stages a) to f).

Advantageously this variant, by introducing the acquisition of further position data over time related to the aforesaid risk region, for example related to at least one two-dimensional section, even only one two-dimensional section, of the risk region on a plurality of cardiac phases, allows applying the method a second time in order to obtain a further, more accurate augmented reality and more precisely indicating the risk region or possibly indicate other risk regions.

In a further variant of the method, steps g) to i) are carried out iteratively until the representation of augmented reality of morphology and hemodynamics of said at least one part of the cardiovascular system remains unchanged. This variant allows indicating with the utmost accuracy the entity and position of the risk regions which can then be examined by the operator.

Alternatively, such an iterative procedure can be stopped by the operator himself, if he considers the investigation already obtained to be fully satisfactory.

Non-limiting examples of pathological risk regions are: regions with high viscous loads and/or regions of blood stagnation and/or regions with high potential for activating platelets and/or regions of hemolysis risk and/or regions of risk of thrombus formation and/or regions with high normal hydrodynamic stress on biological tissues and/or regions with high hydrodynamic shear stress on biological tissues.

In particular, by virtue of the accurate representation of augmented reality of morphology and hemodynamics of said at least one part of the cardiovascular system of the single patient, it is possible to obtain with known calculations clinical data of the patient which cannot be measured in-vivo with non-invasive techniques, such as the field of instantaneous three-dimensional blood velocity, the instantaneous three-dimensional pressure field, the mechanical hemolysis, the hemodynamic loads generated by blood flow on tissues and/or others.

The three-dimensional blood velocity field can be used to identify regions of blood stagnation and regions with high viscous loads in said part of the cardiovascular system which induce hemolysis and clot formation (thrombi). By means of the method of the invention it is possible to identify, for example, without the use of invasive techniques, regions with high viscous loads.

The regions with high viscous loads are obtained, by means of the post-processor, from the three-dimensional blood velocity field (in post processing) by calculating the velocity gradient tensor and calculating the scalar equivalent load (see, for example, De Tullio, MD, A. Cristallo, E. Balaras, and R. Verzicco. "Direct numerical simulation of the pulsatile flow through an aortic bileaflet mechanical heart valve." Journal of Fluid Mechanics 622 (2009): 259-290).

By means of the method of the invention it is possible to identify, for example, without the use of invasive techniques, regions of blood stagnation.

The regions of blood stagnation are obtained, by means of the post-processor, from the three-dimensional blood velocity field (in post processing) by solving a transport equation to obtain the residence time Tr of the blood within said part of the cardiovascular system (see Vu, Vi, Lorenzo Rossini, Ricardo Montes, Josue Campos, Juyeun Moon, Pablo Martinez-Legazpi, Javier Bermejo, Juan C. Del Alamo, and Karen May-Newman. "Mitral valve prosthesis design affects hemodynamic stasis and shear in the dilated left ventricle." Annals of biomedical engineering 47, no. 5 (2019): 1265-1280). In particular, the spatial regions with a high blood residence time (for example Tr> 2 cardiac periods) correspond to regions of blood flow stagnation.

By means of the method of the invention it is possible to identify, for example, without the use of invasive techniques, regions with a high potential for activating platelets (shear activation platelets SAP).

The platelet activation potential is calculated (in post processing) from the three- dimensional blood velocity field and viscous loads (see Vu, Vi, Lorenzo Rossini, Ricardo Montes, Josue Campos, Juyeun Moon, Pablo Martinez-Legazpi, Javier Bermejo, Juan C. Del Alamo, and Karen May-Newman. "Mitral valve prosthesis design affects hemodynamic stasis and shear in the dilated left ventricle." Annals of biomedical engineering 47, no. 5 (2019): 1265-1280).

By means of the method of the invention it is possible to identify, for example, without the use of invasive techniques, regions at risk of hemolysis. Hemolysis depends on the exposure time of red blood cells to high hydrodynamic loads and is estimated through the blood damage index (BDI) which is calculated (in post processing) from the three-dimensional blood velocity field and viscous loads (see De Tullio, MD, A. Cristallo, E. Balaras, and R. Verzicco. "Direct numerical simulation of the pulsatile flow through an aortic bileaflet mechanical heart valve." Journal of Fluid Mechanics 622 (2009): 259-290).

By means of the method of the invention it is possible to identify, for example, without the use of invasive techniques, regions with high blood stress on cardiac tissues.

The blood stress on the tissues is calculated (in post-processing) from the instantaneous three-dimensional blood velocity field and the instantaneous three- dimensional pressure field.

In particular, the hydrodynamic stress vector x(X(t)) applied in the instantaneous position X(t) of the heart tissue is obtained by multiplying the hydrodynamic stress tensor (which depends on the pressure field and the blood velocity field) for the vector normal to the instantaneous position of the heart tissue n(X(t)). The normal load on the cardiac tissue is given by the normal component of the hydrodynamic stress vector Tn(X(t)) = x(X(t))n(X(t)), while the shear load (WSS, wall shear stress) corresponds to the modulus of the non-normal part of the hydrodynamic stress vector WSS(X(t)) = |x(X(t)) - Tn(X(t))n(X(t)) |.

Average hydrodynamic normal and/or shear loads on the surface of heart tissues (or on a part thereof, such as heart valves) are obtained by integrating the local hydrodynamic normal and/or shear loads on the surface of heart tissues and dividing by the wet surface of heart tissues.

The average hydrodynamic normal and/or shear loads over time are obtained by integrating the instantaneous hydrodynamic normal and/or shear loads over time and dividing by the time interval considered (for example some cardiac period).

By way of example, Figure 1 diagrammatically shows a system 100 comprising an imaging device 102, such as a Doppler echocardiography device and/or a magnetic resonance (MR) device and/or a CT scanner and/or an X-ray device and/or other device based on further imaging techniques. The imaging device 102 includes a probe 104 used by the operator to examine an examination region 106. A support 108, such as a bed, supports an object or subject 110 containing the examination region 106. The probe 104 emits ultrasonic pulses which pass through the examination region 106 and are reflected on the probe 104.

A reconstructor 112 reconstructs at least one subset of the morphology, for example in the form of a two-dimensional section and/or a volume of tissue, from the acoustic impedance. In one case, the data are several two-dimensional images of different sections of the cardiovascular system over a plurality of cardiac phases of the heart. In another case, the data are three-dimensional images from ultrasound and/or MRI and/or CT scans over a plurality of cardiac phases of the heart. In another case, the data is a combination of the data from the previous cases.

The system 100 can further include a processing system 114 which, in this example, acts as a console for the operator. The processing system 114 includes hardware 1 16 (with microprocessor, central processing unit, graphics processing unit, etc.) and a computer-readable storage medium 118, which includes a nontransient medium such as a physical memory device, etc. The processing system 114 further includes a user-readable output device 124, comprising a display, and an input device, such as a keyboard, mouse, etc. The computer readable storage medium 1 18 includes instructions 120 for a biophysical simulator 122. The hardware 1 16 is configured to execute instructions 120 and/or to run a software which allows the operator to interact and/or use the imaging device 102 by means of, for example, a graphical user interface (GUI).

In a variant, the biophysical simulator 122 is part of a further processing system, which is separate from the console 114 and from the system 100. In this case the further processing system is similar to the console 114 in that it includes hardware, computer readable storage medium, an input device, and an output device, but does not include the software which allows the operator to interact and/or use the imaging device 102. This further processing system can be a dedicated processing system (for example a computer workstation, a cluster, etc.) and/or part of the computer's processing resources are shared, for example cloud-based computing.

In any case, the biophysical simulator 122 is configured to process the image data (e.g., ultrasound, CT, MRI, X-rays) and perform a biophysical simulation. As described in more detail below, this includes reconstructing the 3D cardiovascular anatomy (e.g., heart chambers, heart valves, aorta and/or pulmonary artery, etc.) from the image data, resolving the blood flow inside the cardiovascular system or a part thereof, determining the hydrodynamic loads on the tissues and/or other clinical indices. The biophysical simulator 122 can be based on physical modeling, machine learning/deep learning techniques (supervised, partially supervised or unsupervised; e.g., neural networks), and/or other methods. The simulation can be performed based on different 2D and/or 3D images acquired on a plurality of cardiac phases to allow a fluid-structure simulation which reproduces the movement of tissues, the blood flows in the heart chambers and veins/arteries and the opening/closing of valves, etc.

Figure 2 diagrammatically shows an example of a biophysical simulator 122. In this example, the biophysical simulator 122 includes a shape reconstructor 202 of the morphology, a segmentor 204, a solver for the fluid-structure interaction (FSI) 206, which includes for example at least one guidance algorithm, and a post processor 208.

The biophysical simulator 122 receives, as input, data acquired by the imaging device 102, a data repository, portable memory and/or other apparatuses containing further data images of the patient's cardiovascular system.

In a variant, the biophysical simulator 122 is accessible by means of a web service. In this variant, the image data is transferred (loaded) from the imaging device 102 and/or other system to the biophysical simulator 122 through a web service. The biophysical simulator 122 remotely processes the image data as described herein and the results are then transferred back (downloaded) to the imaging device 102 and/or other system.

Alternatively, or in addition, the results are displayed and/or further analyzed by means of the web service and/or other services. In a first variant, only two-dimensional ultrasound data acquired on a plurality of subsequent cardiac phases are used to reconstruct one or more parts of the patient's cardiovascular system. For example, it has been found that, to obtain a reconstruction of the augmented reality of morphology and hemodynamics of the part under examination of the cardiovascular system, with the method of the invention at least one two-dimensional section of said part of the cardiovascular system on at least 20 cardiac phases per cardiac period is sufficient. This reconstruction is possible by virtue of the use of at least the position guidance force fNx(t).

Instead in another variant, a combination of two-dimensional ultrasound images and/or three-dimensional images acquired by ultrasound and/or MRI and/or CT can be used. In any case, the accuracy of the reconstruction depends on the number of two-dimensional and/or three-dimensional images acquired. Figure 3 diagrammatically shows an example of a shape reconstructor 202 which, in step a) of the method of the invention, reconstructs the three-dimensional geometry of the morphology of the at least one part of the cardiovascular system, e.g., ventricles, atria, heart valves, aorta, pulmonary veins and/or others.

In one case, the anatomical regions to be simulated are completely reconstructed from 3D image data acquired by the imaging device 102 (blocks 304 and 306).

In another case (blocks 304-318), the data contains 2D images which do not allow directly determining the complete geometry of the part or the entire cardiovascular system. In this case, the two-dimensional images are compared with a database of cardiovascular geometries organized, in a known manner, in classes by age of the patients, diseases and geometric parameters. The 3D geometry of the database closest to the 2D images acquired by the imaging device 102 is determined.

A possible embodiment to determine the 3D geometry of the anatomical region to be simulated involves converting the 2D images acquired by the imaging device 102 into matrices M'ref (where M'ref indicates the i-th matrix corresponding to the i- th 2D image) which are used to determine some of the geometric parameters p f of the patient (where p^j _ref indicates the j-th geometric parameter of interest), such as the length of the main axes of the ventricles (block 308). In the query step of the 3D database, the geometries belonging to patients in the same age group and with the same diseases as the patient are extracted (block 310) and then filtered and processed to determine the matrices M'db and geometric parameters p^jdb corresponding to the 2D images of the patient (block 312). The 3D geometry closest to that of the patient is determined as the one which minimizes a determined similarity functional (block 314) or is arbitrarily chosen by the operator. An example of a similarity functional is:

where || ■ || indicates an appropriate norm (e.g., L2 norm), | ■ | indicates the absolute value and a_s and ps are weights determined with the construction of the database.

The 3D geometry most similar to that of the patient is then used in block 316 to interpolate the 2D data acquired by the imaging device 102 and obtain the three- dimensional geometry of the morphology of the anatomical regions to be simulated which are then outputted (block 318). The accuracy of the reconstruction of the geometry of the patient's cardiovascular system depends on the number and type of 2D images acquired with the imaging device 102 and the variety and quantity of 3D geometries present in the database.

In a variant, if the value of the functional J_s, corresponding to the 3D mesh of the database closest to that of the patient, is not less than a threshold value, the reconstructor 202 provides an alert message by means of the output device 124 and the operator can decide to regardless proceed with the three-dimensional reconstruction method of the clinical data or re-initialize the analysis by providing additional 2D or 3D images of the patient.

Figure 4 diagrammatically shows an example of a 3D surface of the patient's heart tissues (right) reconstructed from 2D MRI clinical data (some of these shown on the left). The 3D geometric surfaces of the volume of interest were reconstructed by interpolating the 2D MRI data with the aid of a 3D geometry database.

Stage b) of the method of the invention includes the production of a three- dimensional calculation grid Xo for the morphology of said at least one part of the cardiovascular system, by means of a segmentor 204, dividing the reconstructed three-dimensional geometry into a plurality of three-dimensional, and possibly also two-dimensional, geometric elements.

Figure 5 shows an example of a three-dimensional calculation grid with tetrahedra (right) created by the segmentor 204 starting from the 3D geometry taken as input by the reconstructor 202. The type and size of the discretization depend on the computational methods used in the solver for the fluid-structure interaction 206.

In one case, thin anatomical regions (e.g., heart valve flaps) can be modeled as shells and are discretized using triangles, quadrangles, and/or others. In another case, the anatomical regions can be modeled as 3D tissues and are discretized using tetrahedra, cubes and/or others.

The segmentor 204 can provide for a mesh quality control which prevents the generation of irregular grid elements such as degenerate or very irregular triangles and high skewness tetrahedra. Geometric regions with higher curvature are automatically refined by locally increasing the density of the grid elements. In order to preserve the accuracy of the numerical pattern used by the solver for the fluidstructure interaction 206, the grid density can vary gradually and continuously in the geometry.

The calculation grid for the morphology generated by the segmentor 204, indicated by Xo, is inputted to the solver for the fluid-structure interaction 206.

Figure 6 diagrammatically shows an example of a solver for fluid-structure interaction 206 with two guidance algorithms, such as nudging algorithms, acting both on the morphology solver and on the hemodynamic field solver (velocity and pressure). Such a fluid-structure interaction solver 206 comprises a structural solver 606 and a blood velocity and pressure solver 612.

The patient's cardiovascular data, which are a function of the cardiac cycle phase, can be broken down into instantaneous position data Xmeas(t) of the biological tissue and instantaneous blood velocity data Umeas(t), which are acquired on subsets of said part of the cardiovascular system, for example on two-dimensional sections. Both Xmeas(t) and Umeas(t) are vector quantities.

These data can be filtered respectively by at least one filter 602 to filter the position data and by at least one filter 608 to filter the blood velocity data. These two filtering operations, which reduce the noise of the clinical data, are independent and can be performed simultaneously. The filters 602 and 608 can be spatial and time low-pass filters, the spatial and temporal frequency range of which depend on the temporal acquisition frequency and the spatial accuracy of the imaging device 102. The filtered position data Xref(t) and the filtered blood velocity data Uref(t) are provided in input respectively to a position guidance algorithm 604 and to a blood velocity guidance algorithm 610, preferably but not necessarily nudging algorithms.

The position guidance algorithm 604 receives, as the first input data, the position data Xmeas(t) or the filtered or interpolated position data Xref(t), and, as second input data, the instantaneous configurations X(t) determined by the structural solver 606, and determines a position guidance force fNx(t), which is inputted to the structural solver 606.

The structural solver 606 reconstructs over time the instantaneous three- dimensional configuration X(t) of the morphology, receiving as input the three- dimensional calculation grid Xo and said position guidance force fNx(t) to guide the above geometric elements in following the position data over time Xmeas(t).

The three-dimensional instantaneous configuration X(t), the three-dimensional calculation grid Xo, and the position guidance forces fNx(t), are vector quantities as well.

The blood velocity and pressure solver 612 instead reconstructs over time the vector field of the instantaneous blood velocity u(t) and the scalar field of the instantaneous blood pressure p(t), receiving as input the instantaneous configuration X(t) from the structural solver 606; and, given said instantaneous blood velocity u(t) and instantaneous blood pressure p(t), the blood velocity and pressure solver 612 determines the instantaneous hydrodynamic force fn(t) acting on the morphology of said at least one part of the cardiovascular system, sending said instantaneous hydrodynamic force fn(t) as input to the structural solver 606 which, taking into account both the three-dimensional calculation grid Xo and the position guidance force fNx(t), reconstructs the instantaneous configuration X(t).

In particular, the blood velocity and pressure solver 612 reconstructs over time the three components of the vectors of the instantaneous blood velocity u(t) and the values of the instantaneous blood pressure p(t) within the entire volume of said part of the cardiovascular system.

In a first variant, the blood velocity guidance algorithm 610 receives as a first input datum the blood velocity data Umeas(t), or filtered or interpolated blood velocity data Uref(t), receives as a second input datum the vector field of the instantaneous blood velocity u(t) determined by the blood velocity and pressure solver 612 in the entire volume of said at least one part of the cardiovascular system, and determines the blood velocity guidance force fNu(t), which is inputted to the blood velocity and pressure solver 612 to follow the blood velocity data Umeas(t) over time.

Therefore, the structural solver 606 takes in input a position guidance force fNx(t) and the instantaneous hydrodynamic force fn(t) acting on the morphology, calculates in a known manner the internal stresses of the morphology taking into account the properties of orthotropicity and non-linearity of the biological tissues, and calculates the new three-dimensional instantaneous configuration X(t) of the morphology. The latter is inputted to the blood velocity and pressure solver 612 to impose the non-flow condition on the biological tissue. The blood velocity and pressure solver 612 further receives as input the blood velocity guidance force fNu(t) and determines the instantaneous blood pressure and velocity fields which, in turn, determine the instantaneous hydrodynamic force fn(t) acting on the morphology which is inputted to the structural solver 606.

The diagram in Figure 6 shows the strongly interconnected dynamics of the guidance algorithms 604 and 610 with the structural solver 606 and the blood velocity and pressure solver 612, where the output of a first block is the input of a second block and, conversely, the output of the second block is the input of the first block.

In one case, such a quadruple coupling is treated by simultaneously solving blocks 604, 610, 606 and 612 as a single dynamic system by means of an iterative procedure (strong coupling) which provides a stable and robust solution method although computationally demanding since it requires iterations between the solvers. In another case, such a quadruple coupling is treated sequentially and the output of each model is used as the input for the next one in an arbitrary order (weak coupling). This last solution strategy provides a considerably faster but more numerically unstable method (especially when phenomena of added mass or structures with reduced inertia play an important role) and, for this reason, limits the integration timestep by requiring less timesteps with respect to the strong coupling.

In a second variant, the clinical data of blood velocity Umeas(t) are not available (non-flow ultrasound data) and the method is modified by isolating blocks 608 and 610, which corresponds to canceling the blood velocity guidance force fNu(t).

Figure 7 diagrammatically shows an example of position guidance algorithm 604, which guides the computational model to reproduce the available clinical data. It should be noted that such an algorithm allows reproducing the biomechanical and hemodynamic dynamics of the patient's cardiovascular system without having to resort to a cardiac electrophysiology model to solve the instantaneous electrical activation of the heart linked to the depolarization of cardiomyocytes. This allows not only reducing the computational cost due to the solution of the electrophysiology equations (such as bidomain and/or monodomain equations and/or eikonal and/or other models), but especially increasing the accuracy of the computational model since the dynamics of the tissues is guided by acquired clinical data, rather than by an electrophysiology model the input parameters of which (such as electrical conduction velocity, fast conduction beam geometry and active tension curve of muscle fibers, etc.) vary from patient to patient and are not measurable in vivo with techniques such as ultrasound and/or MRI and/or CT and/or X-rays.

A possible embodiment of the position guidance algorithm 604 is a first nudging algorithm which projects, by means of a projector 701 , the instantaneous configuration of the morphology X(t), determined by the structural solver 606 in the subsets of the morphology in which the position datum Xmeas(t) is acquired, obtaining (t), and determines the instantaneous deviation thereof with respect to the position data Xmeas(t), or the filtered or interpolated position data ex(t) = /(t) - Xmeas(t), Or 6x(t) = ^(t) — Xref(t), where ex(t) is a vector quantity which is provided to a first position guidance force generator 702 which, through an operator lx, defines e_x(t) in the space of the instantaneous configuration of the morphology X(t) and interpolates e_x(t) over time, and in which the field kex(t) is weighed (block 704, also called first block of nudging intensity) by means of a first penalty coefficient, a_x ⁽¹⁾, which determines the amplitude of a first component of the position guidance force f Nx⁽¹⁾(t) fNx<¹>(t) = Qx⁽¹⁾ lx ( (t) - Xmeas(t)), Or fNx<¹>(t) = a ¹’ lx ( (t) - Xref(t)).

This first penalty coefficient, a_x ⁽¹⁾, is determined empirically and is proportional to the ratio between the density of the biological tissue and the square of the characteristic time (for example the period of a heartbeat) of said at least one part of the cardiovascular system.

In a variant of the method of the invention the guidance force fNx(t) coincides with said first component fNx⁽¹⁾(t).

It can also be provided the use, by means of said position guidance algorithm 604, of at least one second component fNx⁽²⁾(t) of the position guidance force to guide the simulation to reproduce at least one instantaneous geometric parameter of a component of said at least one part of the cardiovascular system.

In this case the guidance force fNx(t), which is inputted to the structural solver 606, coincides with the sum of the first component fNx⁽¹⁾(t) of the position guidance force and of the at least one second component fNx⁽²⁾(t) of the position guidance force, thus providing a guide to the numerical simulation to simultaneously reproduce the instantaneous configuration of the morphology X(t) and said at least one instantaneous geometric parameter.

Preferably, if said instantaneous geometric parameter is the instantaneous volume, for example of the heart chambers, a first geometric measurer 706 measures the volume Vmeas(t) or the filtered volume Vref(t) of the component using position data Xmeas(t) or filtered position data Xref(t), respectively, and a second geometric measurer 708 measures the volume V(t) of the component using the instantaneous configuration X(t) determined by the structural solver 606 and projected, by means of the projector 707, into the subsets of the morphology where Xmeas(t) has been acquired.

The difference between V(t) and Vmeas(t), or Vref(t), is supplied to a second position guidance force generator 710 which generates the second component of the position guidance force fNx⁽²⁾(t), or volume force component, which, inputted to the structural solver 606, tends to increase the instantaneous volume in the simulation if V(t) < Vmeas(t) or V(t) < Vref(t), or, vice versa, to decrease the instantaneous volume if V(t) > Vmeas (t) Or V(t) > Vref(t).

Preferably, the second component of the position guidance force fNx⁽²⁾(t) is weighed (block 712, also called second block of nudging intensity) by means of a second penalty coefficient, a_x ⁽²⁾, which determines the amplitude of said second component of the nudging guidance force.

This second penalty coefficient, o_x ⁽²⁾, is determined empirically and is proportional to the ratio between the density of the biological tissue and the square of the product of characteristic time and length (for example the period of a heartbeat and the major axis of the ventricle in the case of intraventricular flow) of said at least one cardiovascular system part.

If further instantaneous geometric parameters which can be measured from the input data of the patient's cardiovascular system were to be considered, further components of the position guidance force could be determined and the sum thereof, fNx(t), should be provided as an output to the system thus providing a guide to the numerical simulation to simultaneously reproduce the instantaneous configuration of the morphology X(t) and of all the aforementioned geometric parameters.

Figure 8a shows an example of instantaneous position of left ventricular endocardial tissues in two cardiac phases: telediastole (left) and telesystole (right). The control points associated with the instantaneous tissue configuration, Xmeas(t) or Xref(t), are indicated by the green dots. Figure 8b diagrammatically shows the effect of the first component of the position guidance force fNx⁽¹⁾ which guides the tissue control points in the computational model (X(t), yellow dots) to track the positions of the tissues measured by the clinical data (Xmeas(t) or Xref(t), green dots). Figures 8 c-d indicate the effect of the second component of the position guidance force fNx⁽²⁾ in the case in which the computational model is to be guided to reproduce the volume of the left ventricle measured in the clinical data. In this case, the geometric measurers 706 and 708 estimate the volume of the left ventricle V_ref according to the clinical data (taking Xref(t) as input) and V according to the computational model (taking (t) as input). In the case of a triangular (tetrahedral) grid, if V(t) > Vref(t) the second component of the force fNx⁽²⁾ is directed as the junction between a given vertex of the structure and the center of gravity of the triangle (tetrahedron) and oriented inwards so as to decrease the volume of the left ventricle in the computational model, as indicated in Figure 8c. Conversely, if V(t) < Vref(t) the second component of the force fNx⁽²⁾ is directed as the junction between a given vertex of the structure and the center of gravity of the triangle (tetrahedron) and oriented outwards in order to increase the volume of the left ventricle in the computational model, as indicated in Figure 8d.

The method of the invention can advantageously be applied starting from a single two-dimensional section on various cardiac phases (at least 20 phases per cardiac period) of the examined part of the cardiovascular system. For example, in the case of a heart chamber, the guidance force of the structure can be used to guide the outline of the heart chamber, intersected by the measurement plane, by means of a position guidance force fNx⁽¹⁾ (Figure 8b). In a particular embodiment, the volume of the heart chamber can be estimated starting from a two-dimensional section in the hypothesis of an ellipsoidal chamber, as commonly used in medical practice. This estimated volume can be used to determine a volume guidance force fNx⁽²⁾.

As is typical in data-driven methods, the accuracy of the reconstruction of the 3D blood and pressure field and of augmented reality improves with the increase in the number of two-dimensional sections provided in input as Xmeas(t).

Figure 9 diagrammatically shows an example of the blood velocity guidance algorithm 610, for guiding the blood field of the patient’s computational model.

A possible embodiment of this blood velocity guidance algorithm 610 is a nudging algorithm which projects, by means of a projector 902, the vector field of the instantaneous blood velocity u(t) determined by the fluid and pressure solver 612 into the subsets of the blood flow in which the blood velocity data Umeas(t), or the filtered blood velocity data Uref(t), is acquired, obtaining u(t), and determines the deviation thereof with respect to the blood velocity data Umeas(t), or the filtered blood velocity data Uref(t) e_u(t) = u(t) - Umeas(t), Or 6u(t) = u(t) - Uref(t), where e_u(t) is a vector quantity which is provided to the blood velocity guidance force generator 904 which, through an operator l_u, defines e_u(t) on a calculation grid of the fluid and pressure solver (612), and interpolates e_u(t) over time, and in which the field l_ue_u(t) is weighed (block 906, also called nudging intensity block) by means of a penalty coefficient, a_u, which determines the amplitude of the blood velocity guidance force f Nu(t) fNu(t) = Qu lu (u(t) — Umeas(t)), O fNu(t) = Qu lu (0(t) - Uref(t)).

The penalty coefficient, a_u, is determined empirically and is proportional to the ratio between the density of the fluid and the characteristic time (for example the period of a heartbeat) of said at least one part of the cardiovascular system.

Figure 10 diagrammatically shows the operation of the structural solver 606. In block 1002, the structural solver 606 takes as input from the position guidance algorithm 604 the position guidance force fNx(t), which can coincide with the first component fNx⁽¹⁾(t) or with the sum of the first component fNx⁽¹⁾(t) and of the at least one second component fNx⁽²⁾(t), and also takes as input, from the blood velocity and pressure solver 612, the instantaneous hydrodynamic force fn(t) acting on the morphology. In block 1004 the internal stresses of the morphology are calculated, in a known manner, according to a nonlinear elastic model for neo-Hookean solid and/or Fung solid and/or Mooney-Rivlin solid and/or Holzapfel-Ogden solid and/or other hyperalistic models. The selected elastic model also takes into account the anisotropic nature of biological tissues the elastic properties of which depend on the local orientation of the tissue fibers. In block 1006 the new instantaneous configuration of the morphology X(t) is calculated by solving, in an equally known manner, the equation of the dynamic equilibrium between the inertial force, the internal stresses of the morphology, the hydrodynamic force exerted by the blood flow on the wet walls of the tissue and the guidance force acting on the morphology, i.e., on the tissues. The new instantaneous morphology configuration X(t) is then used as input for the blood velocity and pressure solver 612. The known operations of blocks 1004 and 1006 are not described in detail here, as they belong to the common general knowledge of those skilled in the art.

Figure 11 diagrammatically shows the operation of the blood velocity and pressure solver 612. In block 1102, the blood velocity and pressure solver 612 takes as input the blood velocity guidance force fNu(t), from the blood velocity guidance algorithm 610, and the vector of the instantaneous configuration X(t) of the morphology, from the structural solver 606. In block 1104, the new instantaneous blood velocity u(t) and the new instantaneous blood pressure p(t) are calculated, in a known manner, for example according to a solver of the Navier-Stokes equations or models thereof, such as for example solvers using Reyonlds Averaged Navier-Stokes Equations or Large Eddy Simulations or mesoscopic approaches or particle methods (without fixed grid). The selected fluid and pressure solver also takes into account the non-Newtonian nature of blood where the viscosity locally depends on the rate of deformation of the blood. Finally, in block 1106 the new instantaneous hydrodynamic force fn(t) acting on the morphology, i.e., on the tissues, is calculated in an equally known manner.

Once obtained, by means of the two solvers 606 and 612, both the instantaneous configurations X(t) and the vector field of the instantaneous blood velocity u(t) and the field of the instantaneous blood pressure p(t) inside the part, or the parts or the entire cardiovascular system, the post-processor 208 is configured to reconstruct, in a known manner, a representation of augmented reality of morphology and hemodynamics.

The post-processor 208 reconstructs the three-dimensional morphology of anatomical regions of interest (e.g., blood vessels, heart chambers, heart valves and/or others) and measures the relative clinical quantities therein such as the velocity vector of blood flows and the pressure field. In one case, this includes a 3D rendering of the geometry of the patient's cardiovascular system as a function of time: i.e., the 3D geometry of the tissues is provided as a sequence of configurations corresponding to different phases of the cardiac cycle. In addition, the iso-contours of the hydrodynamic shear and pressure loads exerted by the blood flow are plotted on the tissue surfaces. In one case, this includes calculating the blood velocity with a very high spatial and temporal resolution (inversely proportional to the size of the spatial grid and the time integration timestep), thus allowing the measurement of turbulent flows within the circulatory system and the computation of the vorticity vector and the velocity gradient tensor. In addition, this can include estimating mechanical intravascular hemolysis due to the shear stress exerted on the red blood cells and estimating normal and shear hydrodynamic loads exerted by the blood flow on the blood vessel walls and/or myocardium and/or heart valve flaps and/or elsewhere. Instantaneous blood flow velocity and pressure fields can be used to evaluate other clinical data of the integral type, such as cardiac output in the aorta, blood flow in the aorta, pulmonary arteries/veins, inferior/superior vena cava and/or others; or of the local type such as the maximum/minimum pressure in systole/diastole in the heart chambers and/or in the aorta and/or in the superior/inferior vena cava and/or in the pulmonary and/or other veins/arteries. The clinical data mentioned here and/or others can be displayed as a function of the cardiac phase (i.e. , as a sequence of images or videos as a function of time) or time-averaged (over one or more cardiac cycles). Alternatively or additionally, these quantities are displayed in the output devices 124 of the console 114 that are readable by man and/or saved on the computer readable storage medium 116.

Figure 12 illustrates a non-limiting embodiment of the method of the invention. In block 1202, the cardiovascular image data is received. In block 1204, the 3D geometry of the cardiovascular anatomy of interest is obtained. In block 1206, the aforementioned 3D geometry is segmented. In block 1208, the guidance force or forces, guided by the data, are determined, as described above. In block 1210, the simulation of blood flow and three-dimensional morphology geometry is performed using the data-based guidance force(s) to replicate the patient's cardiovascular tissue dynamics. In block 1212, the augmented reality reconstruction of morphology and hemodynamics is performed and the relevant clinical quantities are measured, and possibly displayed and/or saved on storage media and/or transferred via the web and/or other suitable means. In block 1214, the postprocessor identifies and indicates possible pathological risk regions of the patient to the operator.

Figure 13 shows an application example of the method of the invention. The ultrasound data is used to reconstruct the patient's cardiovascular geometry and guide a computational model which reproduces the 3D dynamics of the left heart tissues and blood flows therein. The shear stresses exerted by the blood flow on the tissues are obtained by post-processing the results of the computational model guided by the clinical data. Furthermore, the computational model driven by clinical data can determine local quantities of blood flow as a function of time such as the evolution of pressure (in the aorta, ventricle, and left atrium) and integral quantities as a function of time such as volume evolution (of the ventricle and left atrium).

Figure 14 shows an application example of the method of the invention to develop a device for the augmented three-dimensional vision and quantification of clinical data to improve the traditional ultrasound machines currently in use or to be integrated directly on next-generation clinical scanning machines. By means of the output device 124, the doctor can have access to the clinical results obtained from the computational model which comprise a three-dimensional rendering of the dynamics of the patient's cardiovascular system and of the hydrodynamic stresses exerted by the blood flow on the tissues. The quantitative and three-dimensional clinical data about the blood flow within the cardiovascular system and the measurements of the shear stresses on the tissues (otherwise not measurable in- vivo) allow achieving a more effective prognostics.

Finally, the post-processor 208 advantageously determines whether the 3D reconstructed blood and pressure fields of the examined part of the cardiovascular system have pathological risk regions of the patient, such as regions with high viscous loads and/or regions of blood stagnation and/or regions with high platelet activation potential and/or hemolysis risk regions and/or thrombus risk regions and/or regions with high hydrodynamic normal stress on biological tissues and/or regions with high hydrodynamic shear stress on biological tissues and/or other.

Therefore, examples of precisely measurable quantities, exclusively by virtue of the efficient augmented reality reconstruction described above, comprise: viscous loads; residence time; platelet activation potential; hemolysis; blood stress on tissues; etc.

Claims

1. An automated method for identifying and indicating pathological risk regions in at least one part of a patient’s cardiovascular system to an operator, the method comprising the stages of

- providing, as input data, position data over time Xmeas(t), acquired by means of imaging techniques, related to at least one subset of the morphology of at least one part of a patient’s cardiovascular system on a plurality of subsequent cardiac phases;

- processing said position data over time Xmeas(t) and performing a simulation of the fluid-structure interaction (FSI) of said at least one part of the cardiovascular system; wherein processing said position data over time Xmeas(t) and performing said simulation comprise the following stages: a) reconstructing the three-dimensional geometry of the morphology of said at least one part of the cardiovascular system, by means of a shape reconstructor (202) of the morphology; b) producing a three-dimensional calculation grid Xo for the morphology of said at least one part of the cardiovascular system, by means of a segmentor (204), dividing the three-dimensional geometry into a plurality of geometric elements; c) quantitatively reconstructing the instantaneous three-dimensional configuration X(t) of the morphology of said at least one part of the cardiovascular system by means of a structural solver (606) which receives as input the three-dimensional calculation grid Xo and a position guidance force fNx(t) for guiding said geometric elements during the tracking of said position data Xmeas(t) over time, said position guidance force fNx(t) being determined by a position guidance algorithm (604); d) quantitatively reconstructing the vector field of the instantaneous blood velocity u(t) and the field of the instantaneous blood pressure p(t) within said at least one part of the cardiovascular system, by means of a blood velocity and pressure solver (612) which receives as input the instantaneous configuration X(t) from the structural solver (606); and, given said vector field of the instantaneous blood velocity u(t) and said field of the instantaneous blood pressure p(t), the blood velocity and pressure solver (612) determines the instantaneous hydrodynamic force fn(t) acting on the morphology, sending said instantaneous hydrodynamic force fn(t) as input to the structural solver (606) which, taking into account both the three-dimensional calculation grid Xo and the position guidance force fNx(t), reconstructs the instantaneous configuration X(t) ; e) constructing by means of a post-processor (208) a representation of augmented reality of morphology and hemodynamics of said at least one part of the cardiovascular system using both the instantaneous configurations X(t) and the vector field of the instantaneous blood velocity u(t) and the field of the instantaneous blood pressure p(t) within said at least one part of the cardiovascular system; wherein said representation of augmented reality is viewed by an operator by means of an output device (124); f) identifying, by means of the post-processor (208), one or more pathological risk regions in said at least one part of the cardiovascular system, and indicating said one or more pathological risk regions to an operator by means of the output device (124).

2. A method according to claim 1 , wherein after stage f) there are provided the stages of: g) acquiring further position data over time X'meas(t), measured by means of imaging techniques, related to said one or more pathological risk regions on said plurality of cardiac phases; h) entering as input data the position data over time Xmeas(t) and said further position data over time X' meas (t) ; i) processing said position data over time Xmeas(t) and said further position data over time X'meas(t), and performing a simulation of the fluid-structure interaction (FSI) of said at least one part of the cardiovascular system by repeating stages a) to f).

3. A method according to claim 2, wherein the stages g) to i) are carried out iteratively until the representation of augmented reality of morphology and hemodynamics of said at least one part of the cardiovascular system remains unchanged.

4. A method according to any one of the preceding claims, wherein said at least one subset of the morphology is at least one two-dimensional section of the morphology of the at least one part of the cardiovascular system on a plurality of subsequent cardiac phases, preferably at least 20 cardiac phases per cardiac period.

5. A method according to claim 4, wherein said at least one part of the cardiovascular system is at least one heart chamber and/or at least one heart valve and/or aorta and/or one pulmonary artery.

6. A method according to any one of the preceding claims, wherein said pathological risk regions can be regions with high viscous loads and/or regions of blood stagnation and/or regions with high potential for activating platelets and/or regions of hemolysis risk and/or regions of risk of thrombus formation and/or regions with high normal hydrodynamic stress on biological tissues and/or regions with high hydrodynamic shear stress on biological tissues.

7. A method according to any one of the preceding claims, wherein said position guidance algorithm (604) receives as a first input datum the position data Xmeas(t), possibly filtered or interpolated position data Xref(t), and as a second input datum the instantaneous configurations X(t) determined by said structural solver (606), and determines said position guidance force fNx(t) which is inputted to the structural solver (606).

8. A method according to any one of the preceding claims, wherein said input data also comprise blood velocity data over time Umeas(t), related to at least one subset of the blood flow within said at least one part of the cardiovascular system; and wherein the velocity and pressure solver (612) receives as input a blood velocity guidance force fNu(t) to track the blood velocity data Umeas(t) over time, said blood velocity guidance force fNu(t) being determined by a blood velocity guidance algorithm (610).

9. A method according to claim 8, wherein said blood velocity guidance algorithm (610) receives as a first input datum the blood velocity data Umeas(t), possibly filtered or interpolated blood velocity data Uref(t), and as a second input datum the vector field of the instantaneous blood velocity u(t) determined by said velocity and pressure solver (612), and determines said blood velocity guidance force fNu(t), which is inputted to the velocity and pressure solver (612).

10. A method according to any one of the preceding claims, wherein said position guidance algorithm (604) determines the instantaneous deviation between X(t), corresponding to the instantaneous configuration X(t) of the morphology determined by the structural solver (606) projected by a projector (701 ) in the subset of the morphology where the position data Xmeas(t) are acquired, and the position datum Xmeas(t), or the filtered or interpolated position datum Xref(t), ex(t) = A (t) - Xmeas(t), Or 6x(t) = (t) — Xref(t), where e_x(t) is a vector quantity which is supplied to a first position guidance force generator (702) which, by means of an operator lx, defines e_x(t) in the space of the instantaneous configuration X(t) of the morphology and interpolates e_x(t) over time, and wherein the field l_xe_x(t) is weighed (704) by means of a first penalty coefficient, □x⁽¹⁾, which determines the amplitude of a first component fNx⁽¹⁾(t) of the position guidance force fNx ) = Ox⁽¹⁾ lx ( (t) - Xmeas(t)), Or f_Nx<¹>(t) = Ox'¹’ lx ( (t) - Xref(t)) ; preferably wherein said position guidance force fNx(t), which is inputted to the structural solver (606), coincides with said first component fNx⁽¹⁾(t).

11. A method according to claim 10, wherein there is provided the generation, by means of said position guidance algorithm (604), of least a second component fNx⁽²⁾(t) of the position guidance force for guiding the simulation to reproduce at least one instantaneous geometric parameter of a component of said at least one part of the cardiovascular system; and wherein said position guidance force fNx(t), which is inputted to the structural solver (606), is the sum of said first component fNx⁽¹⁾(t) and said at least one second component f Nx⁽²⁾(t), thus providing a guidance to the numerical simulation for simultaneously reproducing the instantaneous configuration X(t) of the morphology and said at least one instantaneous geometric parameter.

12. A method according to claim 11 , wherein said instantaneous geometric parameter is the instantaneous volume; wherein a first geometric measurer (706) measures the volume Vmeas(t) or the filtered volume Vref(t) of the component using position data Xmeas(t) or filtered position data Xref(t), respectively, and a second geometric measurer (708) measures the volume V(t) of the component using the instantaneous projected configuration (t) determined by the structural solver (606) and projected by a projector (707) in the subset of the morphology in which the position data Xmeas(t) have been acquired; wherein the difference between V(t) and Vmeas(t), or Vref(t), is supplied to a second position guidance force generator (710) which generates the second component fNx⁽²⁾(t) of the position guidance force, or volume force, which, inputted to the structural solver (606), tends to increase the instantaneous volume in the simulation if V(t) < Vmeas (t) or V(t) < Vref(t), or, vice versa, to decrease said instantaneous volume if V(t) > V meas (t) or V(t) > Vref(t); preferably wherein the second component fNx⁽²⁾(t) of the position guidance force is weighed (712) by means of a second penalty coefficient, a_x ⁽²⁾ which determines the amplitude of said second component of the position guidance force.

13. A method according to claim 8 or 9, wherein said blood velocity guidance algorithm (610) is an algorithm which projects, by means of a projector (902), the vector field of the instantaneous blood velocity u(t) determined by the fluid and pressure solver (612) on the blood flow subset where the blood velocity data over time Umeas(t) are acquired, obtaining u(t), and determines the deviation thereof with respect to the blood velocity datum Umeas(t), or the filtered blood velocity datum Uref(t), e_u(t) = U(t) - Umeas(t), Or e_U(t) = 0(t) - Uref(t), where e_u(t) is a vector quantity which is supplied to a blood velocity guidance force generator (904) which, by means of an operator l_u, defines eu(t) on a calculation grid of the fluid and pressure solver (612) and interpolates e_u(t) over time, and wherein the field l_ue_u(t) is weighed (906) by means of a penalty coefficient, a_u, which determines the amplitude of the blood velocity guidance force f Nu(t) fNu(t) = du lu (u(t) - Umeas(t)), Or fl\lu(t) = du lu (u(t) — Uref(t)).

14. A method according to any one of the preceding claims, wherein said position guidance algorithm (604) is a nudging algorithm.

15. A method according to claim 8, wherein said blood velocity guidance algorithm (610) is a nudging algorithm.

16. A device for identifying and indicating pathological risk regions in at least one part of a patient’s cardiovascular system to an operator by means of an augmented reality vision of morphology and hemodynamics of said at least one part of the cardiovascular system, said device comprising a computer program configured to perform the method according to any one of the preceding claims.

17. A machine for acquiring cardiographic images comprising a device according to claim 15.