DESCRIPTION

FIELD OF THE INVENTION

The present invention is related to a non-invasive method for determining a vessel damage indicator in a patient. The invention is a computer implemented invention that characterize the blood flow inside the coronary tree by simulating numerical blood flow models based on CT-scan 3D images analysis. The simulated numerical blood flow model of the invention determines a vessel damage indicator as the rate between the pressure values at different locations of the artery.

PRIOR ART

One of the technical fields with a more intensive development is the evaluation of invasive physiological indices to determine the functional importance of coronary stenosis.

Physiological measurements have been very useful in the catheterization laboratory to evaluate the functional importance of the coronary stenosis. The fractional flow reserve (FFR) and the instant flow reserve (iFR) are used to assess whether coronary lesions should be revascularized.

Fractional Flow Reserve (FFR) is a technique to evaluate the hemodynamic relevance of coronary artery stenoses and is the gold standard method for assessing coronary lesion severity during invasive coronary angiography (ICA) with the risks involved.

FFR measures the ratio between coronary pressure distal to a coronary artery stenosis and aortic pressure under conditions of maximum myocardial hyperemia. This ratio represents the potential decrease in coronary flow distal to the coronary stenosis. iFR measures the ratio of distal coronary pressure to the aortic pressure during an isolated period during diastole, called the "wave-free period". These methods are performed using a pressure sensor cable or micro-catheter to record the pressure distal to the target lesion and, at the same time, record the proximal coronary pressure through the guide catheter.

FFR is measured after administration of intracoronary nitroglycerin to dilate the vessel, followed by adenosine to induce maximal hyperemia and minimal resistance microvascular.

These methods are invasive methods that have disadvantages such as cost or procedure time. Furthermore, these methods may cause serious complications and pain in the patient.

According to the prior art, FFR, iFR and similar parameters are invasive measurements since the pressure or other measurements are obtained from measurements taken from the patient. Nonetheless, along the description, the same parameters may be obtained by simulating a numerical model avoiding any invasive measurement. In this case, such expressions (FFR, iFR) will be maintained for such parameters.

According to this invention, the method uses a unique non-invasive test that allows the evaluation of anatomy and function coronary arteries, with a high predictive value, allowing an accurate evaluation of intermediate anatomic stenosis. The invention involves CT-images analysis and numerical simulations over a numerical model adapted to simulate the patient response.

This non-invasive strategy provides detailed information on the FFR for the entire coronary tree as well as providing additional information such as wall shear stress without the need for radiation, exploration time, medication or additional contrast to allow tailored management of patients with ischemic heart disease.

DESCRIPTION OF THE INVENTION

The present invention provides a solution for the aforementioned problems, by means of a non-invasive method for determining a vessel damage indicator in a patient according to claim 1, a system for determining a vessel damage estimator in a patient according to claim 25 and a computer program according to claim 26. In dependent claims, preferred embodiments of the present invention are defined.

A first inventive aspect provides a non-invasive method for determining a vessel damage indicator in a patient, comprising: a) inputting a CT-scan 3D image of a region of the patient, the region at least comprising coronary arteries and aortic arteries; b) processing in a computer system the CT-scan image carrying out the steps: identifying at least one blood cavity and a boundary limiting the cavity; identifying those portions of the boundary corresponding to blood inlets, blood outlets, and walls; c) generating a numerical blood flow model in the cavity, said numerical blood flow model at least comprising the pressure of the blood and the velocity of the blood; d) imposing boundary conditions on the numerical blood flow model; e) simulating the numerical blood flow model; determining a vessel damage indicator as the rate between the pressure value at a first location of the artery and, the pressure value at a second location of the artery distant from the first location, the pressure values taken from the simulated numerical blood flow model.

Throughout all this document, "CT-scan" also called computed tomography scan, will be understood as a medical imaging technique that uses computer-processed combinations of multiple X-ray measurements allowing to see inside the body without cutting.

Throughout all this document, "vessel damage indicator" will be understood as a variable characterizing the blood flow conditions allowing the evaluation of anatomy and function coronary arteries and helps clinicians to study cardiac pathologies.

The invention consists in a non-invasive technique that allows determining a vessel damage indicator in a patient.

The non-invasive method uses a CT-scan image of a region of the patient wherein at least one blood cavity is identified along with its boundary and the corresponding blood inlets and outlets. The CT-scan is a 3D image comprising voxels. The cavity is identified by using a segmentation process which identify the blood cavity and the rest of the image. The interface between the blood cavity and the rest of the image is the wall of the cavity limiting said cavity. The cavity is the computational domain for a numerical blood flow model being generated for modeling the flow of the blood in the artery tree of the patient.

The generated numerical blood flow model may use a different data structure for representing the shape of the wall limiting the computational domain, the blood cavity. According to a specific embodiment, the numerical blood flow model uses a finite volume method for a discretization of the domain, the blood cavity. Boundary conditions are imposed on the walls limiting the blood cavity and over those boundaries defined as the inlets coming from the heart and outlets.

That is, in a preferred example, the numerical blood flow model includes a representation of the cavity, the walls, the inlets and the outlets to the cavity on which the boundary conditions are imposed. The numerical blood flow model is completed with the set of differential equations that determine its behavior.

The numerical blood flow model comprises a numerical characterization of the behavior of the flow, wherein the numerical characterization comprises a discretization of the Navier-Stokes equations involving at least the pressure of the blood and the velocity field.

In a preferred example, the blood is considered as a Newtonian fluid, incompressible with constant density flowing in laminar and steady state conditions. A Newtonian fluid is a fluid whose viscosity can be considered constant.

In a preferred example, the numerical blood flow model further comprises the parameters of the density and the viscosity of the blood.

In particular, steady state equations may be used for simulating the flow without requiring to integrate time dependent variables that require to integrate the flow until transient conditions reaches the steady state. According to another example, the set of differential equations comprises the time variant terms allowing to determine transient conditions. In this case the steady state may be simulated if said set of differential equations are integrated under steady boundary conditions during a period of time until the systems evolves reaching the steady state.

In a particular example, as boundary conditions the pressure inlet and the mass flow inlet are imposed. Rigid walls are considered as well and no-slip conditions are applied.

In an example, the pressure inlet is a pressure function according to a standard profile being scaled such that the minimum pressure value and the maximum pressure value are those measured on the patient.

The numerical blood flow model is simulated and as output, the simulation provides a large number of variables that can be used to analyze the flow inside to make further decisions.

In the present invention, pressure values of two different locations distant from each otherare obtained from the simulation in orderto determine a vessel damage indicator.

Advantageously, the method provides a large number of variables in a single computing process. Another variable involved in the computation of the numerical blood flow model is the velocity of the blood allowing to measure parameters such as the shear stress which highly relevant for determining blood flow conditions causing the generation of thrombus.

In a particular embodiment, the numerical blood flow model comprises a turbulence model causing to modify the mean velocity field under the influence of small movement scales.

The method provides the medical team with any type of data related to blood flow that may be of interest to them, without increasing computational and post-processing time. Moreover, another advantage of the present invention is the reduction of computing times.

The non-invasive method of the present invention allows the evaluation of anatomy and function coronary arteries avoiding disadvantages such procedure time, cost, complications and pain in the patients of the traditional invasive methods. ln a particular embodiment, the simulated numerical blood flow model is simulated under conditions of maximum myocardial hyperemia.

During maximum coronary hyperemia, the relation between coronary blood pressure and flow is linear, pressure and flow are proportional only at the point of maximal hyperemia. This relation is linear during hyperemia, so it is evident that the proportion between two intracoronary pressures is identical to the proportion between the two coronary flows corresponding to these pressures.

The existing linear relation between pressure and flow during maximal hyperemia makes it possible to infer, in accordance with pressure measurements, the degree of limitation to flow caused by epicardial stenosis.

The hyperemia conditions may be caused in a patient through vasodilation, however, in the context of the invention hyperemia conditions are simulated. In a preferred embodiment, the hyperemia conditions are those imposed to the numerical blood flow model as inlet boundary conditions. The pressure and/or the mass flow parameters in the inlet of the numerical blood flow model are corrected in order to simulate maximum hyperemia conditions. Therefore, the hyperemia conditions affect blood flow conditions and the CT-scan 3D image from a region of a patient is taken in resting conditions.

In a particular example, a corrective formula based on the patient's age, weight and heart rate is applied to correct the mass flow parameter of the numerical blood flow model in order to simulate maximum hyperemia conditions.

In a particular example, a reduction of the mean arterial pressure (MAP) is applied to correct the inlet boundary conditions in order to simulate maximum hyperemia conditions, wherein the MAP in normal conditions can be approximated using the following formula:

In order to detect the presence and extent of myocardial ischemia, maximal hyperemia conditions are necessary. ln a particular embodiment, the simulated numerical blood flow model is simulated under pulse wave-free conditions and under conditions of non-maximum myocardial hyperemia.

The "wave-free period" is an isolated period during diastole. During the diastolic wave- free period coronary blood flow is passive permitting an adenosine free measure of stenosis severity.

In a particular embodiment, the vessel damage indicator is a FFR (Fractional Flow Reserve) wherein the first location of the artery is a location of the coronary artery and, the second location is a location of aortic artery.

Fractional flow reserve (FFR) is calculated as the ratio between coronary pressure distal to a coronary artery stenosis and aortic pressure under conditions of maximum myocardial hyperemia. This ratio represents the potential decrease in coronary flow distal to the coronary stenosis.

Maximal hyperemia is the critical prerequisite for FFR assessment wherein said condition is imposed to the numerical blood flow model as inlet boundary conditions for example by imposing the specific conditions previously disclosed. FFR is a specific technique for the hemodynamic assessment of stenosis and evaluates coronary lesion severity.

The method of the present invention allows an accurate evaluation of intermediate anatomic stenosis obtaining the values of the coronary pressure distal to a stenosis and the aortic pressure from the simulation of the numerical blood flow model.

In a particular embodiment, the vessel damage indicator is an iFR (instantaneous wave- free ratio) wherein the first location of the artery is a location of the coronary artery and, the second location is a location of aortic artery.

Instantaneous wave-free ratio (iFR) measures the ratio of distal coronary pressure to the aortic pressure during an isolated period during diastole, called the "wave-free period". During the diastolic wave-free period coronary blood flow is passive permitting an adenosine free measure of stenosis severity such as iFR. The iFR indicator is used to determine the severity of a coronary stenosis. The method of the present invention allows an accurate evaluation of a coronary stenosis obtaining the corresponding pressure values from the simulation of the numerical blood flow model.

In a particular embodiment, the vessel damage indicator is AFFR, wherein the AFFR is computed based on two measurements of FFR. AFFR is defined as the change in FFR throughout a lesion, preferably a stenosis. AFFR is defined for each lesion by computing the difference between the proximal and distal FFR values in a predetermined stenosis located in a vessel conduit. According to a more preferred embodiment, a proximal measurement of FFR (the rate of the pressure before the lesion divided by the aortic pressure) is taken and a distal measurement of FFR (the rate of the pressure after the lesion divided by the aortic pressure) is further taken (such as at 1 cm from stenosis). FFR can be determined in steady or transient state. An increase in the value of AFFR, the difference of the proximal FFR and the distal FFR, is an indication of greater vascular damage.

In a particular embodiment, before processing the CT-scan image, the image is filtered with a noise filter, an smooth filter or both.

Filtering is performed in order to improve the quality of the images which determine the location and shape of the walls after applying a segmentation process to the image. The noise and smooth filters are used to reduce or eliminate the noise of the images and to soft the images. Otherwise perturbations on the shape of the walls may induce fluctuations that may cause turbulence or a distorted flow.

Once the filtering is performed, the CT-scan images are processed in order to easily identify the blood cavities and their boundaries.

In a particular embodiment, the numerical blood flow model is corrected by removing those regions identified with calcified regions in the CT-scan image from the region identified as the cavity.

Different set of voxels from the blood cavities identified in the CT-scan image representing calcified and non-calcified regions are identified using different threshold values. Once the calcified regions are identified in the CT-scan 3D image, they are subtracted from numerical blood flow model.

In a particular embodiment, boundary conditions at the blood outlets are a flow resistance determined as an estimation of the resistance to the flow through the systemic arterial system.

According to this embodiment, as boundary conditions at the blood outlets the flow resistance encountered by the blood as it flows through the systemic arterial system downstream the outlet is considered. This condition allows the method avoid to extend the computational domain to the whole blood system.

In a particular embodiment,

-the numerical blood flow model comprises non-stationary terms;

-when imposing boundary conditions for the numerical blood flow model, the method further imposes initial conditions for said numerical blood flow model.

According to this embodiment, the numerical blood flow model is a non-stationary model that comprises terms depending on the time allowing the system to evolve in time. When determining the boundary conditions, the terms that are considered such pressure inlet, mass flow inlet or flow resistant are variable terms allowing to simulate transitional period of times.

In order to simulate the numerical blood flow model, the method imposes boundary conditions with variable terms such as the flow and pressure at the inlets. This is the case when taking into account the influence of the pulse. By additionally initial conditions the simulation is integrated in time for determining the non-stationary model.

In a particular embodiment, the method further comprises: generating a numerical elastic model of the walls; imposing boundary and initial conditions for the numerical elastic model and further imposing initial conditions for the numerical blood flow model, and; when simulating the numerical blood flow model, simulating the numerical elastic model of the walls taking into account the interaction between the blood flow and the wall.

According to this embodiment, in the method of the present invention a numerical elastic model of the walls of the blood cavity is generated in order to define the behavior of the walls when they interact with the blood flowing therein. In this embodiment hyperelastic walls are considered.

Modelling elasticity allows to make a more realistic analysis of the patients since the influence of the elasticity of the vascular tissues into the flow are taken into account. Furthermore, elasticity has a relevant role when there are elements such us calcifications or stents inside the blood vessel shows a rigidity different to the vascular tissues.

The numerical elastic model of the walls is a transient model since the shape of the cavity is time dependent due to the deformation caused by the blood pressure fluctuations. As a result, the walls of the blood cavities move depending on the blood flow model. On the contrary, the deformation of the elastic model of the walls depends on the forces acting on the surface of the wall and said forces mainly depends on the pressure value of the blood at the wall locations. Therefore, the numerical blood flow model and the numerical elastic model are two coupled models. The walls react to changes in pressure and in turn the deformation of the wall modify the shape of the computational domain located in the simulated cavity and therefore influence the flow blood establishing the coupled system.

After imposing the initial conditions on both models, the numerical blood flow model and the numerical elastic model, both models are integrated in time taking into account the coupled values. According to an specific embodiment, at each time step of the numerical integration an iterative process is used transferring in one way the force caused by the pressure from the numerical blood flow model to the numerical elastic model and transferring in the opposite way the shape of the computational domain of the numerical blood flow model imposed by the deformations according to the numerical elastic model.

In a particular embodiment, steady state conditions are simulated combining: a non-stationary numerical blood flow model; imposing steady state inlet boundary conditions and, simulating in time until the simulated flow reaches a steady state.

A steady state is reached when all the terms and boundary conditions, such the velocity distribution inside the cavity or the outlet pressure, computed in the numerical flood model remains invariable. This happens when, after the integration of the initial value problem, enough time passes for the transient model to reach a permanent value.

According to this embodiment, steady state conditions are simulated from a non- stationary numerical blood flow model by imposing steady state inlet boundary conditions and simulating the model in time until a steady state is reached.

In a particular example, the simulation stops when the stationary state is reached. According to this example, a stopping condition can be imposed in order to stop the simulation and consider a steady state. According to this example, there are several possible stopping conditions in order to stop the simulation of the numerical model. The first stopping condition can be imposed depending on the simulation time. That is, the simulation is stopped after a predetermined period of time or, alternatively after a a plurality of iterations when the above mentioned pressure or velocity variables comprised in the non-stationary model stop oscillating and are stable. The further stopping condition can be imposed depending on the value of predetermined residue being computed at each iteration during the simulation. That is, when the predefined residue reaches a minimum threshold value (for instance 10 ^-5 ) calculated during the simulation and thus, the pressure variable stop oscillating, the simulation is stopped. An example of predetermined residue is that being defined over momentum and continuity terms of the Navier-Stokes equations.

In a particular embodiment, the numerical blood flow model comprises a first discretization of the cavity, the numerical elastic model comprises a second discretization of an elastic structure representing a wall limiting the cavity and, the first discretization and the second discretization comprises compatibility conditions at the boundary of the cavity.

According to this embodiment, the method of the present invention generates two models, the numerical blood flow model and the numerical elastic model, that are two coupled models. The walls of the cavities are considered elastic and are deformed as the blood flows in the cavities and presses the walls. The walls react to changes in pressure and in turn influence the flow blood establishing the coupled system.

Both models are numerical models involving a discretization, the numerical blood flow model comprises a first discretization of the cavity and, numerical elastic model comprises a second discretization of an elastic structure representing a wall limiting the cavity. For instance, in a preferred embodiment, the numerical blood flow model uses a finite volume discretization and the numerical elastic model comprises a finite element discretization. According to a further example, the numerical blood flow model also uses a finite element discretization.

In any case, the discretization of the numerical blood flow model shows a boundary limited by the elastic wall discretized by the second discretization. According to this specific embodiment the first discretization and the second discretization comprises compatibility conditions at the boundary of the cavity allowing the interaction between the two models.

The numerical blood flow model and the numerical elastic model are iteratively simulated until the two models converge while imposing the compatibility conditions.

In a particular embodiment, compatibility conditions at the boundary of the cavity are: the first discretization and the second discretization comprises a common interface with at least one node of the first discretization and one node of the second discretization at the same location of the common interface and, wherein said nodes at the same location being restricted to have the same displacement.

According to this embodiment, the first discretization of the numerical blood flow model and the second discretization of the numerical elastic model comprises nodes and have a common interface with at least one common node, that is, at least one node of the first discretization has the same location as a node of the second discretization. The common nodes from the common interface have the same displacement. The displacement of a common node of one of the first or second discretization causes the same displacement of the common node of the other discretization. ln a particular embodiment, compatibility conditions at the boundary of the cavity are: an interface defined by nodes of the first discretization located at the boundary of the cavity and an interface defined by nodes of the second discretization located at the boundary of the cavity are impose to be close under a predetermined proximity criterion.

According to this embodiment, it is not required that the first discretization and the second discretization have common nodes. The interface of the first discretization may be defined by interpolating nodes located at the boundary of the first discretization, the boundary of the discretization of the cavity, and, the interface of the second discretization may be defined by interpolating nodes located at the external surface of the wall, that is, the boundary of said wall. This conditions imposes a proximity condition, under a predetermined threshold value, between the two interfaces interpreted as interface surfaces.

In a particular embodiment, boundary conditions at the blood inlets are flow conditions according to a pulsatile profile in pressure, mass flow or both.

In this embodiment, the pulsatile profile of the patient taking into account pressure or mass flow in the blood inlet is used for the inlet boundary conditions of the numerical blood flow model.

According to a particular example, the pulsatile profile is obtained from the maximum and minimum pressure values. A standard pulsatile profile is shifted and scaled to match with the maximum and minimum pressure value of the patient.

In a particular embodiment, the vessel damage indicator is determined at a plurality of locations of the boundary of the cavity generating a map of the surface of the cavity and, wherein those regions having a vessel damage indicator value less than a predetermined value is identified as being a damaged region.

The vessel damage indicator can be determined in different locations of the boundary of the cavity and the method generates a general map of the blood cavity showing healthy and damaged regions. Damaged regions are identified in the surface of the cavity because their vessel damage indicator value is less than a predetermined value whereas the vessel damage indicator value for healthy areas is higher.

In a particular embodiment, the method further comprises: predetermining a vessel damage indicator; selecting a patient carrying out a method according to the present invention for determining an estimated value of the predetermined vessel damage indicator for said patient wherein a pulse function characterizing the pulse of the patient is used during the simulation of the numerical blood flow model; selecting a pulse function representative of a pathology; repeating steps e) and f) wherein the simulation is carried out using the pulse function representative of the pathology; determining the ratio or the difference between the estimated value of the predetermined vessel damage indicator measured on the patient and the estimated value of the predetermined vessel damage indicatorfor the pulse function representative of the pathology as an estimator of the progress of the specific pathology.

According to this embodiment, the method is able to estimate the progress of a specific pathology, predicting possible future complications.

Firstly, a vessel damage indicator such as FFR, or i FR is selected.

Once a patient is selected, a first simulation of the method is carried out determining an estimated value of the predetermined vessel damage indicator for said patient. A pulse function characterizing the pulse of the patient is used during the simulation for the inlet boundary conditions of the numerical blood flow model.

A pulse function representative of a specific pathology is defined. Said pulse function may be defined in different ways. In an embodiment a group of patients is selected according to the specific pathology and a pulse function characterizing the pathology from said group is defined. In another embodiment a pulse function is designed from the patient's own pulse, wherein the designed pulse function recreates a situation representative of the pathology, such as hypertension or arterial stiffness.

Once the pulse function representative of the specified pathology is defined, a second simulation of the method of the invention is carried out with the numerical blood flow model of the initial patient and the pulse function representative of the pathology. The pulse function representative of the pathology is used during the simulation forthe inlet boundary conditions of the numerical blood flow model.

Finally, the ratio or the difference between the estimated values of the vessel damage indicator obtained with the pulse function of the patient and the pulse function representative of the pathology is determined. This ratio or the difference between the estimated values allow to evaluate the progress of the pathology on the patient. From the estimated values, potential future risk regions can be identified on the patient. In this way, interventions can be planned before the heart degenerates and when the patient is still able to withstand the surgery.

In a particular embodiment, the pulse function is imposed in the inlet boundary conditions on the numerical blood flow model.

The pulse function of the patient obtained from the maximum and minimum pressure values by scaling a standard profile is imposed as inlet boundary condition for the numerical blood flow model.

In a particular embodiment, the method comprises comparing with at least one threshold the determined ratio or difference between the estimated value of the predetermined vessel damage indicator measured on the patient and the estimated value of the predetermined vessel damage indicatorfor the pulse function representative of the pathology.

In a particular embodiment, the method comprises: predetermining a second variable representative of the vessel damage, the second variable being different from the predetermined vessel damage indicator; determining an estimated value of the predetermined second variable for said patient from a simulation of the numerical blood flow model using the pulse function characterizing the pulse of the patient; determining an estimated value of the predetermined second variable from a simulation of the numerical blood flow model using the pulse function representative of the pathology; determining the ratio or the difference between the estimated value of the predetermined second variable measured on the patient and the estimated value of the predetermined second variable for the pulse function representative of the pathology as an estimator of the progress of the specific pathology.

Along the description, the expression "using the pulse function" in a simulation has to be interpreted as the pulse is used as a boundary condition in the inlet of the domain of the cavity of the simulation.

According to this embodiment, a second variable representative of the vessel damage is predetermined. Said "second variable" will be understood as a variable additional to, and different from, the predetermined vessel damage indicator, the second variable also characterizing the blood flow conditions allowing the evaluation of anatomy and function coronary arteries and helping clinicians to study cardiac pathologies.

Once the second variable is selected, an estimated value of the second variable is determined for the patient from a simulation of the numerical blood flow model using the pulse function characterizing the pulse of the patient.

Also, an estimated value of the second variable is determined from a simulation of the numerical blood flow model using the pulse function representative of the pathology.

Finally, the ratio or the difference between the estimated values of the second variable obtained with the pulse function of the patient and the pulse function representative of the pathology is determined. Advantageously, using a predetermined second variable in addition to the predetermined vessel damage indicator makes the estimation of the progress of a specific pathology more robust and provides additional information on vascular damage. Also, using a predetermined second variable is useful to evaluate the progress of the pathology on the patient and to identify potential future risk regions in cases where the predetermined vessel damage indicator does not provide a conclusive result.

The estimated values of the second variable may be obtained as a result of the simulations performed to determine the estimated values of the predetermined vessel damage indicator or may be obtained performing additional simulations. ln a particular embodiment, the method comprises comparing with at least one threshold the determined ratio or difference between the estimated value of the predetermined second variable measured on the patient and the estimated value of the predetermined second variable for the pulse function representative of the pathology.

In a particular embodiment, the second variable is FFR, iFR, AFFR, a Time Averaged Wall Shear Stress, a Stenoses Resistance, a Relative Residence Time or a Q-Criterion.

The Wall Shear Stress (WSS) indicator is a key parameter in cardiovascular flows because of its direct relationship to the development of cardiovascular disease and atherosclerosis in general. WSS is also a parameter used to determine which zones are more prone to form plaque. WSS accounts for the frictional forces between the circulating flow and the vessel walls, and it becomes zero when the flow stops. Time averaged wall shear stress (TAWSS) is measured at the top portion of maximal stenosis (stenosis crest) in basal conditions and in transient state (as an average of WSS over two complete cardiac cycles). An increase in the value of the TAWSS is an indication of greater vascular damage.

The calculation of the stenosis resistance (SR) combines pressure and the average peak flow velocity measured distal to the coronary lesion.

_CD > Pa - Pd

^SR -~APV ~ where p _a and p _d are the mean aortic pressure and mean distal pressure, and APV is the average peak flow velocity, measured distal to the coronary lesion.

From SR two different parameters may be calculated: HSR (hyperaemic stenosis resistance) calculated under hyperaemic conditions and BSR (basal stenosis resistance) calculated in basal conditions. An increase in the value of this parameter is an indication of greater vascular damage.

Q-Criterion is measured throughout the coronary segment (providing information about the general evolution of the entire 3D geometry) and in the local area affected by the lesion (providing information about the evolution of the lesion) in basal conditions, and it is defined by Q=(V ² -S ² ) where V is the spin tensor and S is the strain tensor. The value of this parameter is calculated considering its average in two different cardiac cycles. When this value is positive it implies that the flow is vorticity-dominated and when it is a negative value it implies it is strain-dominated. An increase in the value of this parameter (an increase of recirculation areas), is an indication of greater vascular risk.

Relative Residence Time (RRT) measures how long some circulating particles, such as LDL (low density lipoprotein), that play a key role in plaque formation, stay nearthe wall, and it is defined as where T is the period of the pulse.

A longer residence time of this type of particles near the arterial wall increases their probability to adhere to the wall and form atherosclerotic plaque, and thus, increase vascular risk.

RRT is measured in transient state and in basal conditions. An increase in the value of this parameter is an indication of greater vascular risk.

In a particular embodiment, the predetermined vessel damage indicator is FFR or iFR.

A second inventive aspect provides a system for determining a vessel damage estimator in a patient, comprising: a CT-scan configured for capturing a CT-scan 3D image of a region of the patient, the region at least comprising coronary arteries and aortic arteries; at least one processor adapted to receive a CT-scan 3D image from the CT-scan and configured for carrying out the steps of the method of the first inventive aspect.

A third inventive aspect provides a computer program comprising instructions which, when the program is executed by a computer, cause the computer to carry out the steps of the method according to the first inventive aspect.

DESCRIPTION OF THE DRAWINGS

These and other features and advantages of the invention will be seen more clearly from the following detailed description of a preferred embodiment provided only by way of illustrative and non-limiting example in reference to the attached drawings.

Figure 1 This figure shows a flow chart of the non-invasive method for determining a vessel damage indicator according to an embodiment of the present invention.

Figure 2 This figure shows the steps of the non-invasive method for determining a FFR indicator in a patient according to a particular example.

Figure 3 This figure shows the output of the non-invasive method for determining a FFR indicator from the example of figure 2 and a grey scale of the FFR values.

Figure 4 This figure shows the location of the FFR values of the non-invasive method from the example of figure 2.

Figure 5 This figure shows an example of the non-invasive method for determining the progress of a specific pathology on a patient.

Figure 6 This figure shows an example of a patient's pulse function and of a pulse function designed from the patient's pulse function to be representative of arterial stiffness.

DETAILED DESCRIPTION OF THE INVENTION

As will be appreciated by one skilled in the art, aspects of the present invention may be embodied as a method, system or computer program product.

The present invention describes a non-invasive method (100) for determining a vessel damage indicator in a patient, by simulating a numerical blood flow model (BM) based on a processed CT-scan 3D image (M).

Figure 1 shows a flow chart of a particular example of the method (100) for determining a vessel damage indicator in a patient, the method (100) comprises the following steps: a) inputting (110) a CT-scan 3D image (M) of a region of the patient, the region at least comprising coronary arteries and aortic arteries; b) processing (120) in a computer system the CT-scan image (M) carrying out the steps: identifying at least one blood cavity (C) and a boundary (B) limiting the cavity (C); identifying those portions of the boundary (B) corresponding to blood inlets (I), blood outlets (O), and walls (W); c) generating (130) a numerical blood flow model (BM) in the cavity (C), said numerical blood flow model (BM) at least comprising the pressure of the blood and the velocity of the blood; d) imposing (140) boundary conditions on the numerical blood flow model (BM); e) simulating (150) the numerical blood flow model (BM); f) determining (160) a vessel damage indicator as the rate between the pressure value at a first location of the artery and, the pressure value at a second location of the artery distant from the first location, the pressure values taken from the simulated numerical blood flow model (BM).

The non-invasive method (100) for determining the a vessel damage indicator uses a CT- scan 3D image (M) of a region of the patient wherein a blood cavity (C) is identified by using a segmentation process along with its boundary (B) and the corresponding walls (W) limiting said cavity (C) wherein additionally the blood cavity (C) is limited by blood inlets (I) and blood outlets (O).

Once the CT-scan image (M) is processed (120) and the blood cavity (C) is identified, a numerical blood flow model (BM) is generated (130). The cavity (C) is the computational domain for the numerical blood flow model (BM) being generated for modeling the flow of the blood in the artery tree of the patient.

In this example, the numerical blood flow model (BM) includes a representation of the cavity (C), the walls (W), the inlet (I) and the outlets (O) to the cavity (C) on which the boundary conditions will be imposed. The numerical blood flow model (BM) is completed with the set of differential equations that determine its behavior.

Next, non-slip boundary conditions are imposed (140) on the walls (W) limiting the blood cavity (C) and over those boundaries (B) defined as the inlet (I) coming from the heart and outlets (O). Inlet (I) boundary conditions are preferably set by defining the flow and the flow pressure according to a pulse function. A flow resistance is imposed at the outlets (O).

The numerical blood flow model (BM) comprises a numerical characterization of the behavior of the flow, wherein the numerical characterization comprises a discretization of the Navier-Stokes equations involving at least the pressure of the blood and the velocity field. In this particular example, the blood is considered as a Newtonian fluid and rigid walls are considered as well.

According to this example, steady state equations are used for simulating the flow without requiring to integrate time dependent variables that require to integrate the flow until transient conditions reaches the steady state.

Finally, the numerical blood flow model (BM) is simulated (150) and pressure values of two different locations, a first location and a second location preferably located downstream of the first location and distant from each other, are obtained from the simulation in order to determine (160) a vessel damage indicator. The vessel damage indicator is calculated as the rate between the pressure value at a first location of the artery and, the pressure value at a second location of the artery distant from the first location.

Figure 2 shows the steps of the non-invasive method (100) for determining a FFR indicator in a patient according to a particular example.

According to this example, CT-scan images (M) are acquired from a region of the patient using computer-processed combinations of multiple X-ray measurements. The CT-scan images (M) comprise voxels representing the blood cavities (C), tissues and boundaries (B) such as the walls limiting the blood cavities (C). ln this example, the images are filtered with a noise and a smooth filter to improve the quality of the images which determine the location and shape of the walls (W), otherwise perturbations on the shape of the walls (W) may induce artificial fluctuations that may cause a distorted flow.

The CT-scan images (M) are processed in order to identify the blood cavities (C) by using a segmentation process which identify the blood cavity (C) and the rest of the image. As it can be seen in figure 2, the images are used to obtain a 3D reconstruction of the region acquired of the coronary tree of the patient, representing the geometric characteristics of the coronary tree.

According to this example, the CT-scan image (M) is analyzed in order to identify the set of voxels representing calcified and non-calcified regions. Once the calcified regions are identified in the CT-scan 3D image (M), they are subtracted from the numerical blood flow model.

In this example, the identified cavity (C) is the computational domain for a numerical blood flow model (BM) being generated for modeling the flow of the blood in the artery tree of the patient and the numerical blood flow model (BM) according to this specific example uses a finite volume method for discretization of the domain.

Non-slip boundary conditions are imposed on the walls (W) limiting the blood cavity (C) by vessel tissues and over those boundaries (B) defined as the inlet (I) coming from the heart and outlets (O).

The numerical blood flow model (BM) comprises a numerical discretization of the domain and the Navier-Stokes equations involving as main variables the pressure of the blood and the velocity field.

The numerical discretization of the domain comprises a characterization of the walls (W) by surfaces identified in the segmentation process of the domain over the CT-scan image (M) once the filtering process and any further post-processing method is applied such as that for removing the calcified regions. Such surfaces will be the boundaries of the domain along with the inlet (I) and the outlets (O). According to this example, the discretization of the inner volume of the domain is carried out using a finite volume discretization using interpolation transformations in order to adapt a structured mesh to the shape of the cavity (C), that is, the computational domain. According to another embodiment, an unstructured mesh is used for the discretization of the domain.

The numerical blood flow model (BM) further comprises parameters of the density and the viscosity of the blood. In this example, some references values for the density and the viscosity of the blood which are widely known in the state of the art are established, the density considered is 1060kg/ m ³ and the viscosity is 0.004 Pa. The Navier-Stokes equations are solved using CFD (computational fluid dynamics) software.

In this example, as inlet boundary conditions the pressure inlet and mass flow inlet are imposed, as outlet boundary condition the flow resistance is imposed and, rigid walls are considered for the boundaries limited by the vessel tissues. Boundary conditions imposed at the inlet (I) are the flow and a pressure profile according to a pulse.

In this example, blood is considered as a Newtonian fluid, incompressible with constant density, flowing in laminar and steady state conditions. Steady state equations are used for simulating the flow without requiring to integrate time dependent variables and a finite volume method is used to solve Navier-Stokes equations.

In this example, the vessel damage indicator determined by the method (100) is the FFR indicator. The FFR indicator evaluate the hemodynamic relevance of coronary artery stenosis and it is calculated as the ratio between coronary pressure distal to a coronary artery stenosis and aortic pressure under conditions of maximum hyperemia.

Maximal hyperemia is the critical prerequisite for FFR assessment, according to this example, the hyperemia conditions are imposed to the numerical blood flow model (BM) as inlet boundary conditions. The CT-scan images (M) are taken from the patient in a resting state, and the pressure and the mass flow parameters in the inlet (I) of the numerical blood flow model (BM) are corrected in order to simulate maximum hyperemia conditions. According to this example, the mass flow parameter is corrected based on the age, weight and heart rate of the patient and the correction increases the inlet pressure in respect to a reference pressure on a healthy patient. Once the numerical blood flow model (BM) is simulated and the Navier-Stokes equations are solved, the vessel damage indicator can be determined as the rate between the pressure value at a first location of the artery and, the pressure value at a second location of the artery distant from the first location measured in the solved numerical blood flow model (BM).

According to this example, the FFR indicator is determined at a plurality of locations of the boundary (B) of the cavity (C) generating a map of the surface of the cavity (C) as it can be seen in the last image in figure 2.

Figure 3 shows the output of the non-invasive method for determining a FFR indicator from the example of figure 2 and the grey scale of the FFR values and figure 4 shows the same output with the location of some FFR values of the non-invasive method from the example of figure 2.

According to the previous example, the FFR indicator is determined at a plurality of locations of the boundary (B) of the cavity (C) generating a map of the surface of the cavity (C) as it can be seen in figure 3.

The FFR indicator can be determined in different locations of the boundary (B) of the cavity (C) and the method (100) generates a general map of the blood cavity (C) showing healthy and damaged regions.

Depending on the FFR value of different locations, each region of the surface of the cavity (C) is represented with its corresponding color. The grey scale can be seen in the bottom of figure 3. If the FFR value of a determined location is between 0.97 and 1 that location is represented in white. As the FFR value of a location decreases, the location is represented in a darker grey. If the FFR value of a location is between 0.84 and 0.87, this location is represented in black.

Figures 3 and 4 show damaged and healthy areas depending on the FFR value obtained. Those regions with a FFR value close to 1 are considered healthy areas and are represented with light colors, whereas those regions having a lower FFR value may be considered as damaged regions and are identified in the surface of the cavity (C) in dark colors.

Figure 4 further shows some specific FFR values in different regions of the surface of the cavity (C), where the regions indicated with high values like 1 or 0.94 are healthy regions that would not present problems, whereas the dark region marked with 0.87 would be a damaged area that could present injuries or stenosis that should be treated.

Figure 5 shows an example of the non-invasive method (100) for determining the progress of a specific pathology on a patient.

According to this example, the fractional flow reserve (FFR) is selected as the vessel damage indicator for a patient.

Once the vessel damage indicator and the patient are selected, the non-invasive method (100) according to the example from figure 2 for determining the FFR value for said patient is carried out.

According to this example, the pulse function characterizing the real pulse of the patient is imposed as inlet boundary condition during the simulation ofthe numerical blood flow model (BM).

In this example, the FFR indicator is determined at a plurality of locations of the boundary (B) of the cavity (C) generating a map of the surface of the cavity (C) as it can be seen in the upper last image in figure 5.

Then, a pulse function representative of a pathology is selected. In an embodiment, a group of patients according to a specific pathology is selected in order to define a pulse function characterizing the pathology from said group.

Once said pulse function characterizing the specified pathology is defined, a second simulation of the method (100) of the invention is carried out with the numerical blood flow model of the initial patient, wherein the pulse function characterizing the group of patients having the specific pathology is used during the simulation for the inlet boundary conditions of the numerical blood flow model. The FFR indicator is obtained with the pulse function characterizing the pathology from the group of patients at a plurality of locations of the boundary (B) of the cavity (C).

From the estimated values obtained with both, the real pulse of the patient and the pulse characterizing the group of patients with the specific pathology, the progress of the specific pathology can be estimated and future diseases can be detected. According to this example, potential future risk regions can be identified on the patient. For instance, if the progress of the specific pathology has no reached a dangerous level, the patient may be treated by surgery with a sufficient level of safety that it would not have had if the damage would progress to a greater degree.

In another embodiment, instead of defining the pulse function representative of the pathology based on a group of patients, the pulse function representative of the pathology is designed from the patient's own pulse, wherein the designed pulse function recreates a situation representative of the pathology.

Figure 6 shows an example of a patient's pulse function (depicted in grey) and of a pulse function designed from the patient's pulse function to be representative of a pathology (depicted in black), in particular representative of arterial stiffness.

In an embodiment, starting from a typical (healthy) pulse profile of the patient, three areas of the pulse function are analyzed: the systolic phase (heart contraction), the dicrotic notch (aortic valve closure) and the diastolic phase (relaxation). These areas are shown in figure 6. Once each of these areas has been identified, one or several areas can be modified in order to reproduce a certain cardiac pathology as, for example, hypertension or arterial stiffness.

The adaptation of the initial pulse function in order to obtain a pulse representative of a pathology may be carried out by using and combining different types of curves, such as Bezier curves, quadratic curves, straight lines, etc. Such curves may be used as a mathematical representation of the curve. The adaptation of the initial pulse function may be carried out by selecting an interval of the pulse function where the shape is modified when the patient presents the pathology. The adaptation of the pulse is limited to said interval, replacing the shape of the curve of the patient with a shape representative of the pathology. The shape representative of the pathology may be obtained from literature where the shape corresponding to the pathology is displayed or disclosed. According to a further embodiment, the shape representative of the pathology taken from literature is scaled in order to enhance the effect of the pathology on the behaviour of the pulse.

In the example of figure 6 each of the systolice phase, the dicrotic notch and the diastolic phase of the patient's pulse function have been modified to obtain the pulse function representative of arterial stiffness.