EA042942B1 - PATIENT-SPECIFIC MODELING OF HEMODYNAMIC PARAMETERS IN THE CORONARY ARTERIES - Google Patents

Description

Background of the invention

Cardiovascular disease is the leading cause of death for men and women in the United States and accounts for at least 30% of deaths worldwide. Although medical advances in recent years have provided important improvements in the diagnosis and treatment of heart disease, the incidence of premature morbidity and mortality is still high. One reason for this is the lack of accurate estimates of patient-specific parameters that accurately characterize the anatomy, physiology, and hemodynamics of the coronary arteries, all of which play an important role in the progression of cardiovascular disease.

Medical imaging-based methods (eg, computed tomography angiogram) are commonly used in clinical practice to characterize the severity of stenosis in the coronary arteries. However, such methods provide only anatomical assessment, which is often insufficient for clinical decision making. In particular, the anatomical assessment of the severity of coronary artery stenosis often leads to an overestimation or underestimation, which in both cases is undesirable. Overestimation of the severity of stenosis may lead to unnecessary intervention and subsequent risk of restenosis, while underestimation is more likely to lead to treatment failure. Accurate functional assessment may require pressure and/or flow measurements, which are determined invasively.

Several computational fluid dynamics (CFD) based methods have been developed for the functional assessment of coronary artery disease. However, they are generally based on simplified coronary artery geometries with general boundary conditions derived from population-wide data. This renders such methods unsuitable for comprehensive patient-specific assessment of coronary artery disease, such as assessing the severity of stenosis in the case of coronary artery stenosis. An example of such a method has been disclosed in the following document: Chung J.H., Lee K.E., Nam C.W., Doh J.H., Kim H.I., Kwon S.S., Shim E.B., Shin E.S. (2017) Diagnostic Performance of a Novel Method for Fractional Flow Reserve Computed from Noninvasive Computed Tomography Angiography (NOVEL-FLOW Study) The American Journal of Cardiology, 120(3):362-368. This study was aimed at reducing the complexity of the computational method, which led to a reduction in the average time to provide results to 185 minutes. In said document, boundary conditions were calculated using estimated blood pressure waveforms obtained by fitting a function obtained from simulation studies to experimental data such as systolic blood pressure, diastolic blood pressure, and heart rate. The document does not unambiguously disclose whether the systolic blood pressure, diastolic blood pressure and heart rate parameters were obtained in a non-invasive manner. A three-dimensional model of the coronary arteries was obtained in a non-invasive way using a coronary computed tomographic angiogram (CCT). The method offers good accuracy compared to known methods.

An example of a method implementing CFD calculation and invasive examinations has been disclosed in the following document: Kousera C.A., Nijjer S., Torii R., Petraco R., Sen S., Foin N., Hughes A.D., Francis D.P., Xu X.Y. , Davies J.E. (2014) Patient-specific coronary stenoses can be modeled using a combination of OCT and flow velocities to accurately predict hyperemic pressure gradients IEEE Transactions on Bio-medical Engineering, 61(6): 1902-1913. This study was aimed at providing a patient-specific numerical study combining the results of a highly accurate optical coherence tomography (OCT) reconstruction technique with an angiogram and patient-specific pressure and velocity waveforms. Angiogram, OCT and pressure measurements were performed using catheters and therefore in an invasive manner. The authors of this study acknowledged the limitations of this method due to invasive measurements and the need for manual data processing, ie. this method was not automated. However, this document does not propose the use of non-invasive measurement methods. The resulting simulations correlated well with the experimental data.

Brief description of graphic materials

A detailed description is given with reference to the accompanying drawings. The drawings are provided for illustrative purposes only and merely depict exemplary embodiments of the present invention. The drawings are provided to facilitate understanding of the present invention and should not be construed as limiting the scope, scope or applicability of the present invention. On drawings, the leftmost digit(s) of the reference number may (may) identify the drawing on which the reference number first appears. The use of like reference numbers indicates like, but not necessarily the same or identical components. However, different reference numbers may also be used to identify such components. In various embodiments, elements or components other than those illustrated in the drawings may be used, and some elements and/or components may not be present in various embodiments. The use of singular terminology to describe a component or element may, depending on the context, encompass the plural of such components or elements, and

- 1 042942 vice versa.

Fig. 1 is a schematic representation of a method for patient-specific modeling of hemodynamic parameters in the coronary arteries in accordance with one or more exemplary embodiments of the present invention.

Fig. 2 is a flow diagram of a method for patient-specific modeling of hemodynamic parameters in the coronary arteries in accordance with one or more exemplary embodiments of the present invention.

Fig. 3 is an exemplary recording of a patient's electrocardiogram.

Fig. 4 is an exemplary Lomb-Scargle periodogram of a patient's cardiac cycle.

Fig. 5 is a schematic representation of a three-component model for use in determining coronary circulation boundary conditions.

In FIG. 6 illustrates four different Windkessel models, specifically two-, three-, four-, and five-element Windkessel models (2WM, 3WM, 4WM, 5WM) suitable for use in a circulatory system (BCS) component model.

In FIG. 7 illustrates several functional blocks (a-c) and an exemplary multi-block system (d) consisting of a functional block (b) for use in a circulatory system (BCS) component model.

In FIG. 8 illustrates a circulatory system (BCS) model containing systemic and pulmonary circulation elements and its relationship to the HPV component.

In FIG. 9 illustrates a lumped parameter function block containing resistance, inertia, and capacitance (RLC) parameters that is suitable for use in a circulatory system (BCS) component model.

In FIG. 10 illustrates schematic diagrams of (a) a ventricular pressure-volume loop, (b) aortic pressure plotted as a function of time, and (c) ventricular volume plotted as a function of time.

In FIG. 11 illustrates the functional block (a) and the entire model (b) of the heart pressure-volume (HPV) components.

Fig. 12 is a graph showing the reconstructed patient-specific ventricular volume and pressure during five cardiac cycles.

In FIG. 13 illustrates the general concept of the coronary blood flow (CBF) model.

In FIG. 14 illustrates six exemplary models suitable for use in a coronary blood flow (CBF) component model.

In FIG. 15 illustrates five different functional blocks (a)-(e) suitable for use in a multisectional coronary flow (CBF) model.

In FIG. 16 illustrates a set of function block parameters suitable for use in a coronary blood flow (CBF) component model.

In FIG. 17 illustrates a multi-layer/multi-section lumped parameter model with descriptive parameters suitable for use in a coronary blood flow (CBF) component model.

In FIG. 18 illustrates in detail a three-component model for use in defining coronary circulation boundary conditions, containing: a circulatory system (BCS) model component (pulmonary and systemic circulation), a heart pressure-volume (HPV) model component, and a coronary blood flow (CBF) model component. .

Fig. 19 is an example of a 3D mesh of a portion of a patient's blood vessel.

In FIG. 20 illustrates a schematic representation for determining the inflow and outflow boundary conditions of the coronary circulation.

Fig. 21 is a flow diagram of a method for patient-specific modeling of hemodynamic parameters in coronary arteries using steady state simulation, in accordance with one or more exemplary embodiments of the present invention.

Fig. 22 is a flow diagram of a method for patient-specific modeling of hemodynamic parameters in coronary arteries using steady state simulation, in accordance with one or more exemplary embodiments of the present invention.

Fig. 23 is a flow diagram of a method for patient-specific modeling of hemodynamic parameters in coronary arteries using transient simulation, in accordance with one or more exemplary embodiments of the present invention.

Fig. 24 is a flow diagram of a method for patient-specific modeling of hemodynamic parameters in coronary arteries using transient simulation, in accordance with one or more exemplary embodiments of the present invention.

Fig. 25 is a receiver performance curve (ROC) comparing fractional flux reserve (FFR) results obtained using a variant of the three-component model with actual results.

- 2 042942

Detailed description

The present invention relates, inter alia, to devices, systems, methods, computer-readable media, methods and techniques for non-invasive patient-specific modeling of coronary artery flow based on volumetric imaging data and continuous blood pressure data. Volumetric data on a patient's coronary arteries can be collected using non-invasive medical imaging techniques such as computed tomographic angiogram (CT) or magnetic resonance angiogram (MRA). Volumetric data can be used to create an anatomical model of the patient's coronary arteries suitable for computational fluid dynamics (CFD) simulation. Continuous blood pressure data can be obtained using non-invasive methods. The continuous blood pressure data can be used to determine the boundary conditions for CFD simulation. Patient-specific CFD simulations can be performed using an anatomical model of a coronary artery, with entry and exit boundary conditions determined based on continuous blood pressure data. Patient-specific hemodynamic parameters in the coronary arteries can be derived from CFD simulations and can be used to characterize/assess cardiovascular disease, such as functional assessment of stenosis in a patient.

CFD simulation can be performed using a patient-specific anatomical model of a coronary artery derived from medical imaging data and patient-specific boundary conditions derived from continuous blood pressure data to determine patient-specific hemodynamic parameters in the patient's coronary arteries. In embodiments, a three-component model may be used to determine coronary artery inflow boundary conditions for CFD simulation. A three-component model may contain a circulatory system (BCS) component that describes the systemic and pulmonary circulations, a chamber pressure-volume (HPV) component that describes the relationship between ventricular or atrial pressure and volume, and a coronary blood flow (CBF) component. which describes the circulation of the coronary tree. The three-component model may provide the ability to determine the volumetric flow waveform at the inlet of a patient's coronary arteries. The determined volume flow waveform at the inlet of the patient's coronary arteries can be used to determine the coronary artery outflow boundary conditions for CFD simulation. For example, a patient's coronary inlet volume flow waveform can be used to determine the patient's coronary outlet volume flow waveform using Murray's law or a similar allometric scaling law (see Sherman T (1981) On connecting large vessels to small - the meaning of Murray's law, Journal of General Physiology, 78(4): 431-453).

Patient-specific modeling of coronary artery flow in accordance with the present invention may use methods that provide advantages over existing methods. For example, a patient-specific anatomical model created can only model the patient's coronary arteries. That is, the created patient-specific anatomical model may not, for example, recreate the patient's aorta or estimate the volume of the heart chamber. This can reduce numerical complexity and simulation time. Additionally, boundary conditions can be derived from non-invasively measured continuous blood pressure data. The advantages of using pressure data to derive boundary conditions include the ease with which pressure can be measured relative to other parameters typically used to determine boundary conditions (e.g. velocity, mass flow) and the reliability of pressure measurements that are not corrupted by error, exceeding the allowable, even when measured non-invasively and in a place remote from the heart.

In the present invention, reference is made to modeling the coronary arteries and coronary artery blood flow. It should be understood that the coronary arteries may include not only the two main coronary arteries, but also the arterial branches extending from them, and any plaques contained therein, unless the context clearly indicates otherwise.

In FIG. 1 and 2 illustrate a method 100 for patient-specific modeling of hemodynamic parameters in coronary arteries in accordance with one or more exemplary embodiments of the present invention. Method 100 may be performed on a computer or on a computer system.

The computer may include one or more non-volatile computer-readable storage media that store instructions that, when executed by a processor, can perform any of the actions described herein for patient-specific modeling of hemodynamic parameters in the coronary arteries. The computer may be, or the computer system may comprise, a desktop or laptop computer, a mobile device (eg, a smartphone), a cloud computing system, a server, or any other computer. A computer may contain a processor, read-only memory (ROM), random access memory (RAM), an input/output (I/O) adapter for connecting peripheral devices (for example,

- 3 042942 input devices, output devices, data storage devices, etc.), a user interface adapter for connecting input devices such as a keyboard, mouse, touch screen and / or other devices, a communication adapter for connecting a computer to a network and an adapter display to connect a computer to the display. The display may be used to display any calculated hemodynamic parameters to the user (eg, displaying images or 3D models of a patient's coronary arteries over which certain hemodynamic parameters are shown).

At 102, the computer system may receive patient-specific anatomical structure data. The computer system may receive patient-specific anatomy data (eg, image data obtained with a CT scanner or x-ray machine) over a communications network and/or from a computer-readable storage medium.

Patient-specific anatomical data may be 2D or 3D images (volumes) of the patient's circulatory system. The images may include at least part or all of the patient's coronary arteries. The images may or may not contain other anatomical structures such as the patient's heart, aorta, and the like. Patient-specific data on the anatomical structure can be obtained non-invasively using various non-invasive medical imaging techniques. For example, data can be obtained using computed tomography (CT), computed tomographic angiogram (CT), magnetic resonance imaging (MRI), or magnetic resonance angiogram (MRA). Alternatively, patient-specific data on the anatomical structure can be obtained using various invasive imaging modalities such as rotational angiogram, dynamic angiogram, or digital subtraction angiogram.

The received patient-specific anatomical structure data may be pre-processed by the user and/or a computer system prior to subsequent use. Pre-processing may include, for example, checking for misregistration, inconsistencies, or blurring in the collected image data, checking for stents shown in the collected image data, checking for other artifacts that may interfere with the visibility of the coronary artery lumen, checking for sufficient contrast between anatomical structures (eg, aorta, major coronary arteries, other blood vessels, and other parts of the patient). During pre-processing, the user and/or the computer system may be able to correct some errors or problems associated with the data. Pre-processing may also include the use of image processing techniques on the received patient-specific anatomical structure data to prepare the data for use in generating an anatomical model (eg, preparing data for segmentation). Image processing may include, for example, adjusting contrast levels between different anatomical structures (eg, heart, aorta, coronary arteries, other vasculature, atherosclerotic plaques, etc.) in images, smoothing anatomical structures (eg, applying a smoothing filter), and etc. At 104, the computer system may receive patient-specific physiological data. The computer system may receive patient-specific physiological data over a communications network and/or from a computer-readable storage medium. The patient-specific physiological data may include continuous blood pressure data (eg, a continuously recorded blood pressure waveform). Continuous arterial blood pressure is time-varying and is measured in real time without any interruption (eg, continuously). In some embodiments, a continuously recorded blood pressure waveform may be obtained over a period of approximately one (1) minute, or a period of time ranging from one (1) minute to two (2) minutes, although and other continuous periods of time. Continuous blood pressure data can be obtained without a percutaneous procedure (eg, non-invasively). For example, data may be acquired using a Nexfin™ monitor, ClearSight™ monitor, CNAP™ monitor, Finapres® NOVA monitor, or subsequent systems (eg, Finometer® and Portapres® monitors), or other similar non-invasive continuous blood pressure measurement devices. Alternatively, continuous blood pressure data can be obtained using various invasive methods such as arterial catheterization. The continuous blood pressure data may be subjected to data processing (eg, signal processing) to prepare the data for use in determining boundary conditions for CFD simulation and/or blood flow simulation in an anatomical model using CFD. For example, pressure signals may be derived from continuous blood pressure data.

Patient-specific physiological data may include physiological data other than continuous blood pressure data, such as the patient's heart electrical activity, baseline heart rate, height, weight, hematocrit, stroke volume, and the like. In general, any physiological data may be subjected to data processing (eg, signal processing) to prepare the data for use in determining boundary conditions for CFD simulation and/or blood flow simulation in an anatomical model using CFD.

Physiological data may include, for example, continuous recording of the electrocardiography (ECG) signal from the patient, an example of which is shown in FIG. 3. The ECG signal can be used to directly recreate the temporal parameters of the cardiac cycle, such as heart rate variability (eg, cardio interval). In the example of FIG. 3, the calculated average cardio interval for patient recording is 0.897 s. The cardio interval can be used, for example, when defining the boundary conditions for a CFD simulation.

Physiological data may include, for example, the dynamics of pressure in the aorta. Aortic pressure dynamics can be used to indirectly determine the timing of the cardiac cycle when the patient's ECG signal is not available, although it is slightly less accurate than ECG. The Lomb-Skargle algorithm can be used to generate a Lomb-Skargle periodogram of a patient's cardiac cycle based on aortic pressure dynamics, an example of which is shown in FIG. 4. The LombScargle algorithm can be used to find and test the significance of weak periodic signals with non-uniform time sampling (see Townsend RHD (2010) Fast calculation of the LombScargle periodogram using graphics processing units. The Astrophysical Journal, Supplement Series, Vol. 191 , 247-253). In the example of FIG. 4, the computed cardio interval for recording the patient's pressure using the Lomb-Skargle algorithm is 0.901 s. The CV interval calculated using the Lomb-Skargle algorithm differs slightly from the CV interval determined from ECG data, but the difference is less than 0.5%. At step 106, the computer system may generate a patient-specific anatomical model of the patient's coronary arteries based on the received patient-specific anatomical data. The patient-specific anatomical model may be a three-dimensional geometric model of the patient's coronary arteries. The created patient-specific anatomical model can only model the patient's coronary arteries. That is, the patient-specific anatomical model created may not, for example, recreate the heart, aorta, non-coronary vasculature, patient, or other tissues. The received patient-specific anatomical data (eg, anatomical images) may include regions of variable optical density that correspond to different anatomical structures such as the aorta, major coronary arteries, coronary arterial branches, myocardium, and the like. The locations of anatomical structure surfaces can be determined based on the contrast (eg, relatively dark and light areas) between different anatomical structures. The contrast between anatomical structures can also allow selective modeling of some anatomical features (eg, coronary arteries) while excluding other anatomical features from the generated model (eg, heart).

The process of forming a patient-specific anatomical model as a whole is called segmentation. The segmentation may be performed automatically by the computer system with or without user input. To generate a patient-specific anatomical model, the coronary arteries may be segmented into patient-specific anatomical data using any suitable coronary artery segmentation technique. Methods for generating an anatomical model of a patient's coronary arteries (for example, methods for segmenting a coronary artery) are described, for example, in the following documents: US patent applications No. 2010/006776 and No. 2012/0072190, as well as US patents No. 7860290, No. each of which is incorporated herein by reference in its entirety for all purposes. Segmented coronary arteries can be viewed and/or corrected by the computer system and/or the user as needed (eg, to correct segmentation if there are any errors, such as omitted or inaccurate coronary arteries or branches extending from them).

A patient-specific anatomical model (eg, a 3D geometric model) can be represented as a surface mesh. A surface mesh may represent the outer boundary of segmented structures such that their shape is represented as a set of connected vertices (eg, a mesh). By using such a representation, shape constraints can be imposed using grid-based shape scores or statistics. A deformable model such as an active mesh model (AMM) (see Dufour, A. et al., Segmenting and tracking fluorescent cells in dynamic 3-D microscopy with coupled active surfaces. IEEE Transactions on Image Processing, 14(9), 1396 -1410, 2005; Dufour, A. et al., J.-C. 3-D active meshes: fast discrete deformable models for cell tracking in 3-D timelapse microscopy, IEEE Transactions on Image Processing, 20(7), 1925 -1937, 2011) may represent a starting point for creating a patient-specific anatomical model. AMM is a three-dimensional extension of the active contour model (ACM) used in image analysis techniques (see Kass, M. et al., Active contour models. Int. J. of Computer Vision 1(4), 321-331, 1988) . In AMM-based methods, segmented structures can be represented as closed surfaces (fronts, grids) that advance at a rate computed as based on

- 5 042942 image-dependent data and based on image-independent geometric properties.

In embodiments, the process of generating a patient-specific anatomical model may include, for example, segmenting visible plaques in the coronary arteries using an AMM-based method, computer and/or user selection of root points (e.g., starting points) for the left and right coronary arteries, segmenting coronary arteries using the method based on AMM and selected root points, as well as confirmation and/or correction of the geometry of segmented plaques and arteries.

After segmentation, the user and/or the computer system may post-process the patient-specific anatomical model to prepare the model for CFD simulations. This may include, for example, determining centerlines for coronary arteries and their branches, determining cross-sectional areas of coronary arteries and their branches, creating models of inflow boundaries (for example, boundaries through which flow is directed into the coronary arteries) and outflow boundaries (for example, through which flow is directed from the coronary arteries and/or branches of the coronary arteries) so that the inflow and outflow boundaries are perpendicular to certain center lines, thereby allowing the application of a boundary condition and smoothing the model (e.g., smoothing out any ridges, dots, etc.). .d.). Post-processing of the patient-specific anatomical model can be reviewed and/or corrected by the computer system and/or the user as needed. At 108, the computer system may determine boundary conditions for simulating computational fluid dynamics (CFD) of blood flow in the anatomical model. At least some of the boundary conditions may be determined using received patient-specific physiological data, such as received continuous blood pressure data. Boundary conditions may include inflow and outflow boundary conditions of the coronary circulation.

The three-component model illustrated in Fig. 5 can be used to determine the boundary conditions of the coronary circulation. A three-component model may contain a circulatory system (BCS) component that describes the systemic and pulmonary circulations, a heart pressure-volume (HPV) component that describes the cardiac pressure-volume loop, and a coronary blood flow (CBF) component that describes the coronary circulation. arteries (see Fig. 5). Each of the BCS, HPV, and CBF components can be selected from various models of each component, which are discussed in more detail below. The three-component model can be taken as an input to the pressure waveform p _sa (t), which can be derived from a patient-specific continuous blood pressure record (eg, patient-specific continuous blood pressure data). An exemplary embodiment of the three-component model is shown in FIG. 18.

The three-component model can be used to directly determine inflow boundary conditions, such as the volumetric flow waveform at the inlet of a patient's coronary arteries (see FIG. 20). The three-component model can be used to indirectly determine outflow boundary conditions, such as the volumetric flow waveform at the outlet of a patient's coronary arteries (see FIG. 20). For example, a patient's coronary inlet volume flow waveform can be used to determine the patient's coronary outlet volume flow waveform using an allometric law of scaling (ALS), such as Murray's law, which describes the relationship between blood flow and vessel radius (see Figure 1). fig. 20) (see Freund J. et al., (2012) Fluid flows and forces in development: functions, features and biophysical principles. Development, 139(7): 1229-1245; Newberry M. et al., VM (2015) Testing foundations of biological scaling theory using automated measurements of vascular networks Public Library of Science Computational Biology, 11(8):e1004455 Sherman T. (1981) On connecting large vessels to small - the meaning of murray's law Journal of General Physiology, 78(4):431-453; Algranati D. et al. (2010) Mechanisms of myocardium-coronary vessel interaction. American Journal of Physiology. Heart and Circulatory Physiology, Vol. 298, No. 3, H861- H873). According to Murray's law, blood flow is proportional to r ³ in each vessel of the Murrey system.

The circulatory system component (BCS) describes the systemic and pulmonary circulations. Circulation can be modeled, for example, using two-, three-, four-, and five-element Windkessel Lumped Function Blocks (2WM, 3WM, 4WM, 5WM) as shown in FIG. 6 (See Garcia D. et al. (2009) Impairment of coronary flow reserve in aortic stenosis. Journal of Applied Physiology, Vol. 106, No. 1, 113-121; Li J. K.-J. (2000) The Arterial Circulation Physical Principles and Clinical Applications, Springer, New York Ostadfar A (2016) Biofluid mechanics Principles and applications Elsevier Pappano A et al (2013) Cardiovascular physiology Elsevier Stergiopulos N et al (1996) Determinants of volume and systolic and diastolic aortic pressure. American Journal of Physiology, Vol. 270, No. 6, Pt. 2, H2050-H2059 Westerhof N et al. (2009) The arterial windkessel. Medical & Biological Engineering & Computing, Vol 47, No. 2, 131-141 Zamir M. (2005) The physics of coronary blood flow Springer-Verlag). The pulmonary and systemic circulations can be modeled in the preferred embodiment using one of the lumped parameter models shown in FIG. 7, while the general circulation can be modeled using the multisectional model shown in FIG. 8.

In an embodiment, a component of the circulatory system model (e.g., systemic circulation and pulmonary circulation model) is built based on the lumped RLC parameters function block resistance (R) - persistence (L) - capacitance (C) shown in FIG. 9. In the lumped parameter function block of FIG. 9 inputs (in) and output (out) of the block are connected in time (t) _ _r dp in

Qin~di' Qout>

_n . , Qout .

Pin ^— ' Qout + L + P° ^u t' where q is the flow rate and p is the pressure of the flowing blood in the selected section.

As shown in FIG. 8, the pulmonary circulation model contains three sections in the form of arteries (C=C _pa , R=R _pa , L=L _pa ), a pulmonary reservoir (C=0, R=R _pr , L=0) and a vein (C =C _pv , R=R _pv , L=0), which leads to six equations (3x2=6). The systemic circulation model contains five sections, namely the aorta (C=C _sa , R=R _sa , L=L _sa ), proximal conducting arteries (C=C _sp , R=R _sp , L=L _sp ), distal muscular arteries (C=C _sd , R=R _sd , L=0), reservoir of the great circle (C=0, R=R _sr , L=0) and veins (C=C _sv , R=R _sv , L=0 ), which leads to ten equations (5x2=10). The resulting system of sixteen equations can be solved numerically. The ventricular or atrial pressure-volume (HPV) component describes the cardiac pressure-volume loop. The cardiac cycle consists of four phases, as shown in Fig. 10 (See Barrett KE et al. (2016) Ganong's review of medical physiology, McGraw-Hill; Mohrman D. et al. (2013) Cardiovascular physiology. McGraw-Hill, Lange, New York; Pappano A. et al. ( 2013) Cardiovascular Physiology Elsevier. Many different models can be used for isovolumetric systolic and diastolic phases, such as, for example, the time-varying elastance (TVE) model, the time-varying compliance (TVC) model, or other models (see Garcia D et al. (2009) Impairment of coronary flow reserve in aortic stenosis Journal of Applied Physiology, Vol 106, No 1, 113-121 Lankhaar JW et al (2009) Modeling the instantaneous pressure-volume relation of the left ventricle: a comparison of six models Annals of biomedical engineering, Vol 37, No. 9, 1710-1726 Stergiopulos N. et al (1996) Determinants of stroke volume and systolic and diastolic aortic pressure American Journal of Physiology, Vol 270, No. 6 , Pt. 2, H2050-H2059). In FIG. 11 illustrates a functional block for building a model of (a) a chamber pressure-volume (HPV) component; and a complete multisectional model (b) of the chamber pressure-volume (HPV) component. In a preferred embodiment, the pressure-volume (HPV) component uses a model based on the idea of varying elastance E(t) as the reciprocal of compliance, which can be written as zs 1 dp ⁼ ~C(t) ⁼ dV'

The pressure in the heart chamber during the isovolumetric phase can be described by the equation p(t) = E(t)-(V(t)-V0), where V(t) is the volume of the heart chamber, V ₀ is the volume cutoff.

The elastance can be calculated based on the convolution of the Archibald Hill function /i(tn) =tn7W' + tn which can be written in the form

W = A (ρ(ΐ _η ) (1 - yy ^max ^min ^{4 7} where

It%T tn - ~ <t _max - t@E(t) - E _max , ^max and T - the duration of the cardiac cycle according to the cardio interval, which can be determined using ECG or calculated based on the pressure dynamics in the aorta. Typical values for empirical parameters of the time-varying elastance model are provided in the table below (see Stergiopulos N. et al. (1996) Determinants of stroke volume and systolic and diastolic aortic pressure. American Journal of Physiology, Vol. 270, No. 6, Pt 2, H2050-H2059; Faragallah G. et al. (2012) A new control system for left ventricular assist devices based on patient-specific physiological demand. Inverse Problems in Science and Engineering, Vol. 20, No. 5, 721- 734).

Emin Emax ai a ₂ I1 m 0.06 2.31 0.303 0.508 1.32 21.9 0.06 2.00 0.700 1.170 1.90 21.9

The time-varying elastance model can only be used during the isovolumetric phases of the cardiac cycle. For the other two phases of the cardiac cycle (Fig. 10), the blood volume is partially

- 7 042942 accumulates in the atrium, while the rest, followed by a transvalvular pressure gradient, flows out. Therefore, the balance of atrial flow can be described as _ _r dp _sv , _ _g ^Vpv .

Tsu - ^RA _dt g Qt, Qp _V - + Q _m , and similarly ventricular flow can be described as dViv - - Yara "Qt> - - Qsa " Qm-

At the same time, the transvalvular flow can be described as

(.Ppp ^- Plv) "/ \ (.PlV ^- Psa) "xx

Qm ^— 7 H\Pp _V — PLvJ'Qsa ^— 7 H(.Plv ^— Psa)' ^K LA

(.Psv - Prv)x (PRV - Ppa)x

Qt - _D H(p _sv Prv)' Qpa ^- _D ^\Prv Ppa)' ^K RA ^K RV where H is the Heaviside step function.

In embodiments, a patient specific calibration (PSC) procedure may be used to optimally estimate the parameters of the HPV and BCS models. The procedure may include: (i) determining initial approximations of model parameters based on systolic and diastolic pressure levels, gender, age, and heart rate (HR) of the patient (see Barrett KE et al. (2016) Ganong's review of medical physiology, McGraw- Hill Li JK-J (2000) The Arterial Circulation Physical Principles and Clinical Applications, Springer, New York Pappano A et al (2013) Cardiovascular physiology Elsevier Zamir M (2005) The physics of coronary blood flow Springer-Verlag Maceira AM et al (2006) Reference right ventricular systolic and diastolic function normalized to age, gender and body surface area from steady-state free precession cardiovascular magnetic resonance European Heart Journal, Vol 27, Issue 23 , Pages 2879-2888 Maceira AM et al (2006) Normalized left ventricular systolic and diastolic function by steady state free precession cardiovascular magnetic resonance Journal of Cardiovascular Magnetic Resonance, Vol 8, Issue 3, 417-426), (ii ) making corrections based on additional information, including smoking habits, fitness habits, and drug use (see Tsanas A. et al. (2009) The Windkessel model revisited: a qualitative analysis of the circulatory system. Medical Engineering & Physics, Vol. 31, Issue 5, 581-588), (iii) model development (HPV + BCS), and (iv) and parameter calibration by fitting them to the calculated pressure and the patient's current pressure record. Thus, a time-varying elastance model (such as that used in the HPV model) in conjunction with a circulatory model (BCS) can be used to recreate the current left and right ventricular volumes (V) and internal pressure dynamics (pv) using the recorded pressure in patient's aorta (p _sa ), as shown in FIG. 12.

The coronary flow component (CBF) describes the circulation of the coronary artery and is shown generally in FIG. 13. The CBF component is based on several findings based on physiology data (see Epstein S. et al. (2015) Reducing the number of parameters in 1D arterial blood flow modeling: less is more for patient-specific simulations. American Journal of Physiology, Heart and Circulatory Physiology, Vol. 309, No. 1, H222-H234; Kheyfets VO et al. (2016) A zero-dimensional model and protocol for simulating patient-specific pulmonary hemodynamics from limited clinical data. Journal of Biomechanical Engineering, Vol 138, Issue 12,1-8 Maruyama Y et al (1994) Recent advances in coronary circulation Springer-Verlag, Berlin and Heidelberg Mohrman D et al (2013) Cardiovascular physiology McGraw- Hill, Lange, New York Ostadfar A (2016) Biofluid mechanics Principles and applications Elsevier Pappano A et al (2013) Cardiovascular physiology Elsevier Zamir M (2005) The physics of coronary blood flow Springer Verlag Algranati D. et al (2010) Mechanisms of myocardium-coronary vessel interaction. American Journal of Physiology. Heart and Circulatory Physiology, Vol. 298, no. 3, H861-H873; Mynard JP et al. (2014) Scalability and in vivo validation of a multiscale numerical model of the left coronary circulation. American Journal of Physiology. Heart and Circulatory Physiology, Vol. 306, no. 4, H517-H528; Westerhof N. et al. (2006) Crosstalk between cardiac muscle and coronary vasculature. Physiological Reviews, Vol. 86, no. 4, 1263-1308), which include the following: (i) the main factor stimulating flow in the coronary arteries is the current pressure in the aorta p _sa (t); (ii) the interaction of the myocardium - the coronary vessel causes a pressure opposite to p _sa (t), with the effect of throttling or even reversing the flow; and (iii) the inertial effect of the blood accumulated in the arteries is negligible. Based on the above, the CBF component shown generally in FIG. 13 is suitable for defining boundary conditions for CFD flow simulations in coronary arteries. The CBF component indicates that coronary artery inlet flow q ₀ (t) is the result of aortic stimulus pressure p _sa (t) throttled by cardiac contraction and reverse accumulation, the latter being determined primarily by ventricular pressure.

The CBF component describes a normal relationship where pressure acts as the independent variable. Because pressure serves as the independent variable in the CBF component, the CBF component and its use in patient-specific numerical simulations are superior to other methods for determining boundary conditions. Some advantages of using pressure as an independent variable include the following: (i) pressure is relatively easy to

- 8 042942 to measure compared to velocity or mass flow, which are much more difficult to measure; and (ii) pressure measurements, even non-invasive and at a location far from the heart, will not be distorted by an error greater than acceptable.

Coronary blood flow can be modeled in many different ways (see Beyar R. et al. (1987) Time-dependent coronary blood flow distribution in the left ventricular wall. American Journal of Physiology, Heart and Circulatory Physiology, Vol. 252, No. 2, Pt. 2, H417-H433 Boileau E et al (2015) OneDimensional Modeling of the Coronary Circulation Application to Noninvasive Quantification of Fractional Flow Reserve (FFR) Computational and Experimental Biomedical Sciences: Methods and Applications, Vol 21, 137 -155 Bruinsma T et al (1988) Model of the coronary circulation based on pressure dependence of coronary resistance and compliance Basic Res Cardiol, 83:510-524 Burattini R et al (1985) Identification of canine intramyocardial compliance on the basis of the waterfall model Annals of Biomedical Engineering, Vol 13, No 5, 385-404 Chadwick RS et al (1990) Phasic regional myocardial inflow and outflow: comparison of theory and experiments American Journal of Physiology, Heart and Circulatory Physiology, Vol. 258, no. 6, H1687H1698; Garcia D et al. (2009) Impairment of coronary flow reserve in aortic stenosis. Journal of Applied Physiology, Vol. 106, no. 1, 113-121; Holenstein R et al. (1990) Parametric analysis of flow in the intramyocardial circulation. Annals of Biomedical Engineering, Vol. 18, no. 4, 347-365; Judd RM et al. (1991) Coronary input impedance is constant during systole and diastole. American Journal of Physiology - Heart and Circulatory Physiology, Vol. 260, no. 6, H1841-H1851; Kresh JY et al. (1990) Model-based analysis of transmural vessel impedance and myocardial circulation dynamics. American Journal of Physiology, Heart and Circulatory Physiology, Vol. 258, no. 1, H262-H276; LeeJ et al. (1984) The role of vascular capacitance in the coronary arteries. Circ Res 55: 751-762; LeeJ et al. (2012) The multi-scale modeling of coronary blood flow. Annals of Biomedical Engineering, Vol. 40, Issue 11, 2399-2413; Li J KJ (2000) The Arterial Circulation. Physical Principles and Clinical Applications, Springer, New York; Mynard JP et al. (2014) Scalability and in vivo validation of a multiscale numerical model of the left coronary circulation. American Journal of Physiology, Heart and Circulatory Physiology, Vol. 306, no. 4, H517-H528; Marsden AL (2014) Thrombotic risk stratification using computational modeling in patients with coronary artery aneurysms following Kawasaki disease. Biomechanics and Modeling in Mechanobiology, Vol. 13, no. 6, 1261-1276; SpaanJAE et al. (1981) Diastolic-systolic coronary flow differences are caused by intramyocardial pump action in the anesthetized dog. Circ Res, Vol. 49, Issue 3, 584-593, some of which are shown in FIG. 14. The coronary flow models shown in FIG. 14 can be summarized as follows: (i) all models have a single source element, usually assumed to be equal to aortic pressure (p _sa ) (ibid.); (ii) the source energy is partially dissipated by the resistive elements in the amount of one (c, e, f) (see Bruinsma T et al. (1988) Model of the coronary circulation based on pressure dependence of coronary resistance and compliance. Basic Res Cardiol, 83:510-524 Burattini R et al (1985) Identification of canine intramyocardial compliance on the basis of the waterfall model Annals of Biomedical Engineering, Vol 13, No. 5, 385-404 Garcia D et al ( 2009) Impairment of coronary flow reserve in aortic stenosis Journal of Applied Physiology, Vol 106, No 1, 113-121 Holenstein R et al (1990) Parametric analysis of flow in the intramyocardial circulation Annals of Biomedical Engineering, Vol.18, No. 4, 347-365;Kresh JY et al.(1990) Model-based analysis of transmural vessel impedance and myocardial circulation dynamics.American Journal of Physiology, Heart and Circulatory Physiology, Vol.258, No. 1 , H262H276; Lee J et al. (1984) The role of vascular capacitance in the coronary arteries. Circ Res 55:751-762; LeeJ et al. (2012) The multi-scale modeling of coronary blood flow. Annals of Biomedical Engineering, Vol. 40, Issue 11, 2399-2413; Li J KJ (2000) The Arterial Circulation. Physical Principles and Clinical Applications, Springer, New York; Mohrman D et al. (2013) Cardiovascular physiology. McGraw-Hill, Lange, New York; Sengupta D et al.; SpaanJAE et al. (1981) Diastolic-systolic coronary flow differences are caused by intramyocardial pump action in the anesthetized dog. Circ Res, Vol. 49, Issue 3, 584-593), two (b) (see Chadwick RS et al. (1990) Phasic regional myocardial inflow and outflow: comparison of theory and experiments. American Journal of Physiology, Heart and Circulatory Physiology, Vol. 258, No. 6, H1687-H1698) or zero (a, d) (see Beyar R et al. (1987) Time-dependent coronary blood flow distribution in left ventricular wall. American Journal of Physiology, Heart and Circulatory Physiology, Vol. 252, No. 2, Pt. 2, H417-H433; Boileau E et al. (2015) OneDimensional Modeling of the Coronary Circulation. Application to Noninvasive Quantification of Fractional Flow Reserve (FFR). Computational and Experimental Biomedical Sciences: Methods and Applications, Vol 21, 137-155 Garcia D et al (2009) Impairment of coronary flow reserve in aortic stenosis Journal of Applied Physiology, Vol 106, No 1, 113-121 Judd RM et al. (1991) Coronary input impedance is constant during systole and diastole American Journal of Physiology - Heart and Circulatory Physiology, Vol. 260, no. 6, H1841H1851; Li J KJ (2000) The Arterial Circulation. Physical Principles and Clinical Applications, Springer, New York; Mynard JP et al. (2014) Scalability and in vivo validation of a multiscale numerical model of the left coronary circulation. American Journal of Physiology, Heart and Circulatory Physiology, Vol. 306, no. 4, H517H528) pieces; (iii) the inflow is usually split between single resistive and capacitive branches, with some models having two capacitance elements (b, f) (see Burattini R et al. (1985) Identification of canine intramyocardial compliance on the basis of the waterfall model. Annals of Biomedical Engineering, Vol 13, No. 5, 385-404 Chadwick RS et al (1990) Phasic regional myocardial inflow and outflow: comparison of theory and experiments American Journal of Physiology, Heart and Circulatory Physiology, Vol. 258, No. 6,

- 9 042942

H1687-H1698; Li J K-J (2000) The Arterial Circulation. Physical Principles and Clinical Applications, Springer, New York; Marsden AL (2014) Thrombotic risk stratification using computational modeling in patients with coronary artery aneurysms following Kawasaki disease. Biomechanics and Modeling in Mechanobiology, Vol. 13, no. 6, 1261-1276; Sengupta D et al); (iv) the capacitive arm may contain its own resistive element (d) (see Garcia D et al. (2009) Impairment of coronary flow reserve in aortic stenosis. Journal of Applied Physiology, Vol. 106, No. l, 113-121 ; Judd RM et al. (1991) Coronary input impedance is constant during systole and diastole. American Journal of Physiology - Heart and Circulatory Physiology, Vol. 260, No. 6, H1841-H1851; Li J K-J (2000) The Arterial Circulation Physical Principles and Clinical Applications, Springer, New York) or source as a function of intraventricular pressure (c, f) (see Burattini R et al. (1985) Identification of canine intramyocardial compliance on the basis of the waterfall model. Annals of Biomedical Engineering, Vol 13, No. 5, 385-404 Garcia D et al (2009) Impairment of coronary flow reserve in aortic stenosis Journal of Applied Physiology, Vol 106, No. 1, 113-121 Kresh JY et al (1990) Model-based analysis of transmural vessel impedance and myocardial circulation dynamics American Journal of Physiology, Heart and Circulatory Physiology, Vol. 258, no. l, H262-H276; LeeJ et al. (2012) The multi-scale modeling of coronary blood flow. Annals of Biomedical Engineering, Vol. 40, Issue 11, 2399-2413; Li J K-J (2000) The Arterial Circulation. Physical Principles and Clinical Applications, Springer, New York; Sengupta D et al.; SpaanJAE et al. (1981) Diastolic-systolic coronary flow differences are caused by intramyocardial pump action in the anesthetized dog. Circ Res, Vol. 49, Issue 3, 584-593), but not both of them; (v) the resistive branch usually contains its own source related to intraventricular pressure (a, b, c, d, e) (see Beyar R et al. (1987) Time-dependent coronary blood flow distribution in the left ventricular wall. American Journal of Physiology, Heart and Circulatory Physiology, Vol 252, No. 2, Pt. 2, H417-H433 Boileau E et al (2015) One-Dimensional Modeling of the Coronary Circulation Application to Noninvasive Quantification of Fractional Flow Reserve (FFR) Computational and Experimental Biomedical Sciences: Methods and Applications, Vol 21, 137-155 Bruinsma T et al (1988) Model of the coronary circulation based on pressure dependence of coronary resistance and compliance Basic Res Cardiol, 83 :510-524 Chadwick RS et al (1990) Phasic regional myocardial inflow and outflow: comparison of theory and experiments American Journal of Physiology, Heart and Circulatory Physiology Vol 258 No 6 H1687-H1698 Garcia D et al (2009) Impairment of coronary flow reserve in aortic stenosis. Journal of Applied Physiology, Vol. 106, no. l, 113-121; Holenstein R et al. (1990) Parametric analysis of flow in the intramyocardial circulation. Annals of Biomedical Engineering, Vol. 18, no. 4, 347-365; Judd RM et al. (1991) Coronary input impedance is constant during systole and diastole. American Journal of Physiology Heart and Circulatory Physiology, Vol. 260, no. 6, H1841-H1851; Kresh JY et al. (1990) Model-based analysis of transmural vessel impedance and myocardial circulation dynamics. American Journal of Physiology, Heart and Circulatory Physiology, Vol. 258, no. 1, H262-H276; LeeJ et al. (1984) The role of vascular capacitance in the coronary arteries. Circ Res 55:751-762; LeeJ et al. (2012) The multi-scale modeling of coronary blood flow. Annals of Biomedical Engineering, Vol. 40, Issue 11, 2399-2413; Li J K-J (2000) The Arterial Circulation. Physical Principles and Clinical Applications, Springer, New York; Mynard JP et al. (2014) Scalability and in vivo validation of a multiscale numerical model of the left coronary circulation. American Journal of Physiology, Heart and Circulatory Physiology, Vol. 306, no. 4, H517-H528; SpaanJAE et al. (1981) Diastolic-systolic coronary flow differences are caused by intramyocardial pump action in the anesthetized dog. Circ Res, Vol. 49, Issue 3, 584-593). In general, they can be considered as multi-sectional models built on the functional blocks shown in Fig. 15.

In a preferred embodiment, coronary flow is modeled using the lumped functional block shown in FIG. 16. Using the coronary flow model shown in FIG. 16 may require solving the following mass flow continuity equation:

_D , d(Psa-Pc) , (Psa - Ry - PzJ „Z h

I ₀ C - + Qo \u003d C +------R----- And (Psa - PR-Pzf).

where H is the Heaviside step function. Throttling pressure p _R , as well as p _C describes the interaction of the myocardium - coronary vessel (MVI), while p _C =kc(CEP+SIP), and p _R =k _R (CEP+SIP. [3 4 9 14 22 25 32 ] ^L , , , , , , ^J. There are three main hypotheses for the mechanism of passive interaction, and descriptions of extravascular pressure may include the following (see Algranati D et al. (2010) Mechanisms of myocardium-coronary vessel interaction. American Journal of Physiology. Heart and Circulatory Physiology, Vol. 298, No. 3, H861-H873; Mynard JP et al. (2014) Scalability and in vivo validation of a multiscale numerical model of the left coronary circulation. American Journal of Physiology. Heart and Circulatory Physiology, Vol. 306, No. 4, H517-H528; Westerhof N et al. (2006) Cross-talk between cardiac muscle and coronary vasculature Physiological Reviews, Vol. 86, No. 4, 1263-1308): (i) interstitial cavity-induced extracellular pressure (CEP=μ ₁ ·p _V ), and (ii) contraction-induced intracellular pressure (SIP=μ ₂ ·E _V ). Current left (or right, respectively) ventricular pressure p _V and elastance E _V can be taken from the HPV component, and zero flow pressure p _zf can be assumed to be 20 mmHg. Art. or less.

Coronary arteries are spatially distributed in the wall of the heart and are not uniformly affected by extracellular pressure, and the blood in them can be additionally slowed down by physical conditions.

- 10 042942 medical or pharmacological stress, especially hyperemia, by administering adenosine receptor agonists (P1 purinergic receptors), such as Adenocardium or Adenoscan, or a more selective A2A receptor agonist (Regadenosone, Binodenosone). In embodiments, the effect of heart wall heterogeneity (further altered by stress) can be described using a multilayer and multisectional tissue pressure ratio model (see Garcia D et al. (2009) Impairment of coronary flow reserve in aortic stenosis. Journal of Applied Physiology, Vol 106, No. 1, 113-121 Holenstein R et al (1990) Parametric analysis of flow in the intramyocardial circulation Annals of Biomedical Enginfeering, Vol 18, No 4, 347-365 Westerhof N et al (2006) Cross-talk between cardiac muscle and coronary vasculature Physiological Reviews Vol 86 No 4 1263-1308), an example of which is shown in FIG. 17. Referring to FIG. 17 ^N d ^NN d

Σ ^R ° ^C n^ + Σ ^4η= Σ ^C Tt( ^{Psa K} p№c(CE ^p + SIP))

P—l P—lP—1 , V Psa - K _p (n)k _R (CEP + SIP) -p _{zf (} .

+ / , d H\Psa K _p (n)k _R (CEP + SIP) Pzf)>

n=i where the pressure coefficient of the heart tissue has the form

At rest, extravascular pressure decreases non-linearly with downward concavity from endocardium to epicardium with exponent k~2.0 or greater. In contrast, with cassation of any active coronary vascular tone (hypothetical maximum coronary dilatation), a linear relationship (k~ 1.0) can be assumed. The vasodilating effect associated with the elimination of active coronary vascular tone may not be limited to cardiac tissue and function. More generally, vasodilation is just one form of cardiac tropism (chronotropism, inotropism, lusitropism, and many others). In addition, endogenous and/or exogenous mediators can cause a decrease in vascular resistance and contribute to an increase in coronary blood flow, as well as blood flow in the systemic and pulmonary circulation. In a preferred embodiment, the net effects of cardiac tropism (E/E _max ) of a purinergic receptor (R) binding endo or exogenous agonists (A) can be modeled using the combined kinetic ratio

E _ [AY] ^P

E^ _x ~ K? + [AR^ where the concentration of occupied receptors has the form

Combining these equations and introducing the transducer factor t=[R ₀ ]/K _e , we get the explicit relation

E _ t ^p [L] ^p ie a combined model of purinergic stimulus receptor agonism (using K _A affinity values and K _E potency values). At 110, the computer system may simulate blood flow in a patient-specific anatomical model (eg, coronary arteries) using CFD and patient-specific boundary conditions. In particular, the CFD simulation may use the coronary artery volumetric flow waveform at the inlets and/or outlets of the coronary arteries, which may be determined at least in part by patient-specific continuous blood pressure data, as boundary conditions for the CFD simulation.

Before running a CFD simulation, a 3D mesh can be created for the patient-specific anatomical model along with separate inflow and outflow junction models to enable CFD simulation (eg, create a 3D computational grid for numerical simulations). The 3D mesh may comprise a plurality of nodes (eg, grid points or grid points) along the surfaces of the patient-specific anatomy model and throughout the interior of the patient-specific anatomy model (see FIG. 19). The generated mesh can be reviewed and/or corrected by the computer system and/or the user as needed (eg, to correct mesh distortion, insufficient spatial resolution in the mesh, etc.).

In CFD simulation, blood can be modeled as a Newtonian fluid or a non-Newtonian fluid, and flow fields can be obtained by numerically solving discretized mass and momentum (Navier-Stokes) balance equations assuming a rigid wall. Numerical methods for solving 3D blood flow equations may include finite difference method, finite volume method, spectral method, lattice Boltzmann method, particle-based method,

- 11 042942 level set method, isogeometric method, or finite element method, or other computational fluid dynamics (CFD) numerical methods. The discretized Navier-Stokes equations can be used to gradually simulate blood flow velocity and pressure in the coronary arteries over time. That is, the CFD simulation can determine the blood flow and pressure in each of the nodes of the mesh anatomical model. The output of CFD simulations may represent a patient-specific distribution of blood flow and pressure in the patient's coronary arteries based on the patient-specific anatomy and patient-specific boundary conditions.

At 112, the computer system may determine one or more hemodynamic parameters associated with the patient's coronary arteries. One or more hemodynamic parameters may be determined based at least in part on the results of the CFD simulation. Examples of hemodynamic parameters may include coronary artery characteristics such as blood pressure, flow rate, wall shear stress (WSS), pulsatile shear index (OSI), relative residence time (RRT), fractional flow reserve (FFR), coronary flow reserve ( CFR), instantaneous waveless ratio (iFR), etc. Hemodynamic parameters can be interpolated from a patient-specific anatomical model to provide the user with information about hemodynamic parameters from the anatomical model.

At 114, the computer system may output one or more specific hemodynamic parameters. The computer system may, for example, display one or more hemodynamic parameters or visualizations (eg, two-dimensional or three-dimensional images) of one or more hemodynamic parameters. The computer system may, for example, present hemodynamic parameters as a 3D interactive visualization. The computer system may send one or more specific hemodynamic parameters to a remote computer for display on the remote computer.

At 116, one or more determined hemodynamic parameters are used to determine and/or as part of a patient-specific treatment plan. In an embodiment, one or more defined hemodynamic parameters are used to plan a coronary revascularization procedure for cardiovascular disease. For example, one or more determined hemodynamic parameters can be used to determine an optimal patient-specific location for placement of a stent in a patient that improves hemodynamic conditions for blood flow in the patient's coronary arteries, and then the stent is positioned at the determined optimal location. As another example, one or more determined hemodynamic parameters can be used to determine the optimal coronary artery bypass procedure for a patient that provides the best hemodynamic conditions for flow in the patient's coronary artery compared to alternative coronary artery bypass procedures, and then the clinician performs the optimal coronary artery bypass procedure. bypass in a patient. In an embodiment, one or more defined hemodynamic parameters are used to provide a virtual cardiopulmonary exercise test. For example, one or more defined hemodynamic parameters may include a fractional flow reserve (FFR) estimate, which may be used to provide a non-invasive estimate of fractional flow reserve and/or oxygen saturation under virtual cardiopulmonary exercise testing conditions. Although the above embodiments have been described with reference to simulating coronary artery flow transient states, it is understood that the present invention also encompasses simulating a steady state coronary artery flow.

The blood flow through the coronary arteries is pulsatile. Its pressure and speed change in time during one heartbeat, and this process is repeated. The easiest way to simulate such a flow is to use a transient solver, but this can be very time consuming. Using a steady state simulation (eg stationary) can be advantageous because it takes relatively less time to solve, but it is not applicable to all non-stationary phenomena. To take advantage of stationary simulation, the coronary arteries can be viewed as a piping system. In such a system, the pressure drop Ap depends on the fluid velocity ν. For normal flow, the pressure drop is a quadratic function of the velocity (Δр=aν ² +bν+с). To determine the coefficients in this equation, you need to find three pairs of values (v,Ap). To do this, you can run three steady state simulations for different boundary conditions for pressure and velocity values (calculated from the flow rate) and you can find the pressure drop values corresponding to these velocities. Because these simulations are independent, they can be run in parallel. This allows you to significantly reduce the time required for the solution. For example, the results of a transient simulation that takes tens of hours to run can be obtained from a stationary simulation in less than an hour. An additional term has been added to the pressure drop equation to account for the effect of inertia (see Bird RB et al. (1960) Transport Phenomena. John Wiley & Sons, New York; Young D et al. (1973) Flow characteristics in models of arterial stenoses II Unsteady flow, Journal of Biomechanics, Vol. No. 1, 99-107): _dv

Δρ = av ^z + bv + c + kl ^K dt where a, b, c are coefficients calculated from stationary simulations, k=1,2 is the inertia coefficient, l is the distance from the entrance.

In FIG. 21-24 show low-detailed or high-detailed flowcharts of a method for patient-specific modeling of hemodynamic parameters in coronary arteries using steady-state or transient-state simulation. As shown in FIG. 21-24, there are several differences between the steady state simulation method and the transient simulation method. However, many of the implementation details for a steady state simulation based method can be applied to a transient simulation based method and vice versa.

Referring to FIG. 21-22, they show low-detail or high-detail flow diagrams of a method 200 for patient-specific modeling of hemodynamic parameters in coronary arteries using steady state simulation.

Referring specifically to FIG. 21, in step 202, patient-specific anatomical data is acquired and pre-processed. At step 204, a three-dimensional model is created based on the received anatomical data. At step 206, the 3D model is prepared for numerical analysis. At step 208, the computational analysis is performed using the 3D model. At 210, patient-specific peripheral arterial pressure recording data is obtained and pre-processed. At 212, boundary conditions are created based on the pressure record data. At step 214, the results of the computational analysis and boundary conditions are collected and output. At 216, a patient-specific treatment plan is prepared based on the results. Referring specifically to FIG. 22, at step 302, the acquired patient-specific anatomical data (eg, CT data) is initially viewed. In step 304, the acquired anatomical data is subjected to image processing. At step 306, which marks the beginning of the creation of a three-dimensional model based on the received anatomical data, the plaque is segmented. At 308, root points of the coronary arteries are selected. At 310, the coronary arteries are segmented. At step 312, the quality of the segmentation is checked. At step 314, the central lines of the arteries are automatically found. At 316, inflow and outflow boundary models are created. At 318, a monolithic model is output and smoothed. At step 320, the derived monolithic model is validated. At step 322, which marks the start of preparing the monolithic model for numerical analysis, the final mesh of the model is generated. At step 324, the mesh is confirmed. At step 326, which marks the beginning of the computational analysis, the set of CFD cases is prepared for numerical analysis. At step 328, a set of CFD cases are solved by hydrodynamic simulations. At step 330, the results of the simulation are confirmed. At 332, the acquired patient-specific anatomical data (eg, recorded pressure data) is initially reviewed. At step 334, at which the creation of boundary conditions based on the recorded pressure data begins, the pressure data is entered into the model of the circulatory system. In step 336, the results from the circulatory system model are entered into the heart chamber model. At step 338, the results from the heart chamber model are fed into the coronary flow model, the inputs of which are used to determine the boundary conditions. At step 340, the results of determining the boundary conditions are confirmed. At step 342, the results of the determination of the boundary conditions and the analysis of computational fluid dynamics are collected. At step 344, the collected results are output.

Referring to FIG. 23-24, they show low-detail or high-detail flow diagrams of a method 400 for patient-specific modeling of hemodynamic parameters in coronary arteries using transient simulation.

Referring specifically to FIG. 23, at step 402, patient-specific anatomical data is acquired and pre-processed. At step 404, a three-dimensional model is created based on the received anatomical data. At 406, patient-specific peripheral arterial pressure recording data is obtained and pre-processed. At 408, boundary conditions are created based on the pressure record data. At 410, the 3D model is prepared for numerical analysis. At 412, a computational analysis is performed using the 3D model and boundary conditions. At 414, the results of the computational analysis are output. At 416, a patient-specific treatment plan is prepared based on the results. Referring specifically to FIG. 24, at step 502, the acquired patient-specific anatomical data (eg, CT data) is initially viewed. At 504, the acquired anatomical data is subjected to image processing. At step 506, which marks the beginning of the creation of a three-dimensional model based on the received anatomical data, the plaque is segmented. At 508, root points of the coronary arteries are selected. At 510, the coronary arteries are segmented. At step 512, the quality of the segmentation is checked. At step 514, the central lines of the arteries are automatically found. At 516, inflow and outflow boundary models are created. At 518, a monolithic model is output and smoothed. At step 520, the derived monolithic model is confirmed. At step 522, the received specifics are initially viewed.

- 13 042942 patient-specific anatomical data (for example, recorded pressure data). At step 524, at which the creation of boundary conditions based on the recorded pressure data begins, the pressure data is entered into the model of the circulatory system. In step 526, the results from the circulatory system model are entered into the heart chamber model. At step 528, the results from the heart chamber model are input into the coronary flow model, the inputs of which are used to determine the boundary conditions. At step 530, the results of determining the boundary conditions are confirmed. At step 532, which marks the start of preparing the monolithic model for numerical analysis, the final mesh of the model is generated. At step 534, the mesh is confirmed. At step 536, which marks the beginning of the computational analysis, the CFD case is prepared for numerical analysis. At step 538, the CFD case is solved by hydrodynamic simulation. At step 540, the results of the simulation are confirmed. At step 542, the results are output. Although the embodiments have been described in language specific to structural features and/or methodological acts, it should be understood that the present invention is not necessarily limited to the specific features or acts described. Rather, specific features and actions are disclosed as illustrative forms of implementation of the embodiments. Conventional language such as, but not limited to, may, could, could, or has the ability, unless specifically noted otherwise or otherwise understood in the context used, is generally intended to convey what certain embodiments may contain, while other embodiments implementation do not contain certain features, elements and/or steps. Thus, such conditional language is generally not intended to indicate that the features, elements, and/or steps are in any way required by one or more embodiments, or that one or more embodiments necessarily contain logic for making a decision using input or prompts the user with or without them about whether these features, elements and/or steps are contained or whether they should be performed in any particular embodiment.

Examples

Example 1

Results from a method for patient-specific modeling of hemodynamic parameters in coronary arteries in accordance with one or more exemplary embodiments of the present invention were compared with real life results. In particular, invasively collected FFR data from 30 patients at 3 hospitals were compared with numerically calculated FFR values using one or more exemplary embodiments of the present invention. The statistical results for a total of 35 stenoses are summarized in the table below and in FIG. 25.

Sensitivity 82.4% Specificity 88.9% Positive Predictive Value 87.5% Negative Predictive Value Accuracy 84.2% 85.7%> Area under the ROC curve 0.863

CLAIM

Claims (22)

1. A method for determining the hemodynamic parameters of blood flow in the coronary vessels of a patient (100, 200, 400), including receiving patient-specific data (102, 202, 302, 402, 502) about the anatomical structure and patient-specific physiological data (104, 210, 322, 406, 522), wherein the anatomical data includes structural information about the patient's coronary arteries and the patient-specific physiological data includes a continuously recorded blood pressure waveform; generating an anatomical model of at least a portion of the coronary arteries (106, 204, 306, 308, 310, 312, 314, 316, 318, 320, 404, 506, 508, 510, 512, 514, 516, 518, 520) of the patient on based, at least in part, on data about the anatomical structure; determination of boundary conditions for a computational fluid dynamics (CFD) simulation of blood flow in an anatomical model (108, 212, 334, 336, 338, 340, 408, 524, 526, 528, 530) based at least in part on a continuously recorded blood waveform pressure; simulation of blood flow in an anatomical model using CFD and boundary conditions (110, 208, 214, 326, 328, 330, 342, 412, 536, 538, 540); and determining one or more hemodynamic parameters associated with the patient's coronary arteries (112, 214, 344, 414, 542) based at least in part on the simulation, characterized in that the continuously recorded blood pressure waveform is based on a non-invasive measurement, while determining the boundary conditions (108, 212, 334, 336, 338, 340, 408, 524, 526, 528, 530) - 14 042942 includes determining data on the volume flow rate of blood flow based at least in part on the model of the circulatory system and continuously recorded blood pressure waveform; determining ventricular pressure data based at least in part on the pressure-volume model of the chambers of the heart and volume flow data; determining coronary artery inlet flow data based at least in part on the coronary flow model, continuously recorded blood pressure waveform, and ventricular pressure data; and determining the coronary outlet flow data based at least in part on the allometric scaling law and the coronary inlet flow data. 2. The method according to claim 1, characterized in that the data on the anatomical structure is based on a non-invasive measurement. 3. The method according to claim 1, characterized in that the data on the anatomical structure is based on a computed tomography angiogram. 4. The method according to claim 1, characterized in that the generation of the anatomical model (106) does not include segmenting the aorta. 5. The method according to claim 1, characterized in that the anatomical model is a model of only the patient's coronary arteries. 6. The method of claim 1, wherein the boundary conditions include inflow boundary conditions for the patient's coronary arteries and outflow boundary conditions for the patient's coronary arteries. 7. The method of claim 1, wherein the circulatory system model comprises at least one lumped parameter functional block selected from the lumped parameter functional blocks: (a) CR, (b) CRL, and (c) RCRL shown in FIG. . 7(a, b, c). 8. The method according to claim 1, characterized in that the pressure-volume model of the chambers of the heart is a time-varying elastance model. 9. The method of claim 1, wherein the coronary flow model comprises at least one lumped parameter functional block selected from lumped parameter functional blocks: (a) CRp, (b) CpR, (c) RCRp, (d) CpRp and (e) RCpRp shown in FIG. 15(a, b, c, d, e). 10. The method of claim 1, wherein the coronary flow model comprises a plurality of functional blocks of lumped parameters (e) RCpRp shown in FIG. 15(f). 11. The method according to claim 1, characterized in that the state of the coronary inlet flow is determined based at least in part on the coupling model of blocks of lumped parameters of the circulatory system and coronary blood flow shown in FIG. 18. 12. The method according to claim 1, characterized in that the flow effects related to the inhomogeneity of the wall of the heart are described using a multi-layer and multi-section model with a variable tissue pressure coefficient. 13. The method of claim 12, wherein the one or more hemodynamic parameters comprise one or more hemodynamic parameters related to cardiac chronotropism, inotropism, or lusitropism derived from a coupled purinergic receptor-irritant agonism model. 14. The method of claim 1, wherein the blood flow simulations are performed using a transient state solver or a steady state solver. 15. The method of claim 1, wherein the pressure drop and flow characteristics of the vessel are determined using a steady state approach. 16. The method of claim 1, wherein one or more hemodynamic parameters are selected from blood pressure, blood flow, flow rate, wall shear stress (WSS), pulsatile shear index (OSI), relative residence time (RRT), fractional flow reserve (FFR), instantaneous waveless ratio (iFR), and coronary flow reserve (CFR). 17. The method of claim 1, further comprising deriving one or more specific hemodynamic parameters. 18. The method of claim 17, wherein the output (214, 344, 414, 542) includes sending one or more determined hemodynamic parameters to a display device. 19. The method of claim 17, wherein the output (214, 344, 414, 542) includes sending one or more determined hemodynamic parameters to a remote computer. 20. The method of claim 17, further comprising determining a patient-specific treatment plan (116, 216, 416) based at least in part on one or more determined hemodynamic parameters. 21. The method of claim 20, wherein the patient-specific treatment plan provides for the optimal patient-specific location for placement of the stent in the patient. 22. The method of claim 17 wherein one or more defined hemodynamic parameters are used as part of a virtual cardiopulmonary exercise test.