Systems and methods for estimating blood flow using response surface and reduced-order modeling

Abstract

Systems and methods for blood flow simulation are disclosed. For example, a method may include: performing multiple blood flow simulations using a first model of vascular blood flow, each of the multiple blood flow simulations simulating blood flow in a patient's vascular system or based on the geometry of the patient's vascular system; generating a response surface based on results of the multiple blood flow simulations, the response surface mapping one or more first parameters of the first model to one or more second parameters of a reduced-order model of the vascular blood; determining values of one or more parameters of the reduced-order model mapped by the response surface from parameter values representing a modified state of the vascular system; and performing a simulation using the reduced-order model parameterized by the determined values to determine blood flow characteristics of the modified state of the vascular system.

Description

[0001] Related applications

[0002] This application claims priority to U.S. Provisional Application No. 62 / 849,489, filed May 17, 2019, the disclosure of which is hereby incorporated by reference in its entirety. Technical Field

[0003] Various embodiments of the present disclosure relate generally to predicting the behavior of complex systems using response surface methods and reduced-order modeling, and particularly to efficient real-time estimation of blood flow using response surface methodology techniques and reduced-order modeling. Background Art

[0004] Modeling and simulation can be performed on real-world physical phenomena to predict outcomes without invasive measurements. For example, many real-world physical phenomena, such as blood flow in arteries, fluid flow in porous media, and large deformation processes, can be modeled using partial differential equations. Modeling and simulation can also be used to design and optimize systems to produce desired outcomes.

[0005] In clinical applications, blood flow characteristics may be relevant to assessing the health or disease of a patient. For example, hemodynamic indices may be used to assess the functional significance of lesions, blood perfusion levels, transport of blood clots, the presence of aneurysms, and other health and disease characteristics. Hemodynamic indices may be measured invasively or assessed using blood flow simulations. While simulation techniques may be used to perform non-invasive assessments of hemodynamics (e.g., based on available imaging data), simulation techniques may also provide the potential benefit of predictive modeling of hemodynamics in response to various events (e.g., progression or regression of lesions), as well as predictive modeling of the outcomes of planned procedures (e.g., surgical interventions). In order for predictive modeling to be realistic or clinically useful, it may be desirable or even necessary for the modeling and simulation system to be able to compute results significantly faster than the average time required to solve a high-fidelity model.

[0006] Rapid computation of simulation results (such as real-time simulation) can assist clinicians and others in planning clinical procedures and predicting the impact of potential future events. In some contexts, such predictions made using simulation may not involve invasive simulations. Thus, without the benefit of simulation results, a clinician may instead need to rely solely on available data, as well as their knowledge, intuition, and experience, when planning a procedure for a patient.

[0007] Therefore, there is a need for systems and methods for efficiently performing real-time simulations using models of blood flow and other physical phenomena. Because accuracy and efficiency can be desirable factors, there is a particular need for systems and methods that can integrate accurate modeling with efficient algorithms to achieve real-time estimation of simulation results.

[0008] In various aspects, the present disclosure is directed to addressing one or more of these aforementioned challenges. The background description provided herein is for the purpose of generally presenting the context of the present disclosure. Unless otherwise indicated herein, the materials described in this section are not prior art with respect to the claims in this application and are not admitted to be prior art or teachings of the prior art by virtue of their inclusion in this section. Summary of the Invention

[0009] According to certain aspects of the present disclosure, systems and methods for blood flow simulation are disclosed.

[0010] For example, a computer-implemented method may include: performing multiple blood flow simulations using a first model of vascular blood flow, each of the multiple blood flow simulations simulating blood flow in a patient's vascular system or based on the geometry of the patient's vascular system; generating a response surface based on results of the multiple blood flow simulations, the response surface mapping one or more first parameters of the first model to one or more second parameters of a reduced-order model of vascular blood flow, the reduced-order model having lower fidelity than the first model; determining values of one or more parameters of the reduced-order model mapped by the response surface from parameter values representing a modified state of the vascular system; and performing a simulation of blood flow in the modified state of the vascular system using the reduced-order model parameterized by the determined values of the one or more second parameters to determine blood flow characteristics of the modified state of the vascular system.

[0011] Additionally, a system may include a memory storing instructions; and one or more processors configured to execute the instructions to perform a method. The method may include: performing a plurality of blood flow simulations using a first model of vascular blood flow, each of the plurality of blood flow simulations simulating blood flow in a patient's vascular system or based on a geometry of the patient's vascular system; generating a response surface based on results of the plurality of blood flow simulations, the response surface mapping one or more first parameters of the first model to one or more second parameters of a reduced-order model of vascular blood flow, the reduced-order model having lower fidelity than the first model; determining values of one or more parameters of the reduced-order model mapped by the response surface from parameter values representing a modified state of the vascular system; and performing a simulation of blood flow in the modified state of the vascular system using the reduced-order model parameterized by the determined values of the one or more second parameters to determine blood flow characteristics of the modified state of the vascular system.

[0012] Additionally, a non-transitory computer-readable medium storing instructions that, when executed by one or more processors, cause the one or more processors to perform a method. The method may include: performing a plurality of blood flow simulations using a first model of vascular blood flow, each of the plurality of blood flow simulations simulating blood flow in a patient's vascular system or based on a geometry of the patient's vascular system; generating a response surface based on results of the plurality of blood flow simulations, the response surface mapping one or more first parameters of the first model to one or more second parameters of a reduced-order model of vascular blood flow, the reduced-order model having lower fidelity than the first model; determining values of one or more parameters of the reduced-order model mapped by the response surface from parameter values representing a modified state of the vascular system; and performing a simulation of blood flow in the modified state of the vascular system using the reduced-order model parameterized by the determined values of the one or more second parameters to determine blood flow characteristics of the modified state of the vascular system.

[0013] Additional objects and advantages of the disclosed embodiments will be set forth in part in the following description and in part will be apparent from the description, or may be learned by practice of the disclosed embodiments. The objects and advantages of the disclosed embodiments will be realized and attained by means of the elements and combinations particularly pointed out in the appended claims.

[0014] It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the disclosed embodiments, as claimed. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate various exemplary embodiments and, together with the description, serve to explain the principles of the disclosed embodiments.

[0016] Figure 1 Depicted is a flow diagram of a method for estimating system behavior using a response surface, in accordance with one or more embodiments.

[0017] Figure 2A Illustrated is a method for generating a response surface based on a high-fidelity simulation according to one or more embodiments.

[0018] Figure 2B Illustrated is a diagram for using a Figure 2A The method shown in the figure uses the response surface generated by the method to predict the simulation results in real time.

[0019] Figure 3 is a flow chart illustrating a method for modeling the effects of changing lumen geometry and boundary conditions on a blood flow simulation in accordance with one or more embodiments.

[0020] Figure 4 is a flow chart illustrating a method for modeling the effects of coronary revascularization in accordance with one or more embodiments.

[0021] Figure 5-6 The present invention illustrates a method according to one or more embodiments. Figure 4 An exemplary implementation of the method.

[0022] Figure 7 An environment is illustrated in which a computer system for performing the methods of the present disclosure may be implemented according to one or more embodiments. DETAILED DESCRIPTION

[0023] In various embodiments, systems and methods allow reduced-order models derived from computational fluid dynamics (CFD) to be used to simulate complex systems in real time with an arbitrarily high degree of accuracy compared to the accuracy of high-fidelity models. High-fidelity models of physical systems can be computationally expensive. Consequently, high-fidelity models can be inappropriate or impractical for real-time simulation. On the other hand, reduced-order models can have a lower computational complexity than the high-fidelity models. Consequently, reduced-order models can be executed more quickly and are therefore more suitable for real-time simulation.

[0024] In order to use the reduced-order model for real-time simulation while achieving arbitrary accuracy, a high-fidelity simulation using the high-fidelity model can be performed for a certain set of configurations. The results of the high-fidelity simulation can then be used to parameterize the reduced-order model. As will be described in more detail below, the reduced-order model can be parameterized using a response surface method technique according to the present disclosure. In this method technique, the results of the high-fidelity simulation performed for the above-mentioned set of configurations can be used to generate a response surface, which can be a mapping of the parameters of the high-fidelity model to the reduced-order model. This response surface can then be used to parameterize the reduced-order model.

[0025] A simulation using a parameterized reduced order model (which may be a real-time simulation) may be able to predict results significantly faster than a high-fidelity simulation using a high-fidelity model, while achieving an accuracy that is arbitrarily close to the accuracy of the high-fidelity simulation. The accuracy of the reduced order model, and therefore the accuracy of the simulation using the reduced order model, may depend on the set of configurations used to generate the response surface. Therefore, the accuracy of the reduced order model and reduced order modeling may be adjusted by adding or otherwise adjusting the configurations used to generate the response surface. For example, by refining the response surface, it is possible to ensure that the simulation using the reduced order model has an accuracy within a certain error tolerance. Additionally, since the high-fidelity simulation used to generate the response surface may be computationally expensive, the high-fidelity simulation may be performed offline before performing the real-time simulation using the reduced order model.

[0026] The methods of the present disclosure can enable rapid prediction of the behavior of complex systems, such as hemodynamic changes in response to changes in patient state. Such changes in patient state can be natural or planned (e.g., procedural). For example, in some embodiments, the methods of the present disclosure can be used to generate real-time updates of FFRCT in response to changes in vessel lumen geometry. Such changes in vessel lumen geometry can, for example, be natural changes or changes that are expected to occur as a result of a candidate treatment.

[0027] In the following description, embodiments of the present disclosure will be described in more detail with reference to the accompanying drawings. The terms used below should be interpreted in their broadest reasonable manner, even though they are used in conjunction with the detailed description of certain specific examples of the present disclosure. In fact, certain terms may even be emphasized below; however, any term intended to be interpreted in any limited manner will be clearly and specifically defined as such in this detailed description. Both the foregoing general description and the following detailed description are merely exemplary and explanatory, and are not limitations of the claimed features.

[0028] In this disclosure, the term "based on" means "based at least in part on." The singular forms "a," "an," and "the" include plural referents unless the context dictates otherwise. The term "exemplary" is used in the sense of "example" rather than "ideal." The terms "comprise," "comprising," "including," "comprising," or other variations thereof are intended to cover a non-exclusive inclusion, such that a process, method, or product that includes a list of elements does not necessarily include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Relative terms, such as "substantially" and "generally," are used to indicate a possible variation of ±10% of a stated value or understanding of a value.

[0029] In this disclosure, reduced-order models may also be referred to as low-fidelity models or fast models. Reduced-order models that can be used for real-time simulation may also be referred to as real-time models. Furthermore, where the context permits, reduced-order models and high-fidelity models may be general models that can be parameterized using different parameter values (e.g., different values corresponding to different configurations). In general, the term "parameter" may refer to any type of parameter, including boundary conditions.

[0030] In the following description, a method technique for fast simulation of partial differential equations is provided. Initially, it is noted that for the purpose of constructing and parameterizing reduced-order models for fast prediction of complex system behavior, the following can be assumed: (i) there is a high-fidelity model that performs well for the system under consideration; (ii) information relevant to the high-fidelity simulation (e.g., the original state of the patient's geometry and the patient's physiological state) is available; and (iii) it is possible to perform offline calculations based on the information in (i) and (ii), where the offline calculations may not be as fast as solving using reduced-order methods. However, it is understood that the method of the present disclosure can be practiced independently of the aforementioned assumptions, and the assumptions presented here are for illustrative purposes only.

[0031] Let the general partial differential equation have the following form:

[0032] exist Chinese (1)

[0033] It has boundary conditions:

[0034] exist Chinese (2)

[0035] in L is an operator (e.g., a differential, integral, function, or a combination thereof), u It is an unknown number, x N Represents the problem dimension,p Indicates a given parameter, is the problem domain, and Mark the boundaries of the domain. Expressions (1) and (2) can represent a system and can be used as a high-fidelity model of the system.

[0036] The reduced-order model of this partial differential equation can be approximated by using simpler operators (e.g., ordinary differential equations) L , the dimension x N Reduced to the input space of the reduced-order model x n —In the input space, the observation of the simulation results is of interest, and / or the parameter set p Simplified to The reduced-order model can be expressed as follows:

[0037] exist Chinese (3)

[0038] It has boundary conditions:

[0039] exist Chinese (4)

[0040] The goal is to make Become a pair A reasonable approximation of x N Can be x n The general approach is to perform simulations on the system, as originally described by expressions (1) and (2) for various boundary domains. , boundary conditions b (.) and parameter(s) are formulated so that a response surface can be used to generate an accurate approximation to the problem. Such a simulation of the system may be referred to as a high-fidelity simulation.

[0041] For the purpose of generating response surfaces, the domain It can have bounds expressed as follows:

[0042] (5)

[0043] The boundary conditions to which the system will be subject can have bounds expressed as follows:

[0044] (6)

[0045] Furthermore, the parameter space can have bounds expressed as follows:

[0046] (7)

[0047] The original governing equation can be solved using a series of domain and boundary conditions:

[0048] (8)

[0049] Where M is the number of high-fidelity simulations performed. Each of the M terms expressed above may correspond to a configuration for which a high-fidelity simulation is to be performed. That is, these M terms may represent M configurations.

[0050] In general, a "configuration" can refer to any modeling or simulation configuration and can include any parameters (and their values). A configuration can be a set of (one or more) values for (one or more) such parameters. In the preceding formula, each of these M configurations can be represented as b (.), and / or p The concept represented by a particular configuration can depend on the system being modeled. For example, if the system is blood flow through a patient's artery, the configuration can represent a certain lumen geometry, a certain physiological state of the patient, or a combination thereof.

[0051] In general, any suitable method can be used when selecting the M configurations, such as a sampling method or a quadrature method. The results of the high-fidelity simulation for the M configurations can be expressed as:

[0052] (9)

[0053] response surface R It can be a mapping of the parameters of a high-fidelity model to a reduced-order model:

[0054] (10)

[0055] in The complexity of the original equation can be captured, so that Can become L The response surface can be obtained by any suitable method. R .if R Using point fitting polynomials, such as Lagrange polynomials, a reduced-order model can be constructed such that, at the M configurations for which high-fidelity simulations have been performed, That is, a reduced-order model can be constructed to exactly match the output of the high-fidelity model of these M configurations. This approach allows computers to solve problems like the following more quickly:

[0056] (11)

[0057] At the same time, it ensures that the results are equivalent under these M configurations. For larger M, the approximation to the high-fidelity result under the intermediate configuration will generally be better, but so will the time required for offline calculation.

[0058] In general, a high-fidelity model can include any number of mathematical relationships. Thus, a high-fidelity model can include multiple different mathematical relationships of the form given by expression (1) above, and can include other mathematical relationships. Similarly, the order reduction can have multiple mathematical relationships, and can have multiple different mathematical relationships of the form given by expression (3) above. In general, a high-fidelity simulation can utilize all available information about the system in question (e.g., a complete spatial and temporal representation), and the high-fidelity model used for the simulation can include any number of full-order governing equations.

[0059] Response surfaces (such as R ) can be a mathematical relationship between one or more quantities or parameters of interest and the underlying variables. A response surface can be a function (e.g., a fitting function) that maps (one or more) input variables (e.g., parameters of a high-fidelity model) to output variables (e.g., parameters of a reduced-order model). A response surface can be constructed in such a way that it explores the parameter space using the reduced-order model. Depending on the application or implementation, multiple response surfaces may exist. Different response surfaces can map between different corresponding parameters of the high-fidelity and reduced-order models.

[0060] Figure 1 is a flow chart illustrating a method for estimating system behavior using a response surface in accordance with one or more embodiments.

[0061] Step 101 may include performing a plurality of simulations using a first model of the system. The first model may be a high-fidelity model as described in this disclosure.

[0062] In some embodiments, the first model can be a high-fidelity model of vascular blood flow, and the simulation can be a blood simulation that simulates blood flow in the patient's vascular system or a vascular geometry based on the patient's vascular system (e.g., a derived vascular system determined based on the patient's vascular system). The term "patient's vascular system" can refer to a vascular system in any part of the patient's body. Examples of vascular systems include, but are not limited to, coronary vascular systems, peripheral vascular systems, cerebral vascular systems, renal vascular systems, visceral vascular systems, and hepatic vascular systems (such as the portal vein). The derived vascular system can be, for example, a hypothetical vascular system that has undergone hypothetical modifications to the patient's vascular system.

[0063] Although various embodiments are described in this disclosure with respect to blood flow, this disclosure is not limited to simulations of blood flow. In general, the formulas and techniques described in this disclosure (including those described for blood flow simulations) can be applied or generalized to other complex systems, including systems that can be characterized using computational fluid dynamics.

[0064] Step 102 may include generating a response surface based on the simulation results obtained in step 101, wherein the response surface maps parameter(s) of the first model to parameter(s) of a second model, the second model having lower fidelity than the first model. The second model may be a model having lower fidelity than the first model, such as the reduced-order model described in the present disclosure. As described above, since the first model and the second model may be a high-fidelity model and a reduced-order model, respectively, the response surface may be a mapping of parameter(s) of the high-fidelity model to parameter(s) of the reduced-order model. The mapping may be a function whose output is the value of the parameter(s) of the reduced-order model and whose input is the value of the parameter(s) of the high-fidelity model.

[0065] Step 103 may include determining values of one or more parameters of the second model mapped by the response surface from the parameter values of the configuration to be analyzed. The parameter values of the configuration to be analyzed may be the values of the aforementioned parameter(s) of the first model. In some embodiments, the first model may be a set of differential equations. Therefore, the parameter values of the configuration to be analyzed may be the values of parameters (including boundary conditions) used in such differential equations. The values of the second parameter(s) may be determined by the response surface as a function of the parameter values of the configuration to be analyzed.

[0066] Step 104 may include performing a simulation using the second model parameterized by the determined values of the parameter(s) of the second model. For example, in the above-described embodiment regarding blood flow simulation, the parameter values of the configuration to be analyzed in step 103 may represent a modified state of the patient's vascular system (e.g., a modified anatomical and / or physiological state), in which case step 104 may determine the blood flow characteristics of the modified state of the vascular system. The simulation may be performed in real time. The blood flow characteristics may be a fractional flow reserve (FFR), a blood flow value, a blood flow direction,

[0067] Figure 2A Illustrated is a method for generating response surfaces based on high-fidelity simulations. Figure 2A The method illustrates Figure 1 An example implementation of the portion of the method corresponding to steps 101 and 102.

[0068] Step 201 may include receiving information indicative of a configuration. The information indicative of a configuration may include, for example, one or more geometries (e.g., geometries in which fluid flow is to be modeled or simulated), one or more boundary conditions, and / or any other parameters that may be part of the configuration. In some embodiments, the information indicative of a configuration may indicate a range of possible configurations, in which case the information received in step 201 may indicate a range of values for the aforementioned parameters. The information received in step 201 may be manually input by a user or automatically determined by a process executed on a computer system.

[0069] Step 202 may include identifying a configuration 220 for high-fidelity simulation. Configuration 220 may be identified based on the information received in step 201. For example, if the information received in step 201 indicates a range of configurations, then the configuration 220 identified in step 202 may be a sample of configurations within the range of configurations. Figure 3 Examples of sampling and quadrature methods are discussed in

[0044] The configuration 220 may be identified automatically or based on user input.

[0070] Step 203 may include performing a high-fidelity simulation for the identified configuration of the high-fidelity simulation. Configuration 220 identified in step 202 may be input into a high-fidelity model, and a high-fidelity simulation may be performed using the high-fidelity model parameterized according to parameter values specified in configuration 220.

[0071] Step 204 may include deriving parameters of the reduced-order model. The parameters derived in step 204 may be derived based on the configuration 220 identified in step 202 and results of a high-fidelity simulation performed using the high-fidelity model.

[0072] Step 205 may include generating a response surface 224. As described above, the response surface may be a mapping of parameters of the high-fidelity model to the reduced-order model. The results of the simulation using the parameters of the high-fidelity model and the reduced-order model may define a correspondence between the parameter values of the high-fidelity model and the parameter values of the reduced-order model. This correspondence may be represented as a set of points 222. The response surface 224 may then be generated based on the set of points 222. For example, the response surface 224 may be a surface fitted to the points 222. The response surface may have an exact fit because the surface 224 includes all of the points 222 (intersects all of the points 222), as shown in FIG. Figure 2A. However, this is not a requirement. Whether surface 224 includes all points 222 may depend on the functional form of surface 224. As noted above, Lagrange polynomials may be used for the exact fit. In other fitting methods, it may be possible for surface 224 to include only a portion of points 223, or to exclude all points 223.

[0073] For example, the parameters of the reduced order model derived in step 204 may be a set of parameter values that, when used in a simulation using the reduced order model, produces the same results as the same results of the high fidelity simulation as calculated by the reduced order model. For example, if the N configurations of the high fidelity simulation specify and this parameter value produces a high-fidelity simulation As a result, the parameter value derived in step 204 can be , making Produces the same results in simulations using reduced-order models Therefore, the set of points 222 can be defined as , and the response surface 224 can be generated as a surface fitted to these points. Therefore, this response surface can provide the mapping relationship described above in conjunction with expression (10).

[0074] Step 206 may include evaluating the accuracy of the response surface 224. Step 207 may determine, based on the accuracy evaluated in step 206, whether the response surface 224 is to be refined to have a higher accuracy.

[0075] The accuracy of the response surface can be defined by any suitable criteria. In some embodiments, the accuracy can be a measure of the accuracy in replicating the results of a high-fidelity simulation. For example, when using response surface 224 to parameterize a reduced-order model for one or more test configurations, the accuracy can be based on the closeness of the results of the reduced-order modeling to the results of the high-fidelity simulation for those one or more test configurations. The one or more test configurations may include one or more configurations other than the configuration represented by point 222, based on which response surface 224 is generated.

[0076] If the accuracy of the response surface 224 evaluated in step 206 is insufficient (e.g., does not meet a predefined threshold condition), then step 207 may resolve to "yes", and if the accuracy of the response surface 224 is evaluated to be sufficient (e.g., meets a predefined threshold condition), then step 207 may resolve to "no". In this context, accuracy may, for example, refer to the accuracy of the reduced-order model for any defined configuration.

[0077] If step 207 resolves to "yes" (eg, the accuracy is insufficient), then Figure 2A The method shown in can proceed to step 208, which can include refining the configuration of the high-fidelity simulation. The process of refining the configuration can include: adding new configurations for the high-fidelity simulation, removing existing configurations, and / or adjusting the values of existing configurations. For example, Figure 2A As shown in , additional configurations can be added to the originally identified configurations 220 to improve the accuracy of the response surface 224, thereby obtaining a refined set of configurations 220A. A simulation using the high-fidelity model can be performed for any newly added configurations (step 203), so that the resulting response surface 224 is updated.

[0078] The decision of step 207 can implement an iterative process in which the configurations of the high-fidelity simulation are refined (e.g., increased) in each subsequent iteration until response surface 224 reaches sufficient accuracy. Each configuration for which the high-fidelity simulation was performed in step 203 can result in a corresponding point 222. Thus, by adding additional configurations, the number of points 222 can be increased. Response surface 224 can then be fitted to the increased number of points 222, potentially resulting in better accuracy.

[0079] When the response surface 224 reaches sufficient accuracy, step 207 can be resolved to "no", and then the response surface 224 can be accepted as the final response surface 224A. As shown in FIG2, the final response surface 224A may have more points 222A (which may also be referred to as control points) than the initial response surface 224. The final response surface 224A also serves as the aforementioned response surface. R In this case, the set of configurations used to generate the final response surface 224A will be used as an example of the aforementioned set of M configurations.

[0080] depends on the time it takes to perform a high-fidelity simulation of all configurations for which the high-fidelity simulation was performed, Figure 2A The method illustrated in may be computationally expensive. Therefore, the method may be performed offline. For example, the final response surface 224A may be generated prior to real-time simulation using a reduced-order model.

[0081] Figure 2B Illustration of the use-based Figure 2A The method generates a response surface 224A to predict simulation results in real time. Figure 2B The method illustrates Figure 1 An example implementation of the portion of the method corresponding to steps 103 and 104.

[0082] Step 241 may include receiving a configuration to be analyzed. The configuration may be defined by any suitable method. For example, the configuration may represent the setup of an experiment to be performed via reduced-order simulation. In this disclosure, the terms "configuration to be analyzed" and "configuration to be explored" are used interchangeably.

[0083] Step 242 may include probing the response surface. The probing process may determine the parameters of the reduced-order model (eg, a parameter set) for the configuration to be analyzed. The detection process is illustrated using point 250, which represents the value of the parameter of the reduced order model for the configuration to be analyzed. As shown, point 250 can be a point mapped from the configuration to be analyzed. For example, the configuration to be analyzed can have the parameters discussed above. p 、 b and , and the response surface can be used as p 、 b and The function of those values is determined That is, point 250 may have a value on response surface 224A corresponding to The location of the above values, p 、 b and Can have can express having Since the position on response surface 224A can be interpolated based on the position of point 224A, the position of point 250 can be at the interpolated position.

[0084] Step 243 may include solving the reduced order model using the mapping given by the response surface 225. Step 204 may include solving expression (11) as described above. Steps 242 and 243 may be performed in real time as part of a real-time simulation.

[0085] Step 244 may include generating and reporting the results of the simulation. For example, the results may be stored in an electronic storage device or presented to a user (e.g., displayed on a display). Because solving the reduced-order model may be a real-time process, the results of the reduced-order model may also be presented in real-time.

[0086] Therefore, predictions about the behavior of complex systems can include: Figure 2A The first process of generating a response surface as described above, and Figure 2BThe second process described is to rapidly explore the response surface to estimate the outcome (e.g., hemodynamic index) for a specific configuration. As noted above, the first process of constructing the response surface can be performed offline and computationally expensive, depending on the time it takes to perform a high-fidelity simulation using the high-fidelity model. Its computational cost may depend on the acceptable error for the second process.

[0087] Figure 3 and Figure 4 illustrates further examples in which the above-described techniques are applied. Figure 3 The present invention is a flow chart illustrating a method for modeling the effects of changing lumen geometry and boundary conditions on a blood flow (e.g., coronary artery flow) simulation. The method can apply the various techniques described above to perform real-time estimation of blood flow in an artery (e.g., a coronary artery) under a given new configuration. In this context, the given new configuration can be, for example, the lumen geometry and / or physiological state of a patient. Figure 3 The method may be performed by any suitable computer system.

[0088] Step 301 may include receiving anatomical information describing a patient's vascular system. The described vascular system may include all arteries of interest in the patient. In some embodiments, the vascular system may be a coronary vascular system, in which case the anatomical information may describe the patient's coronary arteries. Figure 1 Examples of other types of vasculature described include, but are not limited to, peripheral vasculature, cerebral vasculature, renal vasculature, visceral vasculature, and hepatic vasculature (such as the portal vein).

[0089] The anatomical information may be received over a computer network from a memory (eg, a hard drive or other electronic storage device) of the computer system performing step 301 or from another computer system (eg, a computer system of a physician or third party provider).

[0090] In some embodiments, the anatomical information may include one or more images of the patient acquired using an imaging or scanning modality, and / or information extracted from (or otherwise obtained based on analysis of) such images of the patient. Examples of imaging or scanning modalities include computed tomography (CT) scans, magnetic resonance (MR) imaging, microcomputed tomography (μCT) scans, micromagnetic resonance (μMR) imaging, dual-energy computed tomography scans, ultrasound imaging, single photon emission computed tomography (SPECT) scans, and positron emission tomography (PET) scans. Such images of the patient may be received from a physician or third-party provider via a computer network and / or stored in the memory of the computer system performing step 301. Because the images depict the specific anatomical and physiological characteristics of the patient, any model derived from or constructed based on such images or other patient-specific information may be considered a patient-specific model. Note that the use of the term "patient" is not intended to be limiting. A "patient" may generally be referred to as a "person."

[0091] Step 302 may include generating an anatomical model of the vascular system based on the anatomical information received in step 301. The anatomical model may have any suitable form and may model any suitable aspect of the vascular system. For example, the anatomical model may describe the patient-specific three-dimensional geometry of the vessels of the vascular system as identified from the anatomical information. In some embodiments, the anatomical model may indicate disease progression or regression, plaque rupture, thrombosis, and other characteristics of the represented vascular system(s). The anatomical model of the vascular system may also be referred to as a patient-specific anatomical model or a patient-specific vascular model. In some embodiments, the anatomical model may model characteristics of the vascular system in one or more physiological states of the patient. In such embodiments, the characteristics of the anatomical model may reflect the characteristics of the vascular system when the patient is in a certain physiological state (e.g., a resting state or an exercise state).

[0092] Examples of methods for generating anatomical models are described, for example, in US 2012 / 0041739 A1 to Taylor ("US '739"), which is hereby incorporated by reference in its entirety. Note that US '739 also provides examples of other aspects discussed in this disclosure, such as reduced-order models and calculation of fractional flow reserve (FFR).

[0093] Steps 301 and 302 may be performed by the same computer system that performs the remaining steps 304 to 307 described below. However, it is also possible that steps 301 and 302 are performed by another computer system, in which case the anatomical model is provided to the computer system that performs the remaining steps via a communication network. Any anatomical model received via the communication network may be stored in the memory of the computer system.

[0094] Step 303 may include performing a high-fidelity simulation based on the anatomical model generated in step 302. The simulation may be a blood flow simulation that simulates blood flow in the artery modeled by the anatomical model. The high-fidelity simulation may involve (one or more) detailed mathematical relationships that describe the system. Such mathematical relationships may include (one or more) partial differential equations in any suitable formulation, such as the Navier-Stokes equations. The high-fidelity simulation may be performed using (one or more) any suitable technique, such as finite element analysis, finite difference methods, lattice Boltzmann methods, etc. The detailed mathematical relationships used in the high-fidelity simulation may constitute a high-fidelity model, which is executed to perform the high-fidelity simulation.

[0095] For example, the detailed mathematical relationships may include the Navier-Stokes equations with boundary conditions and / or other parameters derived from the anatomical model. The boundary conditions and / or other parameters may, for example, represent the geometry or other properties of the artery modeled by the anatomical model.

[0096] Step 304 may include performing a high-fidelity simulation on the extreme values of the configuration to be explored. Such a simulation may be a blood flow simulation that simulates blood flow in a structure represented by the extreme values of the configuration to be explored.

[0097] In this context, a configuration to be explored can be any configuration that is intended to be explored (e.g., simulated or otherwise studied) using reduced-order simulation as described below. The extremes of the configuration to be explored can depend on the extremes of the parameter space and domain that can be explored using the reduced-order model. Bounds can be imposed based on the limits of the exploration. Such bounds can be application-specific. Note that, as described above, the extremes of the configuration to be explored can be configurations for the purpose of generating a response surface and can also be referred to as extreme configurations.

[0098] In some embodiments, one or more limits can be imposed based on anatomical limits. For example, an upper limit on the anatomical model can be imposed based on the maximum allowable dilation of the patient-specific model. In this case, the patient-specific model can model the reduction of lumen narrowing at various locations, the effect of applying higher levels of nitrates, or a combination thereof. The maximum allowable dilation in this treatment scenario can be expressed as an upper limit on the anatomical model. In some embodiments, one or more limits imposed based on anatomical limits can represent the addition or removal of vessels. For example, in the case of a bypass graft, the upper limit can be based on the maximum number of anastomoses of the available graft.

[0099] Additionally or alternatively, one or more limits can be imposed based on physiological limits. For example, to assess different physiological states of a patient, upper and / or lower limits can be assessed based on resting state and exercise conditions, or based on other extremes of boundary conditions. For example, the upper (or lower) limit can represent the patient's resting state, and the lower (or upper) limit can represent the patient's exercise state.

[0100] Step 305 may include: identifying one or more configurations for which high-fidelity simulation is to be performed; and performing high-fidelity simulation on the one or more identified configurations. Figure 2A An example of steps 202 and 203 of the method discussion.

[0101] The larger the parameter set and domain, the better the accuracy of the response surface and the accuracy of real-time predictions. Any sampling or quadrature method can be used to identify one or more configurations, including but not limited to: Monte Carlo sampling, Latin Hypercube sampling, Gaussian quadrature, sparse grid quadrature, adaptive sparse grid quadrature, and combinations thereof. Monte Carlo sampling may be appropriate for sampling large-dimensional parameter spaces, but may converge very slowly for problems with medium-dimensional parameter spaces. Latin Hypercube sampling can achieve separation of parameter spaces and can converge better than Monte Carlo for medium-dimensional parameter spaces. In the Gaussian quadrature method, Gaussian points can be used to generate configurations, and tensor product interpolation can be used to scale the points to higher dimensions. The sparse grid quadrature method may be the same as the Gaussian quadrature method for one dimension, but can have a sparser grid to reduce the number of simulations. The adaptive sparse grid quadrature method may be the same as the sparse grid quadrature method, but can be adapted to the function so that regions of shallow variation are less explored than regions of significant variation.

[0102] After identifying one or more configurations for which to perform high-fidelity simulations, step 305 may further include performing high-fidelity simulations on the one or more identified configurations.

[0103] Step 306 may include generating a response surface based on the solution of the high-fidelity simulation. As described above, any functional form may be used to create a response surface based on the high-fidelity solution under multiple configurations (e.g., M configurations). Figure 3 In the context of , the M configurations mentioned in the preceding discussion may include any configuration identified in step 305 and may also include any configuration simulated in step 303 and / or step 304. Local linear interpolation or Lagrange polynomial interpolation may be performed to ensure that the real-time simulated solution at the control point matches the fully simulated solution. In general, step 306 may utilize the above combined Figure 2A Any of the techniques described in steps 204, 205, 206 and 208.

[0104] In some embodiments, multiple response surfaces may be generated. For example, if the high-fidelity simulation involves multiple mathematical relationships (e.g., a mathematical relationship in the form of expression (1)) and / or the reduced-order model includes multiple mathematical relationships (e.g., a mathematical relationship in the form of expression (3)), multiple response surfaces may be generated to map between different combinations of high-fidelity and reduced-order mathematical relationships. Furthermore, the response surface of step 306 may be modified by refining the configuration used to generate the response surface, as described above in conjunction with Figure 1 Just as described.

[0105] Step 307 may include performing a reduced order simulation based on the response surface. The reduced order simulation may be informed by the interpolated values estimated by the response surface. For example, as described above in conjunction with Figure 2B As described, the response surface may be probed based on one or more configurations to be explored to obtain interpolated values. The one or more configurations to be explored may depend on the application of the method.

[0106] The reduced order simulation may be performed using the reduced order model, which may be constructed to exactly match the output of the high fidelity model for the M configurations in which the high fidelity simulation was performed. The reduced order simulation may be performed in real time.

[0107] Figure 3 The method may include any one or more of the additional exemplary aspects described below, all of which are optional. These aspects may be implemented as one or more steps of the method described above, or as additional steps of the method.

[0108] In some examples, Figure 3The method may include: quantifying confidence intervals. For example, the response surface created in step 306 can be explored to run many simulations, from which confidence interval estimates for the unknown domain can be calculated. For the purpose of quantifying confidence intervals, the configurations to be explored may include any configurations suitable for quantifying confidence intervals. For example, a configuration may represent a configuration on which reduced-order modeling is intended to be performed. Confidence interval estimates can, for example, be used to assist a clinician performing reduced-order simulations in understanding the accuracy of the reduced-order model when performing similar types of simulations. Alternatively, the confidence interval estimates can be used to correct the response surface generated in step 306.

[0109] In some examples, Figure 3 The method may include modeling disease progression and / or regression. For example, the response surface generated in step 306 may also be explored to predict the impact of lesions that may progress or regress. This, in turn, may be used for patient management and monitoring. Configurations to be explored may include any configuration suitable for modeling or simulating disease progression and / or regression.

[0110] In some examples, Figure 3 The method may include modeling different physiological conditions. For example, the response surface generated in step 306 may also be explored to model the effects of different physiological conditions (e.g., resting and exercise conditions) or pharmaceutical agents. The configurations to be explored may include any configuration suitable for modeling or simulating physical conditions.

[0111] Although some applications related to blood flow have been described Figure 3 method, but for Figure 3 The techniques described in the method can be applied to other complex systems, including other fluid dynamic systems.

[0112] Figure 4 is a flow chart illustrating a method for modeling the effects of coronary revascularization.The method can apply the various techniques described above to perform real-time calculations of the effects of coronary revascularization on blood flow. Figure 5-6 Pictured Figure 4 Exemplary implementations of the method are also discussed below. Figure 4-6 The method may be performed by any suitable computer system.

[0113] Step 401 may include receiving anatomical information describing the patient's coronary arteries. Step 401 may include any aspects of step 301 described above. In some embodiments, step 401 may include receiving anatomical information obtained from an analysis of a coronary artery CT scan. For example, Figure 5As shown in , anatomical information describing the patient's anatomical characteristics, such as blood vessel centerlines and lumens, can be extracted from an acquired CCTA image 502 of the patient.

[0114] Step 402 may include generating a patient model, which may include a base patient model and a modified patient model. The base patient model may be generated based on the anatomical information received in step 401. The modified patient model may be a modification of the base patient model. In some embodiments, the patient's coronary arteries may have narrowed lumens, and the modified patient model may represent complete revascularization of the coronary arteries.

[0115] The base patient model may be an anatomical model that models the actual anatomical characteristics of the patient's coronary arteries as described by the anatomical information (eg, vessel centerline and lumen). Figure 5 As shown in , a base patient model 503 can be generated based on the vessel centerlines and lumens extracted from the CCTA image 502. Figure 5 , a base patient model 503 is illustrated as having narrowed geometries at various locations 503A, 503B, and 503C of the model. The narrowed geometries may model, for example, stenosis at corresponding locations of the patient's coronary arteries.

[0116] The modified patient model can be a base patient model that has been modified to model changes in the patient's coronary artery characteristics. For example, the modified patient model can model hypothetical conditions of the patient's coronary arteries. Such conditions can be, for example, idealized conditions corresponding to extreme values of the configuration to be explored, in which case the modified patient model can be referred to as an idealized model. Figure 5 In FIG, the idealized model 504 is an example of a modified patient model that models the coronary arteries under the condition that the entire anatomy represented by the base patient model is revascularized. Figure 5 As shown in , the idealized model 504 does not indicate stenosis at locations 503A, 503B, and 503C of the base patient model 503. In such an embodiment, the modified patient model may be a revascularized anatomical model.

[0117] Step 403 may include performing a high-fidelity simulation of blood flow using boundary conditions derived from the patient model to simulate the effect of adenosine on hyperemia and obtain a first high-fidelity solution. Generally, the boundary conditions in step 403 may be derived from characteristics of the patient, such as the patient's anatomy, myocardium, and scaling laws for resting blood flow. Such boundary conditions may include boundary conditions derived from (e.g., derived from) the patient model. However, the present disclosure is not limited thereto, and it is also possible that some or all of the boundary conditions are derived from other models or information.

[0118] The high-fidelity simulation of step 403 can be performed by constructing a computational model in the form of a high-fidelity model. The computational model can include mathematical relationships (such as the Navier-Stokes equations) and boundary conditions derived from the patient's anatomy, the myocardium, and scaling laws for resting blood flow. Such boundary conditions can simulate the effects of adenosine on hyperemia. Therefore, to perform the high-fidelity simulation, the computer system performing step 403 can solve the Navier-Stokes equations for the coronary arteries using the aforementioned boundary conditions.

[0119] Step 404 may include performing a high-fidelity simulation of blood flow using boundary conditions obtained based on the modified patient model to obtain a second high-fidelity solution. Generally speaking, the high-fidelity simulation of step 404 may be performed on an extreme value corresponding to a configuration (or configurations) in which the coronary arteries are fully revascularized. This extreme value serves as the basis for the above-mentioned combination of Figure 3 The examples of extreme values of the configurations to be explored are described in step 304. The revascularization may be one in which the entire anatomical structure of the patient's specific geometry is revascularized. The high-fidelity simulation of step 404 may be performed using a computational model constructed as a high-fidelity model that may include boundary conditions derived from the modified patient model described above. The computational model of step 403 and the computational model of step 404 may be based on the same mathematical relationships, but have different boundary conditions and / or other parameters applied.

[0120] Step 405 may include performing additional high-fidelity simulations of blood flow at different flow rates for each of the base patient model and the modified patient model to obtain third and fourth high-fidelity solutions. For example, the high-fidelity simulation performed in step 402 may be performed for a first flow rate, and step 405 may include performing a high-fidelity simulation in the same or substantially the same manner (e.g., using boundary conditions based on the base patient model), but with a flow rate that is higher (e.g., 10%, 15%, 25%, 50%, or 75% higher) than the first flow rate. Similarly, the high-fidelity simulation performed in step 403 may be performed for a second flow rate (which may be the same as the first flow rate), and step 405 may include performing a high-fidelity simulation in the same or substantially the same manner (e.g., using boundary conditions based on the modified patient model), but with a flow rate that is higher (e.g., 10%, 15%, 25%, 50%, or 75% higher) than the second flow rate. By performing additional simulations at different flow rates, the high-fidelity solution obtained across steps 403-405 can be used to inform a reduced-order model in which the fluid resistance parameter depends on the flow rate. In the case of one additional simulation in each configuration associated with the base patient model and the modified patient model, respectively, the fluid resistance in the reduced-order model can be linearly dependent on the flow rate.

[0121] Step 406 may include generating response surfaces for the intercept and slope of the fluid resistance function, respectively. The response surfaces may be generated based on the four high-fidelity solutions obtained across steps 403-405 and may include two response surfaces, a first response surface for the intercept of the fluid resistance function and a second response surface for the slope of the fluid resistance function. Both the first and second response surfaces may be based on the one-dimensional Navier-Stokes equations. The first response surface may have a functional form 1 / r for the intercept: 4 The second response surface may have a functional form for the slope (dA / dz * 1 / r 6 ). In these expressions, r is the local radius, A is the area, and dA / dz is the gradient of the area along the vessel. Note that step 406 is an example of step 306 described above. Therefore, any technique described in conjunction with step 306 is applicable to step 406.

[0122] Step 407 may include receiving a modified geometry. The modified geometry may be a geometry that will be subjected to reduced-order simulation and may be a revascularized geometry, including, for example, the location at which the coronary arteries will be revascularized and the final size(s) of the vessel lumens. The revascularized geometry may be a simulation input input by a user or defined by the simulation process. One or more configurations for reduced-order modeling and simulation may be defined based on the revascularized geometry. For example, values for attributes of the vascularized geometry (such as values for the location of the revascularization and / or the final size of the vessel lumens) may be used as a configuration or as part of a configuration. Such a configuration may be used on the response surface(s) to obtain parameters for the reduced-order model(s) used in step 408 described below.

[0123] Step 408 may include performing a reduced order simulation based on the revascularized geometry and the two response surfaces. The reduced order simulation may be informed by interpolated values estimated using the response surfaces on the revascularized geometry. The reduced order simulation may be performed in real time and may use one or more reduced order models constructed as described above. Such reduced order models may have mathematical relationships in the form of expressions (3) and (4) and may be constructed to produce the same results as the high fidelity model of process 510 for four high fidelity measurements. Note that step 408 is an example of step 307 described above. Therefore, the techniques described in conjunction with step 307 are generally applicable to step 408.

[0124] For the configuration in step 403 , the output of the low-fidelity simulation can be used to output updated flow rate, blood pressure, FFR, or any other quantity of interest, such as wall shear stress.

[0125] exist Figure 5 In the illustration of FIG, process 510 is used as an example of a high-fidelity simulation of steps 403 to 405. Figure 5 As shown in , four Navier-Stokes simulations may be performed. These simulations may include a first Navier-Stokes simulation using a hyperemic boundary condition applied based on an idealized model 504, a second Navier-Stokes simulation using a superemic boundary condition applied based on the idealized model 504, a third Navier-Stokes simulation using a superemic boundary condition applied based on a base patient model 503, and a fourth Navier-Stokes simulation using a hyperemic boundary condition applied based on the base patient model 503. It should be noted that the above boundary conditions are used as examples of simulation parameters, and the corresponding simulation parameters of the four simulations may differ from each other in aspects other than the above boundary conditions.

[0126] The four sets of simulation parameters applied to the Navier-Stokes simulation can each yield four high-fidelity solutions, as shown above. Figure 4 The four high-fidelity solutions may then be used to construct a response surface (step 520), which may include deriving parameters for the reduced-order model. Figure 4 Item 504 in is a visual depiction of the parameters of the reduced order model. The reduced order model can be a reduced order model having mathematical relationships in the form of expressions (3) and (4), and can be constructed so that the reduced order model produces the same results as the high-fidelity model of process 510 for the four high-fidelity simulations.

[0127] Figure 6 Detection of response surfaces for reduced-order modeling is illustrated. As shown, response surface(s) may be detected based on the configuration indicated by modified geometry 601. Modified geometry 601 may be the revascularized geometry described above for step 407 and may be representable in a graphical form, such as a three-dimensional graphical model (e.g., a surface mesh), as shown. Figure 6 . The modified geometry 601 may be an anatomical model and may represent a specific anatomical geometry to be explored or analyzed by simulation; for example, the geometry may be a natural or planned state of a patient. The modified geometry 601 may differ from the idealization 505.

[0128] Probing the response surface(s) can yield values for the parameters of the reduced-order model. The reduced-order model can be executed to obtain a hemodynamic solution. In process 610, the hemodynamic solution can be graphically displayed along with the three-dimensional graphical model of the modified geometric shape 601. For example, the hemodynamic solution can be represented graphically, and the graph of the hemodynamic solution can be overlaid or otherwise combined with the three-dimensional graphical model of the modified geometric shape 610 to obtain a mapped model 602. The mapped model 602 can be displayed, for example, on an electronic display. This display can be performed in real time.

[0129] The methods described in the present disclosure can have various clinical applications, including: planning percutaneous coronary intervention (PCI) procedures; planning bypass graft surgery; modeling disease progression and lesion regression; modeling positive and negative remodeling of lesions; sensitivity analysis, uncertainty quantification, and / or confidence interval estimation for flow simulations; modeling different physiological conditions (such as exercise); and modeling the effects of drugs, altitude, or autoregulatory mechanisms.

[0130] In some embodiments, the methods described in the present disclosure may be used to generate real-time updates of a fractional flow reserve (FFR) (e.g., a fractional flow reserve derived from computed tomography (FFRCT)) in response to a change in a patient's vascular lumen geometry. The change in vascular lumen geometry may be a natural change, or a change that is expected to occur as a result of a candidate treatment for the patient. For example, the luminal geometry may be represented as one or more parameters, and a user or a simulation process may adjust the values of such parameters to reflect the change in vascular lumen geometry. In response to the adjustment of the modeling parameters, a computer system performing the simulation may identify a configuration for reduced-order modeling, probe (one or more) response surfaces based on the configuration to parameterize the reduced-order model, and solve the reduced-order model to calculate (one or more) values of FFRCT. According to the present disclosure (e.g., Figure 3 and Figure 4 ), the response surface(s) may have been generated prior to the simulation. The calculated value(s) of the FFRCT may be output in any suitable manner (e.g., displayed on a display device or transmitted to another computer system for display on a display device). The vessel lumen geometry may be a portion of a coronary artery of the patient, or a portion of another portion of the vascular system.

[0131] Any method discussed in this disclosure that is understood to be computer-implementable—including the methods shown in Figures 2-6 and any computations described in conjunction with Expressions (1) to (11)—can be performed by one or more processors of a computer system. Method steps performed by one or more processors may also be referred to as operations.

[0132] Figure 7 An example of an environment in which such a computer system may be implemented as a server system 740 is depicted. In addition to the server system 740, Figure 7 The environment further includes a plurality of doctors 720 and third-party providers 730, any of which may be connected to an electronic network 710, such as the Internet, via one or more computers, servers, and / or handheld mobile devices. Figure 1 In FIG, doctor 720 and third-party provider 730 can both represent computer systems and organizations using such systems. For example, doctor 720 can be a hospital or a computer system of a hospital.

[0133] Doctor 720 and / or third party provider 730 can create or otherwise obtain medical images, such as images of the heart, blood vessels, and / or organ systems of one or more patients. Doctor 720 and / or third party provider 730 can also obtain any combination of patient-specific information, such as age, medical history, blood pressure, blood viscosity, a combination of the above, Figure 3The anatomical information described in step 301 of the method, as well as other types of patient-specific information, can be transmitted by the physician 720 and / or the third-party provider 730 to the server system 740 via the electronic network 710 .

[0134] The server system 740 may include one or more storage devices 760 for storing images and data received from the physician 720 and / or third-party provider 730. The storage device 760 may be considered a component of the memory of the server system 740. The server system 740 may also include one or more processing devices 750 for processing the images and data stored in the storage device and for executing any computer-implemented processes described in this disclosure. Each of the processing devices 750 may be a processor or a device including at least one processor.

[0135] In some embodiments, the server system 740 may have a cloud computing platform with scalable resources for computing and / or data storage, and may run applications for performing the methods described in the present disclosure on the cloud computing platform. In such embodiments, any output may be transmitted to another computer system (such as a personal computer) for display and / or storage.

[0136] Other examples of computer systems for executing the methods of the present disclosure include desktop computers, laptop computers, and mobile computing devices such as tablet computers and smartphones.

[0137] One or more processors may be configured to perform such processes by having access to instructions (e.g., software or computer-readable code) that, when executed by the one or more processors, cause the one or more processors to perform such processes. The instructions may be stored in a memory of the computer system. The processor may be a central processing unit (CPU), a graphics processing unit (GPU), or another type of processing unit.

[0138] A computer system (such as server system 740) may include one or more computing devices. If one or more processors of the computer system are implemented as multiple processors, the multiple processors may be included in a single computing device or distributed among multiple computing devices. If the computer system includes multiple computing devices, the memory of the computer system may include the corresponding memory of each of the multiple computing devices.

[0139] Generally speaking, a computing device may include one or more processors (e.g., a CPU, GPU, or other processing unit), memory, and one or more communication interfaces (e.g., a network interface) for communicating with other devices. Memory may include volatile memory, such as RAM, and / or non-volatile memory, such as ROM, and storage media. Examples of storage media include solid-state storage media (e.g., solid-state drives and / or removable flash memory), optical storage media (e.g., optical disks), and / or magnetic storage media (e.g., hard drives). The aforementioned instructions (e.g., software or computer-readable code) may be stored in any volatile and / or non-volatile memory components of the memory. In some embodiments, the computing device may further include one or more input devices (e.g., a keyboard, mouse, or touchscreen) and one or more output devices (e.g., a display, printer). The aforementioned elements of the computing device may be connected to each other via a bus, representing one or more buses. In some embodiments, the computing device's processor(s) include both a CPU and a GPU.

[0140] Instructions executable by one or more processors may be stored on a non-transitory computer-readable medium. Thus, whenever a computer-implemented method is described in this disclosure, the disclosure should also be understood to describe a non-transitory computer-readable medium storing instructions that, when executed by one or more processors, configure or cause the one or more processors to perform the computer-implemented method. Examples of non-transitory computer-readable media include: RAM, ROM, solid-state storage media (e.g., solid-state drives), optical storage media (e.g., optical disks), and magnetic storage media (e.g., hard drives). The non-transitory computer-readable medium may be part of the memory of a computer system or separate from any computer system. An “electronic storage device” may include any of the non-transitory computer-readable media described above.

[0141] It should be appreciated that in the above description of exemplary embodiments, various features are sometimes grouped together in a single embodiment, figure, or description thereof for the purpose of simplifying the disclosure and aiding understanding of one or more of the various inventive aspects. However, this approach to the present disclosure should not be interpreted as reflecting an intention that the claimed invention requires more features than are expressly recited in each claim. Rather, as reflected in the following claims, inventive aspects lie in less than all features of a single, preceding disclosed embodiment. Therefore, the claims following the detailed description are hereby expressly incorporated into this detailed description, with each claim standing on its own as a separate embodiment of the present disclosure.

[0142] Furthermore, while some embodiments described herein include some features but not other features included in other embodiments, combinations of features from different embodiments are intended to be within the scope of this disclosure and to form different embodiments, as will be understood by those skilled in the art. For example, in the following claims, any of the claimed embodiments can be used in any combination.

[0143] Thus, while certain embodiments have been described, those skilled in the art will recognize that other and further modifications may be made thereto without departing from the spirit of the present disclosure, and it is intended that all such changes and modifications be claimed as falling within the scope of the present disclosure. For example, functionality may be added or deleted from the block diagrams, and operations may be interchanged between functional blocks. Steps may be added to or deleted from the described methods within the scope of the present disclosure.

[0144] The subject matter disclosed above is to be considered illustrative, not restrictive, and the appended claims are intended to cover all such modifications, enhancements, and other implementations that fall within the true spirit and scope of the present disclosure. Therefore, to the maximum extent permitted by law, the scope of the present disclosure will be determined by the broadest permissible interpretation of the following claims and their equivalents, and should not be limited or restricted by the foregoing detailed description. Although various implementations of the present disclosure have been described, it will be clear to those skilled in the art that more implementations and implementations are possible within the scope of the present disclosure. Therefore, the present disclosure will not be limited.

Claims

1. A computer-implemented method for blood flow simulation, the method comprising: performing a plurality of blood flow simulations using a first computational fluid dynamics model of vascular blood flow, each of the plurality of blood flow simulations simulating blood flow in a respective configuration of the patient's vascular system or in a respective configuration based on a geometry of the patient's vascular system, wherein each of the plurality of configurations includes first values of one or more first parameters of the first computational fluid dynamics model, the first values of the first parameters representing at least a respective vascular geometry in which blood flow is simulated in the respective blood flow simulation, and the plurality of configurations includes: representing a first configuration of the patient's vascular system; and one or more further configurations, each further configuration representing a vessel geometry derived from the geometry of the vascular system, and / or a physiological state different from the physiological state represented by the first configuration, wherein the plurality of blood flow simulation results are first simulation results obtained for the plurality of configurations respectively; generating a response surface that maps one or more of the first parameters of the first computational fluid dynamics model to one or more second parameters of a reduced-order model of vascular blood flow, the reduced-order model having a lower fidelity than the first computational fluid dynamics model, the generating of the response surface comprising: determining, for each of the plurality of configurations, a second value for the one or more second parameters that, when used in a low-fidelity blood flow simulation performed using the reduced-order model, produces a corresponding second simulation result that matches the corresponding first simulation result; and generating, for each of the plurality of configurations, the response surface based on first values of the one or more first parameters and determined second values of the one or more second parameters; determining values for the one or more first parameters for a configuration representing a modified state of the patient's vascular system; determining values of one or more second parameters of a reduced order model mapped by the response surface from first parameter values determined for a configuration representing a modified state of the vascular system; and A simulation of blood flow in the modified state of the vascular system is performed using the reduced order model parameterized by the determined values of the one or more second parameters to determine blood flow characteristics of the modified state of the vascular system of the patient.

2. The method according to claim 1, further comprising: receiving patient-specific image data of a patient's vascular system; generating a patient-specific anatomical model of the vascular system based on the image; as well as Based on the patient-specific anatomical model, values of one or more first parameters are determined for a first configuration to represent the patient-specific geometry of the vascular system.

3. The method of claim 1, wherein the one or more additional configurations include one or more extreme configurations, each extreme configuration representing a state of the vascular system at an anatomical limit or a physiological limit.

4. The method according to claim 3, wherein The vascular system is at least a portion of a coronary artery of the patient, and At least one of the one or more extreme configurations represents complete revascularization of at least the portion of the coronary artery.

5. The method of claim 3, wherein the one or more additional configurations further comprise: One or more configurations determined using a sampling or quadrature method based on the one or more extreme value configurations.

6. The method according to claim 1, wherein The response surface is a surface fitted to the set of points, and Each point in the point set includes: The determined values of the one or more second parameters are determined for respective configurations of the plurality of configurations.

7. The method of claim 1, wherein the vascular system comprises at least one of a coronary vascular system, a peripheral vascular system, a cerebral vascular system, a renal vascular system, a splanchnic vascular system, or a hepatic vascular system.

8. The method according to claim 1, wherein performing an experimental blood flow simulation in real time such that the value of the blood flow characteristic is determined in real time, and The method further includes presenting the value of the blood flow characteristic to a user in real time.

9. The method of claim 1, wherein the blood flow characteristic is fractional flow reserve.

10. A computer system for blood flow simulation, comprising: a memory for storing instructions; One or more processors configured to execute instructions to perform the method according to any one of claims 1-9.

11. A non-transitory computer-readable medium storing instructions that, when executed by one or more processors, cause the one or more processors to perform the method according to any one of claims 1 to 9.

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