Systems and methods for blood flow estimation using response surfaces and reduced order modeling - Patents.com

Abstract

A system and method for blood flow simulation is disclosed. For example, 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 within a patient's vasculature or a geometry based on the patient's vasculature; generating a response surface based on results of the plurality of blood flow simulations that maps one or more first parameters of the first model to one or more second parameters of a reduced-order model of vascular blood; determining values ​​for one or more parameters of the reduced-order model mapped from parameter values ​​representing a modified state of the vasculature by the response surface; 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 vasculature.

Description

[Technical field]

[0001] (CROSS REFERENCE TO RELATED APPLICATIONS) This application claims priority to U.S. Provisional Application No. 62 / 849,489, filed May 17, 2019, the disclosure of which is incorporated herein by reference in its entirety.

[0002] Various embodiments of the present disclosure relate generally to predicting the behavior of complex systems using response surfaces and reduced order modeling, and more particularly, to efficient real-time estimation of blood flow using response surface methodology and reduced order modeling. [Background technology]

[0003] Modeling and simulation of real-world physical phenomena can be performed 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-scale 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.

[0004] In clinical applications, blood flow characteristics may be relevant to the assessment of a patient's health or disease. For example, hemodynamic indices may be used to assess the functional significance of lesions, blood perfusion levels, clot transport, the presence of aneurysms, and other health and disease characteristics. Hemodynamic indices may be measured invasively or assessed using blood flow simulation. Simulation techniques may be used to perform non-invasive assessment of hemodynamics (e.g., based on available imaging data), but simulation techniques may also provide the potential advantage of predictive modeling of hemodynamics in response to various events (e.g., lesion progression or regression) and of the outcome of planned procedures (e.g., surgical interventions). For predictive modeling to be realistic or clinically useful, it may be desirable or even necessary for the modeling and simulation system to be capable of calculating results significantly faster than the average time required to solve a high-fidelity model.

[0005] Rapid computation of simulation results, such as real-time simulation, can aid clinicians and others in planning clinical procedures and predicting the impact of potential future events. In some situations, such predictions using simulation may not have an invasive analog. Thus, without the benefit of simulated results, clinicians may instead need to rely solely on available data and their knowledge, intuition, and experience when planning procedures for patients.

[0006] Thus, there is a need for systems and methods for effectively performing real-time simulations using models of blood flow and other physical phenomena. Since accuracy and efficiency can be desirable factors, there is a need, in particular, for systems and methods that can integrate accurate modeling with efficient algorithms to enable real-time estimation of simulation outcomes.

[0007] The present disclosure is directed, in various aspects, to addressing one or more of these above-referenced problems. The background discussion provided herein is generally for the purpose of presenting the context of the present disclosure. Unless otherwise indicated herein, the material described in this section is not prior art to the claims in this application, and is not admitted to be prior art or an indication of prior art by inclusion in this section. Summary of the Invention [Means for solving the problem]

[0008] According to one aspect of the present disclosure, a system and method for blood flow simulation is disclosed.

[0009] For example, a computer-implemented 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 within a patient's vasculature or a geometry based on the patient's vasculature; generating a response surface based on results of the plurality of blood flow simulations that maps one or more first parameters of the first model to one or more second parameters of a reduced-order model of vascular blood flow having lower fidelity than that of the first model; determining values ​​for one or more parameters of the reduced-order model mapped from the parameter values ​​representing a modified state of the vasculature by the response surface; and performing a simulation of blood flow in the modified state of the vasculature using the reduced-order model parameterized by the determined values ​​for the one or more second parameters to determine blood flow characteristics of the modified state of the vasculature.

[0010] Additionally, the 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 vasculature of a patient or a geometry based on the patient's vasculature, generating a response surface based on results of the plurality of blood flow simulations that maps one or more first parameters of the first model to one or more second parameters of a reduced-order model of vascular blood flow having a lower fidelity than that of the first model, determining values ​​for one or more parameters of the reduced-order model mapped from the parameter values ​​representing a modified state of the vasculature by the response surface, and performing a simulation of blood flow in the modified state of the vasculature using the reduced-order model parameterized by the determined values ​​for the one or more second parameters to determine blood flow characteristics of the modified state of the vasculature.

[0011] Additionally, the non-transitory computer-readable medium stores instructions that, when executed by the one or more processors, cause the one or more processors to perform a method that 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 vasculature of a patient or a geometry based on the patient's vasculature, generating a response surface based on results of the plurality of blood flow simulations that maps one or more first parameters of the first model to one or more second parameters of a reduced-order model of vascular blood flow having a lower fidelity than that of the first model, determining values ​​for one or more parameters of the reduced-order model mapped from parameter values ​​representing a modified state of the vasculature by the response surface, and performing a simulation of blood flow in the modified state of the vasculature using the reduced-order model parameterized by the determined values ​​for the one or more second parameters to determine blood flow characteristics of the modified state of the vasculature.

[0012] Additional objects and advantages of the disclosed embodiments will be set forth in part in the description which follows, and in part will be obvious 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.

[0013] It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not limitations of the disclosed embodiments as claimed. The present specification also provides, for example, the following items: (Item 1) 1. A computer-implemented method for blood flow simulation, the method comprising: 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 within a patient's vasculature or a geometry based on the patient's vasculature; generating a response surface that maps one or more first parameters of the first model to one or more second parameters of a reduced-order model of vascular blood flow having a lower fidelity than that of the first model based on results of the plurality of blood flow simulations; determining values ​​for one or more parameters of the reduced order model mapped from parameter values ​​representing a modified state of the vasculature by the response surface; performing a simulation of blood flow in the modified state of the vasculature using a reduced order model parameterized by the determined values ​​for the one or more second parameters to determine blood flow characteristics of the modified state of the vasculature; A method comprising: (Item 2) the plurality of blood simulations are performed for a plurality of configurations, respectively; each of the plurality of configurations includes a value for the first parameter that represents at least an individual vascular geometry in which blood flow is simulated in the individual blood flow simulation; The plurality of configurations include: a first configuration representing the patient's vasculature; one or more further configurations, each of which represents a vascular geometry derived from the geometry of the vasculature and / or a physiological condition different from the physiological condition represented by the first configuration; The method according to item 1, comprising: (Item 3) receiving patient-specific image data of the patient's vasculature; generating a patient-specific anatomical model of the vasculature-based image; determining values ​​of the one or more first parameters for the first configuration to represent a patient-specific geometry of the vasculature based on the patient-specific anatomical model; The method according to item 2, further comprising: (Item 4) 3. The method of claim 2, wherein the one or more further configurations include one or more extreme configurations, each of which represents a state of the vasculature at an anatomical or physiological limit. (Item 5) the vascular system is at least a portion of a coronary artery of the patient; at least one of the one or more limit configurations represents a complete revascularization of at least a portion of the coronary artery; The method according to item 4. (Item 6) 5. The method of claim 4, wherein the one or more further configurations further include one or more configurations determined using sampling or quadrature techniques based on the one or more extreme configurations. (Item 7) the plurality of blood flow simulation results are first simulation results obtained for the plurality of configurations, respectively; each of the plurality of configurations includes a first value for the one or more first parameters; Generating the response surface comprises: determining, for each of the plurality of configurations, second values ​​for the one or more second parameters that, when used in a low-fidelity blood flow simulation performed using the reduced-order model, produce respective second simulation results that match the respective first simulation results; generating the response surface based on the first values ​​for the one or more first parameters and second values ​​determined for the one or more second parameters for each of the plurality of configurations; The method according to item 2, comprising: (Item 8) The response surface is a surface that is fitted to a set of points; each point in the set of points includes a determined value for the one or more second parameters determined for a respective one of the plurality of configurations. The method according to item 7. (Item 9) 2. The method of claim 1, wherein the vascular system comprises at least one of the coronary vascular system, the peripheral vascular system, the cerebral vascular system, the renal vascular system, the splanchnic vascular system, or the hepatic vascular system. (Item 10) the experimental blood flow simulation is performed in real time such that values ​​of the blood flow properties are determined in real time; The method further includes presenting the values ​​of the blood flow characteristics to a user in real time. The method according to item 1. (Item 11) 2. The method of claim 1, wherein the blood flow characteristic is fractional flow reserve. (Item 12) A computer system for blood flow simulation, comprising: A memory for storing instructions; one or more processors, the one or more processors comprising: 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 within a patient's vasculature or a geometry based on the patient's vasculature; generating a response surface that maps one or more first parameters of the first model to one or more second parameters of a reduced-order model of vascular blood flow having a lower fidelity than that of the first model based on results of the plurality of blood flow simulations; determining values ​​for one or more parameters of the reduced order model mapped from parameter values ​​representing a modified state of the vasculature by the response surface; performing a simulation of blood flow in the modified state of the vasculature using a reduced order model parameterized by the determined values ​​for the one or more second parameters to determine blood flow characteristics of the modified state of the vasculature; one or more processors configured to execute instructions for performing a method including: A computer system comprising: (Item 13) the plurality of blood simulations are performed for a plurality of configurations, respectively; each of the plurality of configurations includes a value for the first parameter that represents at least an individual vascular geometry in which blood flow is simulated in the individual blood flow simulation; The plurality of configurations include: a first configuration representing the patient's vasculature; one or more further configurations, each of which represents a vascular geometry derived from the geometry of the vasculature and / or a physiological condition different from the physiological condition represented by the first configuration; Item 13. The computer system of item 12, comprising: (Item 14) receiving patient-specific image data of the patient's vasculature; generating a patient-specific anatomical model of the vasculature-based image; determining values ​​of the one or more first parameters for the first configuration to represent a patient-specific geometry of the vasculature based on the patient-specific anatomical model; Item 14. The computer system of item 13, further comprising: (Item 15) 14. The computer system of claim 13, wherein the one or more further configurations include one or more extreme configurations each representing a state of the vasculature at an anatomical or physiological limit. (Item 16) the vascular system is at least a portion of a coronary artery of the patient; at least one of the one or more limit configurations represents a complete revascularization of at least a portion of the coronary artery; Item 16. The computer system according to item 15. (Item 17) 20. The computer system of claim 15, wherein the one or more further configurations further include one or more configurations determined using sampling or quadrature based on the one or more extreme configurations. (Item 18) the plurality of blood flow simulation results are first simulation results obtained for the plurality of configurations, respectively; each of the plurality of configurations includes a first value for the one or more first parameters; Generating the response surface comprises: determining, for each of the plurality of configurations, second values ​​for the one or more second parameters that, when used in a low-fidelity blood flow simulation performed using the reduced-order model, produce respective second simulation results that match the respective first simulation results; generating the response surface based on the first values ​​for the one or more first parameters and second values ​​determined for the one or more second parameters for each of the plurality of configurations; Item 14. The computer system of item 13, comprising: (Item 19) The response surface is a surface that is fitted to a set of points; each point in the set of points includes a determined value for the one or more second parameters determined for a respective one of the plurality of configurations. Item 19. The computer system of item 18. (Item 20) A non-transitory computer readable medium having instructions stored thereon that, when executed by one or more processors, cause the one or more processors to: 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 within a patient's vasculature or a geometry based on the patient's vasculature; generating a response surface that maps one or more first parameters of the first model to one or more second parameters of a reduced-order model of vascular blood flow having a lower fidelity than that of the first model based on results of the plurality of blood flow simulations; determining values ​​for one or more parameters of the reduced order model mapped from parameter values ​​representing a modified state of the vasculature by the response surface; performing a simulation of blood flow in the modified state of the vasculature using a reduced order model parameterized by the determined values ​​for the one or more second parameters to determine blood flow characteristics of the modified state of the vasculature; A non-transitory computer readable medium for carrying out a method comprising: [Brief description of the drawings]

[0014] 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.

[0015] [Figure 1]FIG. 1 depicts a flowchart of a method for estimating the behavior of a system using response surfaces, according to one or more embodiments.

[0016] [Figure 2A] FIG. 2A illustrates a method for generating a response surface based on a high-fidelity simulation, according to one or more embodiments.

[0017] [Figure 2B] FIG. 2B illustrates a method for predicting simulation results in real time based on a response surface generated using the method illustrated by FIG. 2A, according to one or more embodiments.

[0018] [Diagram 3] FIG. 3 is a flowchart illustrating a method for modeling the effects of varying lumen geometry and boundary conditions on blood flow simulations, according to one or more embodiments.

[0019] [Figure 4] FIG. 4 is a flowchart illustrating a method for modeling the effects of coronary revascularization, according to one or more embodiments.

[0020] [Diagram 5] 5-6 illustrate example implementations of the method of FIG. 4 according to one or more embodiments. [Figure 6] 5-6 illustrate example implementations of the method of FIG. 4 according to one or more embodiments.

[0021] [Figure 7] FIG. 7 illustrates an environment in which a computer system for performing the methods of the present disclosure may be implemented, according to one or more embodiments. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0022] 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 arbitrary accuracy compared to the accuracy of high-fidelity models. High-fidelity models of physical systems may be computationally expensive. Thus, high-fidelity models may be unsuitable or impractical for real-time simulation. On the other hand, reduced-order models may have lower computational complexity than that of high-fidelity models. Thus, reduced-order models may run more quickly, making them more suitable for real-time simulation.

[0023] To use a reduced-order model for real-time simulation while achieving arbitrary accuracy, a high-fidelity simulation using a high-fidelity model may be performed for a set of configurations. The results of the high-fidelity simulation may then be used to parameterize the reduced-order model. As will be explained in more detail below, the reduced-order model may be parameterized using response surface methodology in accordance with the present disclosure. In this methodology, the results of the high-fidelity simulation performed for the set of configurations described above may be used to generate a response surface, which may be a mapping of parameters of the high-fidelity model and the reduced-order model. The response surface may then be used to parameterize the reduced-order model.

[0024] 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 arbitrarily close to that 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. Thus, the accuracy of the reduced-order model and reduced-order modeling may be adjusted by increasing or otherwise adjusting the configurations used to generate the response surface. For example, refining the response surface may ensure that the simulation using the reduced-order model has an accuracy within a certain tolerance. In addition, because the high-fidelity simulation used to generate the response surface may be computationally expensive, the high-fidelity simulation may be performed offline prior to performing a real-time simulation using the reduced-order model.

[0025] The disclosed methods may enable rapid prediction of the behavior of complex systems, such as changes in hemodynamics in response to changes in patient condition. Such changes in patient condition may be natural or planned (e.g., procedural). For example, in some embodiments, the disclosed methods may be used to generate real-time updates of FFRCT in response to changes in vascular lumen geometry. This change in vascular lumen geometry may be, for example, a natural change or a change expected to occur as a result of a candidate therapy.

[0026] In the following description, the embodiments of the present disclosure will be described in more detail with reference to the accompanying drawings. The terminology used below may be interpreted in its broadest reasonable manner, even when combined with the detailed description of certain specific examples of the present disclosure. In fact, certain terms may be further emphasized below. However, any terminology intended to be interpreted in any limited manner will be so clearly and specifically defined in the section for implementing the invention. Both the general description above and the detailed description below are merely illustrative and explanatory, and are not limitations of the features as claimed.

[0027] In this disclosure, the term "based on" means "based at least in part on." The singular forms "a," "an," and "the" include plural references unless otherwise dictated by context. The term "exemplary" is used in the sense of "example" rather than "ideal." The terms "comprises," "comprising," "includes," "including," or other variations thereof are intended to cover a non-exclusive inclusion, such that a process, method, or product that comprises a list of elements does not necessarily include only those elements, but may also 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 possible variations of ±10% of the stated or understood value.

[0028] In this disclosure, a reduced-order model may also be referred to as a low-fidelity model or a high-speed model. A reduced-order model usable for real-time simulation may also be referred to as a real-time model. Furthermore, where the context permits, the reduced-order model and the high-fidelity model may be general models that may be parameterized using different parameter values, such as different values ​​corresponding to different configurations. In general, the term "parameter" may refer to any type of parameter, including boundary conditions.

[0029] In the following description, a methodology for fast simulation of partial differential equations is provided. First, for the purpose of constructing and parameterizing a reduced-order model for fast prediction of the behavior of a complex system, it is noted that the following may be assumed: (i) a high-fidelity model that performs well for the system under consideration exists; (ii) information related 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) based on the information in (i) and (ii), an offline calculation can be performed, which may not be as fast as a solution using a reduced-order method. However, it should be understood that the method of the present disclosure may be practiced independently of the aforementioned assumptions, and the assumptions are presented here for illustrative purposes only.

[0030] Let a general partial differential equation be of the form [ka] With the following boundary conditions: [ka] where L is an operator (e.g., a differential, integral, function, or a combination thereof), u is an unknown, and x N denotes the problem dimension, p denotes a given parameter, [ka] is the problem domain, [ka] denotes the boundary of the region. Equations (1) and (2) may represent a system and serve as a high-fidelity model of the system.

[0031] A reduced-order model of a partial differential equation is a model of a system of dimensions x that uses simpler operators (e.g., ordinary differential equations) to approximate the operator L. NLet x be the reduced-order model in which the observation of the simulation results is focused. n and / or the parameter set p [ka] The reduced order model can be expressed as: [ka] With the following boundary conditions: [ka]

[0032] The goal is, [ka] u(x N ) with a reasonable approximation of x N x n A general approach is to solve various boundary regions so that the response surface can be used to generate an accurate approximation to the problem. [ka] , the boundary conditions b(.), and the parameters, as originally formulated by equations (1) and (2). Such a simulation of the system may be referred to as a high-fidelity simulation.

[0033] For the purposes of generating response surfaces, the domain [ka] may have bounds as expressed below: [ka] The boundary conditions to which the system will comply may have the bounds as expressed below. [ka] Furthermore, the parameter space may have bounds as expressed below: [ka]

[0034] The original fundamental equations can be solved for a set of domains and boundary conditions. [ka] where M is the number of high fidelity simulations to be performed. Each of the M terms represented above may correspond to a configuration for which the high fidelity simulations should be performed. That is, the M terms may represent M configurations.

[0035] In general, a "configuration" may refer to any modeling or simulation configuration and may include any parameters (and their values). A configuration may be a collection of values ​​for such parameters. In the above formula, each of the M configurations is represented by b(.), [ka] , and / or a set of values ​​for the parameters of p. The concept represented by a particular configuration may depend on the system being modeled. For example, if the system is blood flow through a patient's arteries, the configuration may represent a certain lumen geometry, a certain physiological state of the patient, or a combination thereof.

[0036] In general, any suitable method, such as sampling or quadrature methods, may be used in selecting the M configurations. The results of the high-fidelity simulation for the M configurations may be expressed as follows: [ka]

[0037] The response surface R can be a mapping of the parameters of the high-fidelity model and the reduced-order model. [ka] During the ceremony, [ka] captures the complexity of the original equation, [ka] This may allow for R to be a less complicated operator than L. The response surface R may be obtained by any suitable method. If R uses point-fitted polynomials, such as Lagrange polynomials, then the reduced-order model may be obtained by: [ka] That is, a reduced-order model can be constructed to exactly match the output of the high-fidelity model for the M configurations. This approach allows a computer to solve the following problem faster while ensuring the results are the same across the M configurations: [ka] The approximation in terms of high fidelity results between configurations will generally be better for larger M, but so will the time required for offline computation.

[0038] In general, a high-fidelity model may include any number of mathematical relations. Thus, a high-fidelity model may include multiple different mathematical relations of the form given by equation (1) described above, and may also include other mathematical relations. Similarly, a reduced-order model may have multiple mathematical relations, and may have multiple different mathematical relations of the form given by equation (3) described above. In general, a high-fidelity simulation may utilize all information available about the system (e.g., a full spatial and temporal representation), and the high-fidelity model used for the simulation may include any number of full-order foundation equations.

[0039] A response surface, such as response surface R, can be a mathematical relationship between a quantity or quantities or parameters of interest and underlying variables. A response surface can be a function (e.g., a fitness function) that maps 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 the response surface explores parameter space using a reduced-order model. Depending on the application or implementation, there can be multiple response surfaces. Different response surfaces can map between different individual parameters of the high-fidelity and reduced-order models.

[0040] FIG. 1 is a flow chart illustrating a method for estimating the behavior of a system using response surfaces, in accordance with one or more embodiments.

[0041] Step 101 may include performing a number of simulations using a first model of the system, which may be a high-fidelity model as described in this disclosure.

[0042] In some embodiments, the first model may be a high-fidelity model of vascular blood flow and the simulation may be a blood simulation that simulates blood flow in a patient's vasculature or a vascular geometry based on the patient's vasculature (e.g., a derived vasculature determined based on the patient's vasculature). The term "patient's vasculature" may refer to vasculature in any part of a patient's body. Examples of vasculature include, but are not limited to, coronary vasculature, peripheral vasculature, cerebral vasculature, renal vasculature, endocrine vasculature, and endovascular vasculature. Viscera The derived vasculature may be, for example, a hypothetical vasculature, with hypothetical modifications to the patient's vasculature.

[0043] Although various embodiments relating to blood flow are described in this disclosure, this disclosure is not limited to simulating blood flow. In general, the formulas and techniques described in this disclosure, including those described with respect to simulating blood flow, may be applied or generalized to other complex systems, including systems that may be characterized using computational fluid dynamics.

[0044] Step 102 may include generating a response surface based on the simulation results obtained from step 101, mapping parameters of the first model to parameters of a second model having a lower fidelity than that of the first model. The second model may be a model having a lower fidelity than that of the first model, such as a reduced-order model as described in this disclosure. Since the first model and the second model may be a high-fidelity model and a reduced-order model, respectively, as described above, the response surface may be a mapping of parameters of the high-fidelity model and parameters of the reduced-order model. This mapping may be a function whose output is a value for the parameter of the reduced-order model and whose input is the value of the parameter of the high-fidelity model.

[0045] Step 103 may include determining values ​​for parameters of the second model mapped from the parameter values ​​of the configuration to be analyzed by the response surface. The parameter values ​​of the configuration to be analyzed may be values ​​for said parameters of the first model. In some embodiments, the first model may be a set of differential equations. Thus, the parameter values ​​of the configuration to be analyzed may be values ​​of parameters (including boundary conditions) used in such differential equations. The values ​​for the second parameters may be determined by the response surface as a function of the parameter values ​​of the configuration to be analyzed.

[0046] Step 104 may include performing a simulation using the second model parameterized by the determined values ​​of the parameters of the second model. For example, in the above-described embodiment of blood flow simulation, the parameter values ​​for the configuration to be analyzed in step 103 may represent a modified state (e.g., modified anatomical and / or physiological state) of the patient's vasculature, in which case step 104 may determine blood flow characteristics of the modified state of the vasculature. The simulation may be performed in real time. The blood flow characteristics may be fractional flow reserve (FFR), blood flow magnitude, blood flow direction.

[0047] 2A illustrates a method for generating a response surface based on a high-fidelity simulation. The method of FIG. 2A illustrates an example implementation of the portions of the method of FIG.

[0048] 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 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 ranges of values ​​for the aforementioned parameters of the information received in step 201, which may be manually entered by a user or automatically determined by a process executed on a computer system.

[0049] Step 202 may include identifying configurations 220 for the high fidelity simulation. The configurations 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, the configurations 220 identified in step 202 may be a sample of configurations within the range of configurations. Examples of sampling and quadrature techniques are discussed below in connection with the method of FIG. 3. The configurations 220 may be identified automatically or based on user input.

[0050] Step 203 may include performing a high-fidelity simulation on the identified configurations for the high-fidelity simulation. The configurations 220 identified in step 202 may be input into a high-fidelity model, and the high-fidelity simulation may be performed using the high-fidelity model parameterized according to parameter values ​​specified in the configurations 220.

[0051] Step 204 may include deriving parameters of the reduced-order model. The parameters derived in step 204 may be derived based on the results of a high-fidelity simulation performed using the configuration 220 identified in step 202 and the high-fidelity model.

[0052] Step 205 may include generating a response surface 224. As explained above, the response surface may be a mapping of parameters of the high-fidelity model and the reduced-order model. Results of a simulation using parameters of the high-fidelity model and the reduced-order model may define a correspondence between values ​​of the parameters of the high-fidelity model and values ​​of the parameters of the reduced-order model. Such 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 that is fitted to the points 222. The response surface may have an exact fit in that the surface 224 includes (intersects) all of the points 222, as illustrated in FIG. 2A. However, that is not a requirement. Whether the surface 224 includes all of the points 222 may depend on the functional form of the surface 224. As mentioned above, Lagrange polynomials may be used for the exact fit. In other fitting methods, it is possible that surface 224 includes only some of points 223 or none of points 223 .

[0053] 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 result as the reduced-order model produces for the same result in a high-fidelity simulation. For example, the N configurations for the high-fidelity simulation may be [ka] , where such parameter values ​​are used to determine the u1, u2, ... u N If this results in: [ka] The same results are obtained in the simulation using the reduced order model. N Such as to bring about [ka] Therefore, the set of points 222 can be [ka] and a response surface 224 may be generated as a surface fitted to these points. Such a response surface may thus provide the mapping relationship as described above in connection with equation (10).

[0054] Step 206 may include assessing the accuracy of the response surface 224. Step 207 may determine, based on the accuracy assessed in step 206, whether the response surface 224 should be refined to have greater accuracy.

[0055] The accuracy of the response surface may be defined by any suitable criteria. In some embodiments, the accuracy may be a measure of the accuracy in replicating the results of a high-fidelity simulation. For example, the accuracy may be based on the closeness of reduced-order modeling results when using the response surface 224 to parameterize a reduced-order model for one or more test configurations 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 that differ from the configurations represented by points 222 based on which the response surface 224 was generated.

[0056] Step 207 may terminate with a "yes" if the accuracy of the response surface 224 assessed in step 206 is insufficient (e.g., does not satisfy a predefined threshold condition) and may terminate with a "no" if the accuracy of the response surface 224 is assessed to be sufficient (e.g., satisfies a predefined threshold). In the present context, accuracy may refer, for example, to the accuracy of a reduced-order model with respect to an arbitrarily defined configuration.

[0057] If step 207 ends in "Yes" (e.g., the accuracy is insufficient), the method shown in FIG. 2A may proceed to step 208, which may include refining the configurations for the high fidelity simulation. The process of refining the configurations may include adding new configurations for the high fidelity simulation, removing existing configurations, and / or adjusting values ​​of existing configurations. For example, as shown in FIG. 2A, additional configurations may be added to the originally identified configurations 220 to obtain a refined set of configurations 220A, improving the accuracy of the response surface 224. Simulations using the high fidelity model (step 203) may be performed for any newly added configurations such that the resulting response surface 224 is updated.

[0058] The determination of step 207 may implement an iterative process in which configurations for high fidelity simulation are refined (e.g., increased) in each subsequent iteration until the response surface 224 reaches sufficient accuracy. Each configuration for which high fidelity simulation is performed in step 203 may result in a corresponding point 222. Thus, by adding additional configurations, the number of points 222 may be increased. The response surface 224 may then be adapted to the increased number of points 222, potentially resulting in better accuracy.

[0059] Once the response surface 224 reaches a sufficient degree of accuracy, step 207 may terminate with a "No" and the response surface 224 may then be accepted as the final response surface 224A. As shown in Figure 2, the points 222A, which may also be referred to as control points, of the final response surface 224A may be more numerous than the points 222 of the initial response surface 224. The final response surface 224A may also serve as an example of the aforementioned response surface R, where the set of configurations used to generate the final response surface 224A would serve as an example of the aforementioned set of M configurations.

[0060] 2A may be computationally expensive depending on the time it takes to perform high-fidelity simulations for all configurations for which high-fidelity simulations are performed. Thus, 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.

[0061] Figure 2B illustrates a method for predicting simulation results in real time based on a response surface 224A generated using the method of Figure 2 A. The method of Figure 2B illustrates an example implementation of the portions of the method of Figure 1 corresponding to steps 103 and 104.

[0062] 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 a set of experiments to be performed via reduced order simulation. In this disclosure, the terms "configuration to be analyzed" and "configuration to be explored" are used synonymously.

[0063] Step 242 may include exploring the response surface. The exploration process may involve selecting values ​​of parameters of the reduced model for the configuration to be analyzed (e.g., a parameter set [ka] The probing process is illustrated using points 250, which represent values ​​of parameters for the reduced order model for the configuration to be analyzed. As shown, points 250 may be points that are mapped from the configuration to be analyzed. For example, the configuration to be analyzed may be a set of points that are mapped from the reduced order model for the parameters p, b, and [ka] and the response surface may have values ​​of p, b, and [ka] as a function of their values ​​of [ka] That is, point 250 may be determined as [ka] , and may have positions on the response surface 224A corresponding to the aforementioned values ​​of p, b, [ka] teeth, [ka] may represent a location having a determined value of . Because locations on response surface 224A may be interpolated from the locations of points 224A, the location of point 250 may therefore be at the interpolated location.

[0064] Step 243 may include solving a reduced order model using the mapping provided by response surface 225. Step 204 may include solving equation (11), as described above. Steps 242 and 243 may be performed in real time, as part of a real time simulation.

[0065] Step 244 may include generating and reporting 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 the solution of the reduced-order model may be a real-time process, the results of the reduced-order model may also be presented in real-time.

[0066] Thus, predicting the behavior of a complex system may include a first process of generating a response surface, as described in connection with FIG. 2A, and a second process of rapid exploration of the response surface to estimate the outcome (e.g., hemodynamic index) for a particular configuration, as described above in connection with FIG. 2B. As mentioned above, the first process of constructing the response surface is performed offline and may be computationally expensive depending on the time it takes to perform a high-fidelity simulation using the high-fidelity model. The computational cost may depend on the acceptable error for the second process.

[0067] Figures 3 and 4 illustrate further examples in which the techniques described above are applied. Figure 3 is a flow chart illustrating a method for modeling the effect of changing lumen geometry and boundary conditions on blood flow (e.g., coronary artery flow) simulation. The method may be applied to 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 may be, for example, the lumen geometry and / or physiological condition of a patient. The method of Figure 3 may be implemented by any suitable computer system.

[0068] Step 301 may include receiving anatomical information describing the patient's vasculature. The described vasculature may include all of the patient's arteries of interest. In some embodiments, the vasculature may be the coronary vasculature, in which case the anatomical information may describe the patient's coronary arteries. As described above in connection with FIG. 1, examples of other types of vasculature include, but are not limited to, peripheral vasculature, cerebral vasculature, renal vasculature, endovascular vasculature, and endovascular vasculature. Viscera The hepatic vascular system includes the vascular system, such as the portal vein, and the hepatic vascular system.

[0069] The anatomical information may be received from the memory (e.g., a hard drive or other electronic storage device) of the computer system performing step 301, or from another computer system (e.g., a physician's or third party provider's computer system) via a computer network.

[0070] In some embodiments, the anatomical information may include one or more images of the patient obtained using an imaging or scanning modality and / or information extracted from (or otherwise obtained based on an analysis of) such images of the patient. Examples of imaging or scanning modalities include computed tomography (CT) scanning, magnetic resonance (MR) imaging, micro-computed tomography (μCT) scanning, micro-magnetic resonance (μMR) imaging, dual-energy computed tomography scanning, ultrasound imaging, single photon emission computed tomography (SPECT) scanning, and positron emission tomography (PET) scanning. 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 describe the specific anatomical and physiological characteristics of the patient, any model derived from or built based on such images or other patient-specific information may be considered a patient-specific model. It should be noted that the use of the term "patient" is not intended to be limiting. "Patient" may be referred to collectively as "person."

[0071] Step 302 may include generating an anatomical model of the vasculature based on the anatomical information received in step 301. The anatomical model may be of any suitable form and may model any suitable aspect of the vasculature. For example, the anatomical model may describe the patient-specific three-dimensional geometry of the vessels of the vasculature as determined 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 vasculature. The anatomical model of the vasculature 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 vasculature under one or more physiological conditions of the patient. In such embodiments, the characteristics of the anatomical model may reflect characteristics of the vasculature when the patient is in a physiological state (e.g., at rest or in an exercise state).

[0072] Examples of methods for generating anatomical models are described, for example, in Taylor, US 2012 / 0041739 A1 ("US '739"), which is incorporated by reference in its entirety. Note that US '739 also provides examples of reduced order models and other aspects discussed in this disclosure, such as calculation of fractional flow reserve (FFR).

[0073] Steps 301 and 302 may be performed by the same computer system that performs the remaining steps 304-307 described below. However, steps 301 and 302 can also be performed by a separate computer system, in which case the anatomical model is provided via a communications network to the computer system that performs the remaining steps. Any anatomical model received via the communications network may be stored in the memory of the computer system.

[0074] 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 the flow of blood in an artery as modeled by the anatomical model. The high-fidelity simulation may involve detailed mathematical relationships that describe the system. Such mathematical relationships may include partial differential equations, such as the Navier-Stokes equations in any suitable formulation. The high-fidelity simulation may be performed using 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 that is executed to perform the high-fidelity simulation.

[0075] For example, the detailed mathematical relationships may include Navier-Stokes equations with boundary conditions and / or other parameters derived from an anatomical model, which may represent, for example, the geometry or other properties of the arteries as modeled by the anatomical model.

[0076] Step 304 may include performing a high-fidelity simulation on the extremes of the configurations to be searched for. Such a simulation may be a blood flow simulation that simulates the flow of blood in the structures represented by the extremes of the configurations to be searched for.

[0077] In the present context, the configuration to be explored may be any configuration that is intended to be explored (e.g., simulated or otherwise studied) using the reduced-order simulation described below. The extremes of the configuration to be explored may depend on the extremes of the parameter space and the domain that can be explored using the reduced-order model. Boundaries may be imposed based on the limits of the search. Such boundaries may be application specific. It is noted that the extremes of the configuration to be explored as described above may be configurations for the purpose of generating a response surface and may also be referred to as extreme configurations.

[0078] In some embodiments, one or more boundaries may be imposed based on anatomical limitations. For example, an upper bound on an anatomical model may be imposed based on a maximum allowable dilation for a patient-specific model. In this case, the patient-specific model may model the relief of luminal stenosis in various locations, the effect of applying higher levels of nitrates, or a combination thereof. The maximum allowable dilation in such a treatment situation may be represented as an upper bound on an anatomical model. In some embodiments, one or more boundaries imposed based on anatomical limitations may represent the addition or removal of vessels. For example, in the case of a bypass graft, the upper bound may be the maximum number of anastomoses based on the available graft.

[0079] Additionally or alternatively, one or more boundaries may be imposed based on physiological limits. For example, to assess different physiological states of the patient, upper and / or lower bounds may be assessed based on resting and exercise conditions, or other extremes of boundary conditions. For example, an upper (or lower) bound may represent the patient's resting state, and a lower (or upper) bound may represent the patient's exercise state.

[0080] Step 305 may include identifying one or more configurations for which a high-fidelity simulation is to be performed and performing the high-fidelity simulation on the one or more identified configurations. Note that step 305 serves as an example of steps 202 and 203 discussed above in connection with the method of FIG. 2A.

[0081] The larger the set of parameters and regions, the better the accuracy of the response surface and the accuracy of the real-time prediction. Any sampling or quadrature method may 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 adequate in sampling large dimensional parameter spaces, but may converge very slowly for problems with moderate dimensional parameter spaces. Latin hypercube sampling may achieve separation of the parameter space and may converge better than Monte-Carlo for moderate dimensional parameter spaces. In Gaussian quadrature, Gaussian points may be used to generate the configurations, and tensor product interpolation may be used to scale the points to higher dimensions. Sparse grid quadrature may be identical to Gaussian quadrature for one dimension, but may have a sparse grid to reduce the number of simulations. The adaptive sparse grid quadrature method may be identical to the sparse grid quadrature method, but may fit a function such that regions of shallow variation are sought below regions of significant variation.

[0082] After identifying one or more configurations on which the high-fidelity simulation is to be performed, step 305 may further include performing the high-fidelity simulation on the one or more identified configurations.

[0083] Step 306 may include generating a response surface based on the high-fidelity simulation solution. As described above, the response surface may be created based on the high-fidelity solutions in multiple configurations (e.g., M configurations) using any functional form. In the context of FIG. 3, the M configurations referred to in the preceding discussion may include any of the configurations identified in step 305 and may also include any of the configurations simulated in step 303 and / or step 304. Local linear or Lagrange polynomial interpolation may be performed to ensure that the real-time simulation solution at the control points matches the full simulation solution. In general, step 306 may utilize any of the techniques described above in connection with steps 204, 205, 206, and 208 of FIG. 2A.

[0084] In some embodiments, multiple response surfaces may be generated. For example, if the high-fidelity simulation involves multiple mathematical relationships (e.g., mathematical relationships in the form of Equation (1)) and / or the reduced-order model includes multiple mathematical relationships (e.g., mathematical relationships in the form of Equation (3)), multiple response surfaces may be generated to map between different combinations of high-fidelity and reduced-order mathematical relationships. Additionally, the response surface of step 306 may be revised by refining the configuration used to generate the response surface, as described above in connection with FIG. 1.

[0085] Step 307 may include performing a reduced order simulation based on the response surface. The reduced order simulation may be informed by an interpolant estimated by the response surface. For example, as described above in connection with FIG. 2B, the response surface may be explored based on one or more configurations to be explored to obtain an interpolant. The one or more configurations to be explored may depend on the application of the method.

[0086] The reduced-order simulation may be performed using a reduced-order model that may be constructed to accurately match the output of the high-fidelity model for the M configurations for which the high-fidelity simulation was performed. The reduced-order simulation may be performed in real time.

[0087] The method of Figure 3 may include any one or more of the additional exemplary aspects described below, all of which are optional. These aspects may be implemented in one or more steps of the methods described above or as additional steps of the methods.

[0088] In some examples, the method of FIG. 3 may include a step of quantifying a confidence interval. For example, the response surface created in step 306 may be explored to launch a number of simulations from which confidence interval estimates for the unknown field may be calculated. For purposes of quantifying the confidence interval, the configurations to be explored may include any configuration suitable for quantifying a confidence interval. For example, the configurations may represent configurations on which reduced-order modeling is intended to be performed. The confidence interval estimates may be used, for example, to assist a clinician performing a reduced-order simulation in understanding the accuracy of the reduced-order model when performing a similar type of simulation. Alternatively, the confidence interval estimates may be used to revise the response surface generated in step 306.

[0089] In some examples, the method of FIG. 3 may include a step of modeling disease progression and / or regression. For example, the response surfaces generated in step 306 may also be explored to predict the impact of lesions, which may progress or regress. These may then be used for patient management and monitoring. The configurations to be explored may include any configurations suitable for modeling or simulating disease progression and / or regression.

[0090] In some examples, the method of Figure 3 may include modeling of different physiological conditions. For example, the response surface generated in step 306 may also be explored to model different physiological conditions (e.g., resting and exercise conditions) or the effects of pharmacological agents. The configurations to be explored may include any configurations suitable for modeling or simulating physical conditions.

[0091] Although the method of FIG. 3 is described for one application relating to blood flow, the techniques described with respect to the method of FIG. 3 may be applied to other complex systems, including other fluid dynamic systems.

[0092] FIG. 4 is a flow chart illustrating a method for modeling the effect of coronary revascularization. The method may apply various techniques described above to perform real-time calculation of the effect of coronary revascularization on blood flow. Exemplary implementations of the method of FIG. 4 are illustrated by FIGS. 5-6, also discussed below. The methods of FIG. 4-6 may be implemented by any suitable computer system.

[0093] Step 401 may include receiving anatomical information describing the patient's coronary arteries. Step 401 may include any of the aspects of step 301 described above. In some embodiments, step 401 may include receiving anatomical information obtained from analysis of a coronary CT scan. For example, as shown in FIG. 5, anatomical information describing the patient's anatomical characteristics, such as vessel centerlines and lumens, may be extracted from a CCTA image 502 obtained from the patient.

[0094] 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 artery may have a narrowed lumen and the modified patient model may represent a complete revascularization of the coronary artery.

[0095] The base patient model may be an anatomical model that models the actual anatomical characteristics (e.g., vessel centerlines and lumens) of the patient's coronary arteries as described by the anatomical information. For example, as shown in FIG. 5, the base patient model 503 may be generated based on the vessel centerlines and lumens extracted from the CCTA images 502. In FIG. 5, the base patient model 503 is illustrated as having stenotic geometries at various locations 503A, 503B, and 503C of the model. The stenotic geometries may, for example, model stenosis at corresponding locations of the patient's coronary arteries.

[0096] The modified patient model may be a base patient model that has been modified to model changes in the characteristics of the patient's coronary arteries. For example, the modified patient model may model hypothetical conditions of the patient's coronary arteries. Such conditions may be idealized conditions, for example, corresponding to extremes of the configuration to be explored, in which case the modified patient model may be referred to as an idealized model. In FIG. 5, the idealized model 504 is an example of a modified patient model that models the coronary arteries under conditions in which the entire anatomical structure represented by the base patient model is revascularized. For example, as shown in FIG. 5, stenosis at locations 503A, 503B, and 503C of the base patient model 503 is not represented by the idealized model 504. In such an embodiment, the modified patient model may be a revascularized anatomical model.

[0097] Step 403 may include performing a high-fidelity simulation of blood flow using boundary conditions obtained based on a patient model, simulating the effect of adenosine on hyperemia, and obtaining a first high-fidelity solution. In general, the boundary conditions in step 403 may be boundary conditions derived from patient characteristics such as the patient's anatomy, myocardium, scaling laws for resting blood flow, etc. Such boundary conditions may include boundary conditions obtained based on (e.g., derived from) a patient model. However, the disclosure is not so limited, and it is also contemplated that some or all of the boundary conditions may be derived from other models or information.

[0098] The high-fidelity simulation of step 403 may be performed by constructing a computational model in the form of a high-fidelity model. The computational model may include mathematical relationships, such as the Navier-Stokes equations, and boundary conditions derived from scaling laws for the patient's anatomy, myocardium, and resting blood flow. Such boundary conditions may simulate the effect of adenosine on hyperemia. Thus, to perform the high-fidelity simulation, the computer system performing step 403 may solve the Navier-Stokes equations for the coronary arteries using the aforementioned boundary conditions.

[0099] 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. In general, the high-fidelity simulation of step 404 may be performed on an extreme value corresponding to a configuration in which the coronary artery is fully revascularized. Such an extreme value serves as an example of an extreme value of the configuration to be explored as described above in connection with step 304 of FIG. 3. The revascularization may be one in which the entire anatomical structure of the patient-specific geometry is revascularized. The high-fidelity simulation of step 404 may be performed using a computational model constructed as a high-fidelity model, which may include boundary conditions derived from the modified patient model as described above. The computational model of step 403 and the computational model of step 404 may be based on the same mathematical relationships, but different boundary conditions and / or other parameters are applied.

[0100] Step 405 may include performing additional high-fidelity simulations of blood flow at different flow rates for each of the baseline 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 high-fidelity simulations performed in the same or substantially the same manner (e.g., using boundary conditions based on the baseline patient model), but with flow rates higher than said first flow rate (e.g., 10%, 15%, 25%, 50%, or 75% higher). 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 high fidelity simulations performed in the same or substantially the same manner (e.g., using boundary conditions based on the modified patient model), but with a flow rate higher than the second flow rate (e.g., 10%, 15%, 25%, 50%, or 75% higher). By performing additional simulations at different flow rates, the high fidelity solutions obtained across steps 403-405 may be used to inform a reduced-order model in which the flow resistance parameters depend on the flow rate. Using one additional simulation in each of the configurations associated with the base patient model and the modified patient model, respectively, the flow resistance in the reduced-order model may depend linearly on the flow rate.

[0101] Step 406 may include generating a response surface for the intercept and slope of the fluid resistance function, respectively. The response surface 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 one-dimensional Navier-Stokes equations. The first response surface is a function of the form 1 / r 4The second response surface may have a functional form for the slope (dA / dz * 1 / r 6 ) where 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. Thus, any of the techniques described in connection with step 306 are applicable to step 406.

[0102] Step 407 may include receiving a modified geometry. The modified geometry may be a geometry to undergo reduced-order simulation, for example, a revascularized geometry including the locations where coronary arteries should be revascularized and the final size of the vessel lumen. The revascularized geometry may be a simulation input defined by a user input or by a simulation process. One or more configurations for reduced-order modeling and simulation may be defined based on the revascularized geometry. For example, values ​​of attributes of the revascularized geometry, such as values ​​of the revascularization locations and / or values ​​of the final size of the vessel lumen, may serve as a configuration or part of a configuration. Such a configuration may be used on the response surface to obtain parameters of a reduced-order model, which are used in step 408 described below.

[0103] 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 an interpolation estimated using the response surface 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 a mathematical relationship in the form of equations (3) and (4) and may be constructed to yield the same results as the high-fidelity models of process 510 for the four high fidelities. It is noted that step 408 is an example of step 307 described above. Thus, the techniques described in connection with step 307 are generally applicable to step 408.

[0104] The output of the low fidelity simulation may be used to output updated flow rate, blood pressure, FFR, or any other quantity of interest for the configuration in step 403, such as wall shear stress.

[0105] In the illustration of FIG. 5, process 510 serves as an example of a high fidelity simulation of steps 403-405. As shown in FIG. 5, four Navier-Stokes simulations may be performed. These simulations may include a first Navier-Stokes simulation using hyperemic boundary conditions applied based on an idealized model 504, a second Navier-Stokes simulation using condensed boundary conditions applied based on an idealized model 504, a third Navier-Stokes simulation using condensed boundary conditions applied based on an underlying patient model 503, and a fourth Navier-Stokes simulation using condensed boundary conditions applied based on an underlying patient model 503. It should be noted that the aforementioned boundary conditions serve as an example of simulation parameters, and that the individual simulation parameters of the four simulations may differ from each other in aspects other than the aforementioned boundary conditions.

[0106] The four sets of simulation parameters applied to the Navier-Stokes simulation may each result in four high-fidelity solutions, as described above in connection with step 406 of FIG. 4. The four high-fidelity solutions may then be used to construct a response surface (step 520), which process may include deriving parameters of a reduced-order model. Item 504 in FIG. 4 is a visual depiction of the parameters of the reduced-order model. The reduced-order model may be a reduced-order model having a mathematical relationship in the form of equations (3) and (4), and may be constructed such that the reduced-order model produces the same results as the high-fidelity model of process 510 for the four high-fidelity simulations.

[0107] FIG. 6 illustrates the steps of exploring a response surface for reduced-order modeling. As shown, the response surface may be explored based on a configuration represented by modified geometry 601. Modified geometry 601 may be a revascularized geometry as described above with respect to step 407, and may be representable in graphical form, such as a three-dimensional graphical model (e.g., a surface mesh), as shown in FIG. 6. Modified geometry 601 may be an anatomical model and may represent a particular anatomical geometry to be explored or analyzed by the simulation, which may be, for example, a patient condition, either natural or planned. Modified geometry 601 may differ from idealization 505.

[0108] Exploration of the response surface may obtain values ​​for the parameters of the reduced order model. The reduced order model may be executed to obtain a hemodynamic solution. In process 610, the hemodynamic solution may be displayed graphically along with a three-dimensional graphical model of the modified geometry 601. For example, the hemodynamic solution may be represented in graphical form, and a graphic of the hemodynamic solution may be overlaid or otherwise combined with the three-dimensional graphical model of the modified geometry 610 to obtain a mapped model 602. The mapped model 602 may be displayed, for example, on an electronic display. Such display may be performed in real time.

[0109] The methods described in this disclosure may have a variety of clinical applications, including planning percutaneous coronary intervention (PCI) procedures, planning bypass graft surgery, modeling disease progression and regression of lesions, modeling positive and negative remodeling of lesions, sensitivity analysis, quantification of uncertainty and / or estimation of confidence intervals for flow simulations, modeling different physiological conditions such as exercise, modeling the effects of drugs, altitude, or autoregulatory mechanisms.

[0110] In some embodiments, the methods described in this disclosure may be used to generate real-time updates of fractional flow reserve (FFR) (e.g., fractional flow reserve derived from computed tomography (FFRCT)) in response to changes in the patient's vascular lumen geometry. This change in vascular lumen geometry may be a natural change or a change expected to occur as a result of a candidate treatment for the patient. For example, the lumen geometry may be represented as one or more parameters, and a user or the simulation process may adjust values ​​of such parameters to reflect changes in the vascular lumen geometry. In response to adjustments of the modeling parameters, a computer system performing the simulation may identify configurations for reduced-order modeling, explore a response surface based on the configurations, parameterize the reduced-order model, solve the reduced-order model, and calculate values ​​of the FFRCT. The response surface may have been generated prior to the simulation according to methods described in this disclosure (e.g., FIGS. 3 and 4). The calculated values ​​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 or another portion of the patient's vasculature.

[0111] Any methods discussed in this disclosure that are understood to be computer-implemented, including the methods illustrated in Figures 2-6 and any calculations described in connection with Equations (1)-(11), may be performed by one or more processors of a computer system. Method steps that are performed by one or more processors may also be referred to as operations.

[0112] 7 depicts an example of an environment in which such a computer system may be implemented as a server system 740. In addition to the server system 740, the environment of FIG. 7 further includes a number of physicians 720 and third party providers 730, any of which may be connected to an electronic network 710, such as the Internet, through one or more computers, servers, and / or handheld mobile devices. In FIG. 1, physicians 720 and third party providers 730 may represent computer systems and institutions that use such systems, respectively. For example, physicians 720 may be a hospital or a hospital's computer system.

[0113] The physician 720 and / or third party provider 730 may create or otherwise obtain medical images, such as images of one or more patients' cardiac, vascular, and / or organ systems. The physician 720 and / or third party provider 730 may also obtain any combination of patient-specific information, such as age, medical history, blood pressure, blood viscosity, anatomical information, and other types of patient-specific information, as described above in connection with step 301 of the method of FIG. 3. The physician 720 and / or third party provider 730 may transmit the patient-specific information to the server system 740 via the electronic network 710.

[0114] The server system 740 may include one or more storage devices 760 for storing images and data received from the physician 720 and / or the third party provider 730. The storage devices 760 may be considered components 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 devices and for performing any computer-implementable processes described in this disclosure. The processing devices 750 may each be a processor or a device including at least one processor.

[0115] In some embodiments, the server system 740 may include a cloud computing platform with scalable resources for computing and / or data storage, and may run applications on the cloud computing platform for implementing the methods described in this disclosure. In such embodiments, any output may be transmitted to another computer system, such as a personal computer, for display and / or storage.

[0116] Other examples of computer systems for implementing the methods of the present disclosure include desktop computers, laptop computers, and mobile computing devices such as tablets and smartphones.

[0117] The one or more processors may be configured to perform such a process 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 a process. 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.

[0118] A computer system, such as server system 740, may include one or more computing devices. If one or more processors of a computer system are implemented as multiple processors, the multiple processors may be included within a single computing device or distributed among the multiple computing devices. If a computer system includes multiple computing devices, the memory of the computer system may include individual memories of each computing device of the multiple computing devices.

[0119] In general, a computing device may include a processor (e.g., CPU, GPU, or other processing unit), a memory, and a communication interface (e.g., network interface) for communicating with other devices. The 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 disk drives). The instructions (e.g., software or computer readable code) may be stored in any volatile and / or non-volatile memory components of the memory. The computing device may further include input devices (e.g., keyboard, mouse, or touch screen) and output devices (e.g., display, printer) in some embodiments. The elements of the computing device may be interconnected through a bus, which represents one or more buses. In some embodiments, the processor of the computing device includes both the CPU and the GPU.

[0120] The 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, it shall be understood that this disclosure also describes a non-transitory computer-readable medium that stores 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 disk drives). A non-transitory computer-readable medium may be part of a computer system or a memory separate from any computer system. An "electronic storage device" may include any of the non-transitory computer-readable media described above.

[0121] In the above description of exemplary embodiments, it should be understood that various features are sometimes grouped together in a single embodiment, figure, or description thereof for the purpose of simplifying the disclosure and aiding in the understanding of one or more of the various inventive aspects. However, this method of disclosure is not to be interpreted as reflecting an intention that the claimed invention requires more features than are expressly recited in each claim. Rather, as the following claims reflect, inventive aspects lie in less than all features of a single foregoing disclosed embodiment. Thus, the claims following the Detailed Description are expressly incorporated into the Detailed Description, with each claim standing on its own as a separate embodiment of this disclosure.

[0122] Moreover, some embodiments described herein include some features but not other features that are included in other embodiments, but combinations of features of different embodiments are intended to be within the scope of the disclosure and form different embodiments, as would be understood by one of ordinary skill in the art. For example, in the following claims, any of the claimed embodiments can be used in any combination.

[0123] Thus, while certain embodiments have been described, those skilled in the art will recognize that other and further modifications may be made therein without departing from the spirit of the disclosure, and all such changes and modifications are intended to be claimed as being within the scope of the disclosure. For example, certain functionality may be added or deleted from the block diagrams, operations may be swapped between functional blocks, steps may be added or deleted from methods described within the scope of the disclosure.

[0124] The above disclosed subject matter is illustrative and not to be construed as limiting, 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. Thus, to the maximum extent permitted by law, the scope of the present disclosure shall be determined by the broadest permissible interpretation of the following claims and their equivalents, and shall not be limited or restricted by the above-described embodiments of the invention. Although various implementations of the present disclosure have been described, it will be apparent to those skilled in the art that many further implementations and implementations are possible within the scope of the present disclosure. Thus, the present disclosure is not intended to be limited.

Claims

1. 1. A computer-implemented method for blood flow simulation, the method comprising: 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 within a patient's vasculature or a geometry based on the patient's vasculature; generating a response surface that maps one or more first parameters of the first model to one or more second parameters of a reduced-order model of vascular blood flow having a lower fidelity than that of the first model based on results of the plurality of blood flow simulations; determining values ​​for one or more parameters of the reduced order model mapped from parameter values ​​representing a modified state of the vasculature by the response surface; performing a simulation of blood flow in the modified state of the vasculature using a reduced order model parameterized by the determined values ​​for the one or more second parameters to determine blood flow characteristics of the modified state of the vasculature; Including, the plurality of blood flow simulations are each performed for a plurality of configurations, each of the plurality of configurations representing a different vascular geometry derived from physiological conditions and / or a geometry of the patient's vascular system; the plurality of blood flow simulation results are first simulation results obtained for the plurality of configurations, respectively; each of the plurality of configurations includes a first value for the one or more first parameters; Generating the response surface comprises: determining, for each of the plurality of configurations, second values ​​for the one or more second parameters that, when used in a low-fidelity blood flow simulation performed using the reduced-order model, produce respective second simulation results that match the respective first simulation results; generating the response surface based on the first values ​​for the one or more first parameters and second values ​​determined for the one or more second parameters for each of the plurality of configurations; A method comprising:

2. each of the plurality of configurations includes a value for the first parameter representing at least a distinct vascular geometry in which blood flow is simulated in a distinct blood flow simulation of the plurality of blood flow simulations; The plurality of configurations include: a first configuration representing the patient's vasculature; one or more further configurations, each of which represents a vascular geometry derived from the geometry of the vasculature and / or a physiological condition different from the physiological condition represented by the first configuration; The method of claim 1 , comprising:

3. receiving patient-specific image data of the patient's vasculature; generating a patient-specific anatomical model of the vasculature based on the patient-specific image data; determining values ​​of the one or more first parameters for the first configuration to represent a patient-specific geometry of the vasculature based on the patient-specific anatomical model; The method of claim 2 , further comprising:

4. The method of claim 2 , wherein the one or more further configurations include one or more extreme configurations each representing a state of the vasculature at an anatomical or physiological limit.

5. the vascular system is at least a portion of a coronary artery of the patient; at least one of the one or more limit configurations represents a complete revascularization of at least a portion of the coronary artery; The method according to claim 4.

6. The method of claim 4 , wherein the one or more further configurations further comprise one or more configurations determined using sampling or quadrature techniques based on the one or more extreme configurations.

7. The response surface is a surface that is fitted to a set of points; each point in the set of points includes a determined value for the one or more second parameters determined for a respective one of the plurality of configurations. The method of claim 2.

8. 2. The method of claim 1, wherein the vasculature comprises at least one of the coronary vasculature, the peripheral vasculature, the cerebral vasculature, the renal vasculature, the splanchnic vasculature, or the hepatic vasculature.

9. the blood flow simulation is performed in real time such that values ​​of the blood flow characteristics are determined in real time; The method further includes presenting the values ​​of the blood flow characteristics to a user in real time. The method of claim 1.

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

11. A computer system for blood flow simulation, comprising: A memory for storing instructions; one or more processors, the one or more processors comprising: 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 within a patient's vasculature or a geometry based on the patient's vasculature; generating a response surface that maps one or more first parameters of the first model to one or more second parameters of a reduced-order model of vascular blood flow having a lower fidelity than that of the first model based on results of the plurality of blood flow simulations; determining values ​​for one or more parameters of the reduced order model mapped from parameter values ​​representing a modified state of the vasculature by the response surface; performing a simulation of blood flow in the modified state of the vasculature using a reduced order model parameterized by the determined values ​​for the one or more second parameters to determine blood flow characteristics of the modified state of the vasculature; one or more processors configured to execute instructions for performing a method including: Equipped with the plurality of blood flow simulations are each performed for a plurality of configurations, each of the plurality of configurations representing a different vascular geometry derived from physiological conditions and / or a geometry of the patient's vascular system; the plurality of blood flow simulation results are first simulation results obtained for the plurality of configurations, respectively; each of the plurality of configurations includes a first value for the one or more first parameters; Generating the response surface comprises: determining, for each of the plurality of configurations, second values ​​for the one or more second parameters that, when used in a low-fidelity blood flow simulation performed using the reduced-order model, produce respective second simulation results that match the respective first simulation results; generating the response surface based on the first values ​​for the one or more first parameters and second values ​​determined for the one or more second parameters for each of the plurality of configurations; 2. A computer system comprising:

12. The method of claim 11, wherein each of the plurality of configurations includes a value for the first parameter that represents at least a respective vascular geometry in which blood flow is simulated in a respective one of the plurality of blood flow simulations; The plurality of configurations include: a first configuration representing the patient's vasculature; one or more further configurations, each of which represents a vascular geometry derived from the geometry of the vasculature and / or a physiological condition different from the physiological condition represented by the first configuration; 12. The computer system of claim 11, comprising:

13. receiving patient-specific image data of the patient's vasculature; generating a patient-specific anatomical model of the vasculature based on the patient-specific image data; determining values ​​of the one or more first parameters for the first configuration to represent a patient-specific geometry of the vasculature based on the patient-specific anatomical model; The computer system of claim 12 further comprising:

14. 13. The computer system of claim 12, wherein the one or more further configurations include one or more extreme configurations each representing a state of the vasculature at an anatomical or physiological limit.

15. the vascular system is at least a portion of a coronary artery of the patient; at least one of the one or more limit configurations represents a complete revascularization of at least a portion of the coronary artery; 15. The computer system of claim 14.

16. 15. The computer system of claim 14, wherein the one or more further configurations further comprise one or more configurations determined using sampling or quadrature techniques based on the one or more extreme configurations.

17. The response surface is a surface that is fitted to a set of points; each point in the set of points includes a determined value for the one or more second parameters determined for a respective one of the plurality of configurations.

13. The computer system of claim 12.

18. A non-transitory computer readable medium having instructions stored thereon that, when executed by one or more processors, cause the one or more processors to: 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 within a patient's vasculature or a geometry based on the patient's vasculature; generating a response surface that maps one or more first parameters of the first model to one or more second parameters of a reduced-order model of vascular blood flow having a lower fidelity than that of the first model based on results of the plurality of blood flow simulations; determining values ​​for one or more parameters of the reduced order model mapped from parameter values ​​representing a modified state of the vasculature by the response surface; performing a simulation of blood flow in the modified state of the vasculature using a reduced order model parameterized by the determined values ​​for the one or more second parameters to determine blood flow characteristics of the modified state of the vasculature; carrying out a method comprising: the plurality of blood flow simulations are each performed for a plurality of configurations, each of the plurality of configurations representing a different vascular geometry derived from physiological conditions and / or a geometry of the patient's vascular system; the plurality of blood flow simulation results are first simulation results obtained for the plurality of configurations, respectively; each of the plurality of configurations includes a first value for the one or more first parameters; Generating the response surface comprises: determining, for each of the plurality of configurations, second values ​​for the one or more second parameters that, when used in a low-fidelity blood flow simulation performed using the reduced-order model, produce respective second simulation results that match the respective first simulation results; generating the response surface based on the first values ​​for the one or more first parameters and second values ​​determined for the one or more second parameters for each of the plurality of configurations; 16. A non-transitory computer readable medium comprising:

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