System and methods for estimation of blood flow using response surface and reduced order modeling
Systems and methods are disclosed for blood flow simulation. For example, a 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 vasculature of the patient; based on results of the plurality of blood flow simulations, generating a response surface mapping one or more first parameters of the first model to one or more second parameters of a reduced order model of vascular blood; determining values for the one or more parameters of the reduced order model mapped, by the response surface, from parameter values representing a modified state of the vasculature; and performing simulation using the reduced order model parameterized by the determined values, to determine a blood flow characteristic of the modified state of the vasculature.
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 in a vasculature of a patient or a geometry based on the vasculature of the patient;
based on results of the plurality of blood flow simulations, generating a response surface, the response surface comprising a polynomial mapping one or more first parameters of the first model to one or more second parameters of a reduced order model of vascular blood flow having lower fidelity than that of the first model;
determining values for the one or more parameters of the reduced order model mapped, by the response surface, from parameter values representing a modified state of the vasculature; and
performing 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 a blood flow characteristic of the modified state of the vasculature,
wherein the plurality of blood simulations are performed for a plurality of configurations, respectively, each configuration representing a different vascular geometry derived from a geometry of the vasculature of the patient and/or a physiological state,
the results of the plurality of blood flow simulations are first simulation results respectively obtained for the plurality of configurations,
each of the plurality of configuration include first values for the one or more first parameters, and
the generating the response surface includes:
for each of the plurality of configurations, determining second values for the one or more second parameters that, when used in low-fidelity blood flow simulation performed using the reduced order model, produce a respective second simulation result that matches the respective first simulation result; and
generating the response surface based on the first values for the one or more first parameters and the determined second values for the one or more second parameters for each of the plurality of configurations.
2. The method of claim 1 , wherein
each of the plurality of configurations including values, for the first parameters, that represent at least a respective vascular geometry in which blood flow is simulated in the respective blood flow simulation, and
the plurality of configurations include:
a first configuration representing the vasculature of the patient; and
one or more further configurations, each representing a vascular geometry derived from a geometry the vasculature and/or a physiological state different from a physiological state represented by the first configuration.
3. The method of claim 2 , further comprising:
receiving patient-specific image data of the vasculature of the patient;
generating a patient-specific anatomical model of the vasculature based the image; and
based on the patient-specific anatomical model, determining values of the one or more first parameters for the first configuration to represent a patient-specific geometry of the vasculature.
4. The method of claim 2 , wherein the one or more further configurations include one or more extrema configurations each representing a state of the vasculature at an anatomical limit or a physiological limit.
5. The method of claim 4 , wherein
the vasculature is at least a portion of coronary arteries of the patient, and
at least one of the one or more extrema configurations represents a full revascularization of the at least the portion of coronary arteries.
6. The method of claim 4 , wherein the one or more further configurations further include one or more configurations determined using a sampling or quadrature method based on the one or more extrema configurations.
7. The method of claim 6 , wherein
the response surface is a surface fitted to a set of points, and
each point in the set of points includes determined values for the one or more second parameters determined for a respective one of the plurality of configurations.
8. The method of claim 1 , wherein the vasculature includes at least one of coronary vasculature, peripheral vasculature, cerebral vasculature, renal vasculature, visceral vasculature, or hepatic vasculature.
9. The method of claim 1 , wherein
each of the plurality of blood flow simulation are performed in real time, such that values of the blood flow characteristic are determined in real time, and
values of the blood flow characteristic are presented to a user in real time.
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 storing instructions;
one or more processors configured to execute the instructions to perform a method including:
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 vasculature of the patient;
based on results of the plurality of blood flow simulations, generating a response surface, the response surface comprising a polynomial mapping one or more first parameters of the first model to one or more second parameters of a reduced order model of vascular blood flow having lower fidelity than that of the first model;
determining values for the one or more parameters of the reduced order model mapped, by the response surface, from parameter values representing a modified state of the vasculature; and
performing 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 a blood flow characteristic of the modified state of the vasculature,
wherein the plurality of blood simulations are performed for a plurality of configurations, respectively, each configuration representing a different vascular geometry derived from a geometry of the vasculature of the patient and/or a physiological state,
the results of the plurality of blood flow simulations are first simulation results respectively obtained for the plurality of configurations,
each of the plurality of configuration include first values for the one or more first parameters, and
the generating the response surface includes:
for each of the plurality of configurations, determining second values for the one or more second parameters that, when used in low-fidelity blood flow simulation performed using the reduced order model, produce a respective second simulation result that matches the respective first simulation result; and
generating the response surface based on the first values for the one or more first parameters and the determined second values for the one or more second parameters for each of the plurality of configurations.
12. The computer system of claim 11 , wherein
each of the plurality of configurations including values, for the first parameters, that represent at least a respective vascular geometry in which blood flow is simulated in the respective blood flow simulation, and
the plurality of configurations include:
a first configuration representing the vasculature of the patient; and
one or more further configurations, each representing a vascular geometry derived from a geometry the vasculature and/or a physiological state different from a physiological state represented by the first configuration.
13. The computer system of claim 12 , further comprising:
receiving patient-specific image data of the vasculature of the patient;
generating a patient-specific anatomical model of the vasculature based the image; and
based on the patient-specific anatomical model, determining values of the one or more first parameters for the first configuration to represent a patient-specific geometry of the vasculature.
14. The computer system of claim 12 , wherein the one or more further configurations include one or more extrema configurations each representing a state of the vasculature at an anatomical limit or a physiological limit.
15. The computer system of claim 14 , wherein
the vasculature is at least a portion of coronary arteries of the patient, and
at least one of the one or more extrema configurations represents a full revascularization of the at least the portion of coronary arteries.
16. The computer system of claim 14 , wherein the one or more further configurations further include one or more configurations determined using a sampling or quadrature method based on the one or more extrema configurations.
17. The computer system of claim 11 , wherein
the response surface is a surface fitted to a set of points, and
each point in the set of points includes determined values for the one or more second parameters determined for a respective one of the plurality of configurations.
18. A non-transitory computer-readable medium storing instructions that, when executed by one or more processors, cause the one or more processors to perform a method 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 in a vasculature of a patient or a geometry based on the vasculature of the patient;
based on results of the plurality of blood flow simulations, generating a response surface, the response surface comprising a polynomial mapping one or more first parameters of the first model to one or more second parameters of a reduced order model of vascular blood flow having lower fidelity than that of the first model;
determining values for the one or more parameters of the reduced order model mapped, by the response surface, from parameter values representing a modified state of the vasculature; and
performing 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 a blood flow characteristic of the modified state of the vasculature,
wherein the plurality of blood simulations are performed for a plurality of configurations, respectively, each configuration representing a different vascular geometry derived from a geometry of the vasculature of the patient and/or a physiological state,
the results of the plurality of blood flow simulations are first simulation results respectively obtained for the plurality of configurations,
each of the plurality of configuration include first values for the one or more first parameters, and
the generating the response surface includes:
for each of the plurality of configurations, determining second values for the one or more second parameters that, when used in low-fidelity blood flow simulation performed using the reduced order model, produce a respective second simulation result that matches the respective first simulation result; and
generating the response surface based on the first values for the one or more first parameters and the determined second values for the one or more second parameters for each of the plurality of configurations.