CN110795808A - Brain environment parameter determination device and method and electronic equipment - Google Patents
Brain environment parameter determination device and method and electronic equipment Download PDFInfo
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Abstract
The application provides a brain environment parameter determination device, a brain environment parameter determination method and electronic equipment, wherein the brain environment parameter determination method comprises the following steps: acquiring brain boundary conditions, brain parameters and whole brain model data of a subject; determining a control equation corresponding to the data of the whole brain model according to the multi-network pore medium elastomechanics model; and (3) bringing the brain parameters and the whole brain model data into a control equation, and carrying out iterative calculation by taking the brain boundary condition as a constraint condition until the control equation is converged to obtain the brain environment parameters of the subject. Therefore, the multi-network pore medium elastomechanics model is used for simulating the transfer condition and tissue deformation among a plurality of fluids in the brain environment, and the penetration of different fluids is considered in the calculation process, so that the accuracy is higher, the physical and physiological characteristics of the brain environment can be better displayed, and researchers can better research the whole brain of a human body according to the brain environment parameters.
Description
Technical Field
The application relates to the field of medical data processing, in particular to a brain environment parameter determining device and method and electronic equipment.
Background
Currently, there are several algorithms applied to brain environment research: the whole brain evaluation is to regard the brain as a whole by a pressure-volume method, a lumped parameter model and the like, study the fitting between input and output and do not consider the interior of the system, so the interaction of a blood network and cerebrospinal fluid cannot be reflected; the brain environment fluid mechanics model mainly considers soft tissue deformation and material exchange of extracellular fluid and capillary vessels, relates to two cavity systems of a blood vessel network and a brain ventricle system, and aims to express the permeability of fluid networks such as blood, cerebrospinal fluid and the like. However, the vascular network in the brain environment is mainly arterial, venous and capillary networks, where differences in the properties of the vessels lead to varying fluid penetration. Therefore, the obtained brain environment data is not accurate by adopting the method in the prior art.
Disclosure of Invention
An object of the embodiments of the present application is to provide a device and a method for determining brain environment parameters, and an electronic device, so as to solve the technical problem that the accuracy of calculated brain environment data is low.
In order to achieve the above purpose, the technical solutions provided in the embodiments of the present application are as follows:
in a first aspect, an embodiment of the present application provides a method for determining brain environment parameters, including: acquiring brain boundary conditions, brain parameters and whole brain model data of a subject; determining a control equation corresponding to the data of the whole brain model according to a multi-network pore medium elastic mechanics model; wherein the governing equation is used for describing momentum conservation and mass conservation of the whole brain; and substituting the brain parameters and the whole brain model data into the control equation, and performing iterative calculation with the brain boundary condition as a constraint condition until the control equation is converged to obtain the brain environment parameters of the subject. Therefore, the multi-network pore medium elastomechanics model is used for simulating the transfer condition and tissue deformation among a plurality of fluids in the human intracranial brain environment, determining a control equation of the whole brain model, and iteratively solving the control equation to obtain brain environment parameters when the control equation is converged. Because the penetration of different fluids is considered in the calculation process, the brain environment parameters have higher accuracy, and can better show the physical and physiological characteristics of the brain environment, so that researchers can better research the whole brain of a human body according to the brain environment parameters.
In an optional embodiment of the present application, before the acquiring the brain boundary condition, the brain parameter, and the whole brain model data of the subject, the method for determining the brain environment parameter further includes: acquiring a whole brain nuclear magnetic resonance image of the subject; constructing a whole brain model of the subject according to the whole brain nuclear magnetic resonance image; and carrying out meshing and mesh marking on the whole brain model to obtain the whole brain model data. Therefore, the whole brain nuclear magnetic resonance image of the subject is utilized to construct the whole brain model of the subject, and the mesh division is carried out on the whole brain model to achieve the purpose of discretization, so that a computer can process discrete data, and meanwhile, due to the fact that the mechanical properties of different substances in the brain are different, the mesh marking is carried out on the whole brain model to distinguish different substances in different areas, and therefore the accuracy of the brain environment parameters obtained through solving is improved.
In an optional embodiment of the present application, the gridding the whole brain model includes: carrying out mesh division on the whole brain model by utilizing the mechanical property of fluid to obtain a quadruple fluid network; wherein the quadruple fluid network comprises an arterial vascular network, an arteriolar and capillary network, a cerebrospinal fluid and interstitial fluid network, and a venous vascular network. Therefore, the whole brain model after meshing comprises four fluid networks, so that the penetration conditions of the four different fluid networks are considered in the process of solving the brain environment parameters, and the brain environment parameters with higher accuracy are obtained.
In an alternative embodiment of the present application, the determining a control equation corresponding to the whole brain model data according to the multi-network pore medium elastomechanics model includes: determining a balance equation and a continuous equation of the quadruple fluid network according to the multi-network pore medium elastic mechanical model; wherein the equilibrium equation represents conservation of momentum for the whole brain model and the continuity equation represents conservation of mass for the quadruple fluid network; before the bringing the brain parameters and the whole brain model data into the control equation, the brain environment parameter determination method further includes: and discretizing the equilibrium equation and the continuous equation. Therefore, based on the mechanical balance for generating elastic deformation, the mass conservation in the fluid network and the Darcy's law for describing fluid flow, the balance equation and the continuous equation of the quadruple fluid network can be determined according to the multi-network pore medium elastic mechanical model, the momentum conservation of the whole brain model and the mass conservation of the quadruple fluid network are respectively expressed, and the balance equation and the continuous equation are subjected to discretization processing, so that the brain environment parameters with higher accuracy are obtained.
In an alternative embodiment of the present application, the balance equation is:
wherein u is the displacement of brain tissue, piIs the pressure in each fluid network, G is the shear modulus, λ is the Lame constant, ε is the expansion strain, αiIs the Biot-Willis coefficient of each fluid network, satisfies phi ≦ αa+αc+αe+αvLess than or equal to 1, phi is the total porosity, αaIs the Biot-Willis coefficient of the arterial vascular network, αcIs the Biot-Willis coefficient of the arteriole and capillary network, αeIs the Biot-Willis coefficient of the cerebrospinal fluid and interstitial fluid networks, αvIs the Biot-Willis coefficient of the venous vascular network.
In an alternative embodiment of the present application, the discretized equilibrium equation is:
Ku-∑Qipi＝F；
wherein u is the displacement of brain tissue, piIs the pressure in the ith fluid network, K is the stiffness matrix:
K＝∫ΩBTDBdΩ；
wherein, B is a strain matrix, D is an elastic constant matrix, and omega is a three-dimensional space domain of simulation calculation;
Qiis the load contributed to the solid phase by the ith fluid network:
Qi＝∫ΩαiBThdΩ；
wherein h is a mapping vector;
f is the external force load:
where N is the interpolation function matrix, tNActing on the boundary gammaNExternal force on, gammaNIs acted by an external force tNThe boundary of (2).
In an alternative embodiment of the present application, the continuity equation is:
wherein S isiIs the water storage rate, k, of each fluid networkiIs the permeability, μ, of each networkiIs the viscosity of each fluid, sjiGreater than 0 indicates fluid inflow, sjiLess than 0 indicates fluid outflow.
In an alternative embodiment of the present application, the discretizing the continuous equation includes: discretizing the continuous equation in a spatial domain to obtain a spatially discretized continuous equation:
Aij＝S∫ΩNiNjdΩ；
where p is the pressure in a fluid network, AijIs an element of the matrix A, S is the water storage rate of the fluid network, NiAnd NjInterpolation functions corresponding to nodes i and j, respectively, omega is the three-dimensional space domain of the simulation calculation, CijIs the element in matrix C, k is the permeability of the fluid network, μ is the viscosity of the fluid, PiIs the element in the vector P, s represents the transmission between the different fluidic networks, α is the Biot-Willis coefficient of the fluidic networks,
is the strain rate, and q is the effect on the boundary Γ in the Neumann boundary condition2Of flow rate of (gamma)2Is the boundary acted on by the specified flow q; discretizing the continuous equation after the space discretization in a time domain to obtain a continuous equation after the time discretization;
where Δ t is the time step, θ is 1, n is the previous time step, and n +1 is the current time step.
In a second aspect, an embodiment of the present application provides a brain environment parameter determination apparatus, including: the first acquisition module is used for acquiring brain boundary conditions, brain parameters and whole brain model data of a subject; the determining module is used for determining a control equation corresponding to the whole brain model data according to the multi-network pore medium elastic mechanical model; wherein the governing equation is used for describing momentum conservation and mass conservation of the whole brain; and the calculation module is used for substituting the brain parameters and the whole brain model data into the control equation, performing iterative calculation with the brain boundary condition as a constraint condition until the control equation is converged, and obtaining the brain environment parameters of the subject. Therefore, the multi-network pore medium elastomechanics model is used for simulating the transfer condition and tissue deformation among a plurality of fluids in the human intracranial brain environment, determining a control equation of the whole brain model, and iteratively solving the control equation to obtain brain environment parameters when the control equation is converged. Because the penetration of different fluids is considered in the calculation process, the brain environment parameters have higher accuracy, and can better show the physical and physiological characteristics of the brain environment, so that researchers can better research the whole brain of a human body according to the brain environment parameters.
In an optional embodiment of the present application, the brain environment parameter determination apparatus further comprises: a second acquisition module for acquiring a whole brain nuclear magnetic resonance image of the subject; a model construction module for constructing a whole brain model of the subject from the whole brain nuclear magnetic resonance image; and the meshing module is used for meshing and marking meshes of the whole brain model so as to obtain the whole brain model data. Therefore, the whole brain nuclear magnetic resonance image of the subject is utilized to construct the whole brain model of the subject, and the mesh division is carried out on the whole brain model to achieve the purpose of discretization, so that a computer can process discrete data, and meanwhile, due to the fact that the mechanical properties of different substances in the brain are different, the mesh marking is carried out on the whole brain model to distinguish different substances in different areas, and therefore the accuracy of the brain environment parameters obtained through solving is improved.
In an optional embodiment of the present application, the meshing module is further configured to: carrying out mesh division on the whole brain model by utilizing the mechanical property of fluid to obtain a quadruple fluid network; wherein the quadruple fluid network comprises an arterial vascular network, an arteriolar and capillary network, a cerebrospinal fluid and interstitial fluid network, and a venous vascular network. Therefore, the whole brain model after meshing comprises four fluid networks, so that the penetration conditions of the four different fluid networks are considered in the process of solving the brain environment parameters, and the brain environment parameters with higher accuracy are obtained.
In an optional embodiment of the present application, the determining module is further configured to: determining a balance equation and a continuous equation of the quadruple fluid network according to the multi-network pore medium elastic mechanical model; wherein the equilibrium equation represents conservation of momentum for the whole brain model and the continuity equation represents conservation of mass for the quadruple fluid network; the brain environment parameter determination apparatus further includes: and the discrete module is used for carrying out discretization processing on the balance equation and the continuous equation. Therefore, based on the mechanical balance for generating elastic deformation, the mass conservation in the fluid network and the Darcy's law for describing fluid flow, the balance equation and the continuous equation of the quadruple fluid network can be determined according to the multi-network pore medium elastic mechanical model, the momentum conservation of the whole brain model and the mass conservation of the quadruple fluid network are respectively expressed, and the balance equation and the continuous equation are subjected to discretization processing, so that the brain environment parameters with higher accuracy are obtained.
In an alternative embodiment of the present application, the balance equation is:
wherein u is the displacement of brain tissue, piIs the pressure in each fluid network, G is the shear modulus, λ is the Lame constant, ε is the expansion strain, αiIs the Biot-Willis coefficient of each fluid network, satisfies phi ≦ αa+αc+αe+αvLess than or equal to 1, phi is the total porosity, αaIs the Biot-Willis coefficient of the arterial vascular network, αcIs the Biot-Willis coefficient of the arteriole and capillary network, αeIs the Biot-Willis coefficient of the cerebrospinal fluid and interstitial fluid networks, αvIs the Biot-Willis coefficient of the venous vascular network.
In an alternative embodiment of the present application, the discretized equilibrium equation is:
Ku-∑Qipi＝F；
wherein u is the displacement of brain tissue, piIs the pressure in the ith fluid network, K is the stiffness matrix:
K＝∫ΩBTDBdΩ；
wherein, B is a strain matrix, D is an elastic constant matrix, and omega is a three-dimensional space domain of simulation calculation;
Qiis the load contributed to the solid phase by the ith fluid network:
Qi＝∫ΩαiBThdΩ；
wherein h is a mapping vector;
f is the external force load:
where N is the interpolation function matrix, tNActing on the boundary gammaNExternal force on, gammaNIs acted by an external force tNThe boundary of (2).
In an alternative embodiment of the present application, the continuity equation is:
wherein S isiIs the water storage rate, k, of each fluid networkiIs the permeability, μ, of each networkiIs the viscosity of each fluid, sjiGreater than 0 indicates fluid inflow, sjiLess than 0 indicates fluid outflow.
In an optional embodiment of the present application, the determining module is further configured to: discretizing the continuous equation in a spatial domain to obtain a spatially discretized continuous equation:
Aij＝S∫ΩNiNjdΩ；
where p is the pressure in a fluid network, AijIs an element of the matrix A, S is the water storage rate of the fluid network, NiAnd NjInterpolation functions corresponding to nodes i and j, respectively, omega is the three-dimensional space domain of the simulation calculation, CijIs the element in matrix C, k is the permeability of the fluid network, μ is the viscosity of the fluid, PiIs the element in the vector P, s represents the transmission between the different fluidic networks, α is the Biot-Willis coefficient of the fluidic networks,
is the strain rate, and q is the effect on the boundary Γ in the Neumann boundary condition2Of flow rate of (gamma)2Is the boundary acted on by the specified flow q; discretizing the continuous equation after the space discretization in a time domain to obtain a continuous equation after the time discretization;
where Δ t is the time step, θ is 1, n is the previous time step, and n +1 is the current time step.
In a third aspect, an embodiment of the present application provides an electronic device, including: a processor, a memory, and a bus; the processor and the memory are communicated with each other through the bus; the memory stores program instructions executable by the processor, the processor invoking the program instructions to perform a method of determining brain environment parameters as in the first aspect.
In a fourth aspect, embodiments of the present application provide a non-transitory computer-readable storage medium storing computer instructions for causing a computer to execute the method for determining brain environment parameters in the first aspect.
In order to make the aforementioned objects, features and advantages of the present application more comprehensible, embodiments accompanied with figures are described in detail below.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings that are required to be used in the embodiments of the present application will be briefly described below, it should be understood that the following drawings only illustrate some embodiments of the present application and therefore should not be considered as limiting the scope, and that those skilled in the art can also obtain other related drawings based on the drawings without inventive efforts.
FIG. 1 is a schematic representation of the direction of fluid transport between quadruple fluid networks in an embodiment of the present application;
fig. 2 is a flowchart of a method for generating an MPET calculation domain according to an embodiment of the present disclosure;
fig. 3 is a flowchart of an MPET simulation calculation method according to an embodiment of the present disclosure;
fig. 4 is a flowchart of a method for determining brain environment parameters according to an embodiment of the present application;
FIG. 5 is a flowchart of a method for iteratively solving a governing equation according to an embodiment of the present disclosure;
fig. 6 is a block diagram illustrating a brain environment parameter determination apparatus according to an embodiment of the present application;
fig. 7 is a block diagram of an electronic device according to an embodiment of the present disclosure.
Detailed Description
The technical solutions in the embodiments of the present application will be described below with reference to the drawings in the embodiments of the present application.
The embodiment of the application provides a method for determining brain environment parameters, and in the method, a multi-network pore medium elastomechanical Model (MPET) is provided, and the multi-pore-medium elastomechanical model with multi-porosity/multi-permeability is used for simulating fluid transportation and tissue deformation in a brain environment.
The MPET theory was originally developed for studying the soil consolidation process and the penetration phenomena in oil and gas fields. The field is a multiphase system comprising solid soil and rock, liquid water and gaseous air, etc. Wherein, the solid soil and rock have pores and fissures inside, which are used as media with permeability property and provide a channel for the transportation of fluid (liquid water and gaseous air, etc.), and the pores and fissures with different sizes are connected in a staggered way. The inventor has long studied and found that the mapping of the physical process to the brain environment corresponds to the transport and perfusion process of nutrients and metabolic wastes in the brain tissue through the fluid network such as blood circulation and cerebrospinal fluid circulation. Since the mechanical properties of the various fluids in the brain environment differ, in one implementation, they can be divided into four fluid networks: arterial, arteriolar and capillary networks, cerebrospinal and interstitial fluid networks, and venous vascular networks, and prescribes the direction of fluid transport between the four fluid networks in the model according to physiological theory, as shown in fig. 1.
When performing simulation using the MPET, a corresponding calculation domain needs to be generated and simulation calculation needs to be performed. Referring to fig. 2, fig. 2 is a flowchart of a method for generating an MPET calculation domain according to an embodiment of the present disclosure, where the generating of the corresponding calculation domain is a preprocessing process of MPET simulation calculation, and the method for generating an MPET calculation domain may include the following steps:
step S201: whole brain nuclear magnetic resonance images of the subject are acquired.
Step S202: and constructing a whole brain model of the subject according to the whole brain nuclear magnetic resonance image.
Step S203: and carrying out meshing and mesh marking on the whole brain model to obtain the whole brain model data.
Illustratively, first, a whole brain Magnetic Resonance Image (MRI) of a subject may be acquired, and a T1 structural image or a T2 structural image thereof is used to identify and divide an intracranial tissue structure through a medical image, so as to reconstruct a three-dimensional model of a brain environment. Wherein the intracranial tissue structure may comprise: left hemisphere brain and right hemisphere brain, left hemisphere cerebellum and right hemisphere cerebellum, brainstem and four parts of ventricular system, and brain tissue wherein includes grey matter and white matter, the ventricular system includes: left and right ventricles, third and fourth ventricles and midbrain aqueduct. Because the whole brain nuclear magnetic resonance images of all the subjects are different, the whole brain models of the subjects constructed according to the whole brain nuclear magnetic resonance images of the subjects are different and have specificity.
In one embodiment, the reconstruction of the three-dimensional model of the brain environment can be performed using the FreeSprofer software. The method specifically comprises the following steps:
in a first step, two closed surfaces are obtained from the MRI images, the outer surface representing the cortex of the brain parenchyma and the inner surface representing the ventricular wall of the ventricle, both surfaces being fully closed and the ventricle being fully contained within the brain parenchyma.
And secondly, removing the cavity occupied by the ventricles of the brain from the space surrounded by the cortex of the brain parenchyma through Boolean operation to obtain a three-dimensional area finally used for analog calculation, namely the brain parenchyma distributed between the inner surface and the outer surface.
And thirdly, further dividing the intracranial tissue structure to obtain a whole brain model of the subject.
It should be noted that, in the embodiments of the present application, the manner of acquiring the whole brain nuclear magnetic resonance image of the subject is not particularly limited, and those skilled in the art can select an appropriate manner to acquire the whole brain nuclear magnetic resonance image of the subject according to the conventional technical means in the art. For example, the whole brain nuclear magnetic resonance image of the subject sent after the nuclear magnetic resonance imaging device collects the image may be directly received, or the whole brain nuclear magnetic resonance image of the subject pre-stored in the server may be obtained.
After the whole brain model of the subject is constructed, since the electronic device cannot solve the continuous physical equation during calculation, discretization processing is performed on the calculation domain of the MPET. The mesh division is carried out on the specific brain environment structure model of the subject, so that the discretization purpose is achieved, and a finite element model is generated. Wherein, the step S203 may include the following steps:
and performing mesh division on the whole brain model by using the mechanical properties of the fluid to obtain a quadruple fluid network.
The surface of the whole brain model of the subject is divided into triangular meshes and the interior is divided into tetrahedral meshes. After the grids are divided, the specific brain environment structure model of the subject forms two closed curved surfaces with the surface of the cerebral cortex as an outer boundary and the surface of a ventricular system as an inner boundary, each tetrahedral grid in the curved surface is a small computing unit, and all the computing units jointly form a computing domain of an MPET simulation computing part. As an embodiment, the whole brain model may be gridded using the existing software ANSYS, and the cells used for gridding are four-node tetrahedral cells.
It should be noted that, in the embodiment of the present application, the number of the divided grids is not specifically limited, and those skilled in the art can appropriately select the number according to the conventional technical means in the art. For example: the number of meshes to divide may be determined by mesh independence analysis. In the mesh independence analysis, four-node tetrahedral units with different sizes can be used for mesh division on the same whole brain model. Analysis of the calculation results shows that the number of the grids of about 2000000 can ensure the convergence of the calculation results, and the use of more grids can not bring about obvious difference of the calculation results.
The divided whole brain model can be regarded as a quadruple fluid network, and the quadruple fluid network comprises an arterial blood vessel network, an arteriolar and capillary blood vessel network, a cerebrospinal fluid and tissue fluid network and a venous blood vessel network. Referring to fig. 1, blood flows into the arterial blood vessel network, fluid in the arterial blood vessel network is transferred into the arteriolar and capillary blood vessel networks, fluid in the arteriolar and capillary blood vessel networks is transferred into the cerebrospinal fluid and tissue fluid networks and the venous blood vessel networks, fluid in the cerebrospinal fluid and tissue fluid networks is transferred into the venous blood vessel networks, and finally blood flows out of the venous blood vessel networks.
In the embodiment of the application, the whole brain model after grid division comprises four fluid networks, so that the penetration conditions of the four different fluid networks are considered in the process of solving the brain environment parameters, and the brain environment parameters with higher accuracy are obtained.
After the whole brain model of the subject is gridded, different parameter values need to be assigned to the gray matter and the white matter when performing simulation calculation due to different mechanical properties of the gray matter and the white matter in the brain tissue, and therefore, it needs to mark whether each tetrahedral grid belongs to the gray matter or the white matter anatomically in the generated gridded whole brain model. As an embodiment, each tetrahedral mesh in the whole brain model may be labeled with a unique cell number and type number, such as: 1 represents white matter in the tetrahedral mesh and 2 represents gray matter in the tetrahedral mesh.
It should be noted that, when the whole brain model is subjected to the grid marking, the gray matter and the white matter in the brain can be marked, so that the MPET shows different expressions of fluid network and tissue deformation in gray matter and white matter areas in the simulation calculation, and more brain tissue structures such as hippocampus, amygdala and the like can be marked according to actual requirements, so that the obtained whole brain model data better conforms to the physiological condition of the human body, and the method is helpful for researchers to perform more detailed analysis on the simulation result.
After the MPET calculation domain is generated, the divided grid node coordinates, the topological relation between the grid nodes and the four-node tetrahedral units, the gray matter and white matter labels and the like can be output as whole brain model data.
In the embodiment of the application, the whole brain nuclear magnetic resonance image of the subject is utilized to construct the whole brain model of the subject, and the mesh division is carried out on the whole brain model to achieve the purpose of discretization, so that a computer can process discrete data, and meanwhile, due to the fact that the mechanical properties of different substances in the brain are different, the whole brain model is subjected to mesh marking to distinguish different substances in different areas, and therefore the accuracy of the brain environment parameters obtained through solving is improved.
Further, after generating the computation domain for the MPET, simulation computations may be performed on the MPET. Referring to fig. 3, fig. 3 is a flowchart of an MPET simulation calculation method according to an embodiment of the present disclosure, where the MPET simulation calculation method includes the following steps:
step S301: and determining an equilibrium equation and a continuous equation of the quadruple fluid network according to the multi-network pore medium elastic mechanical model.
Step S302: discretizing the equilibrium equation and the continuous equation.
Illustratively, the MPET is a highly coupled model, and the control equation of the MPET of the quadruple fluid network can be determined by comprehensively considering the mechanical balance for generating elastic deformation, the mass conservation in the fluid network and the Darcy's law for describing the fluid flow on the basis of the MPET. Wherein, in the control equation, the original variables are the displacement u of the brain tissue and the pressure p of the four fluid networksi(i＝a,c,e,v)。
As an embodiment, the governing equations may include an equilibrium equation representing conservation of momentum for the whole brain model and a continuous equation representing conservation of mass for the quadruple fluid network.
The equilibrium equation can be expressed as:
wherein u is the displacement of brain tissue; p is a radical ofiIs the pressure in each fluid network, G is the shear modulus, lambda is the Lame constant,. epsilon.is the expansion strain, which can be determined by the displacement of brain tissue αiIs the Biot-Willis coefficient of each fluid network, satisfies phi ≦ αa+αc+αe+αvLess than or equal to 1, phi is the total porosity, αaIs the Biot-Willis coefficient of the arterial vascular network, αcIs the Biot-Willis coefficient of arteriole and capillary networks, αeIs the Biot-Willis coefficient of the cerebrospinal fluid and interstitial fluid networks, αvBiot-Wil, which is a venous vascular networklis coefficient.
In the above data, u and piIs variable, and the rest data are constants, and the values of the constants are determined by the individual difference of the subjects. Physical forces (e.g., gravity, inertial forces, electromagnetic forces, etc.) and inertia may be ignored in the control equations based on the assumption that the fluid flow rate in the living body is relatively low.
The continuity equation can be expressed as:
wherein S isiThe water storage rate of each fluid network represents the fluid volume change corresponding to the unit pore pressure change of the voxel under the normal strain condition; k is a radical ofiIs the permeability of each network, k is when the four fluid networks have isotropic permeability propertiesiIs a constant; mu.siIs the viscosity of each fluid; sjiGreater than 0 indicates fluid inflow, sjiA value of less than 0 is representative of fluid outflow, and is determined by the local hydrostatic pressure gradient, which can be determined without using the pressure difference between the fluid networks.
The governing equations (equilibrium equations and continuity equations) can be discretized by finite element methods, the displacement u of the brain tissue and the pressure p of the four fluid networksi(i ═ a, c, e, v) are approximated by continuous piecewise linear polynomials.
Based on the principle of minimum potential energy, the equilibrium equation after dispersion can be obtained as follows:
Ku-∑Qipi＝F；
K＝∫ΩBTDBdΩ；
Qi＝∫ΩαiBThdΩ；
wherein K is a stiffness matrix; u is the displacement of brain tissue; qiIs the load contributed to the solid phase by the ith fluid network; p is a radical ofiIs the pressure in the ith fluid network; f is an external force load; b is a strain matrix; d is an elastic constant matrix; Ω is the three-dimensional spatial domain of the simulation calculation; h is a mapping vector; n is an interpolation function matrix; t is tNActing on the boundary gammaNAn external force; gamma-shapedNIs acted by an external force tNThe boundary of (2).
When discretizing the continuous equation, step S302 may further include the steps of:
firstly, discretizing the continuous equation in a spatial domain to obtain the continuous equation after spatial discretization.
And step two, discretizing the continuous equation after the space discretization in a time domain to obtain the continuous equation after the time discretization.
As an embodiment, the continuous equation of the quadruple fluid network can be discretized in the spatial domain by a weighted residue method and a continuous Galerkin method, and the continuous equation after spatial discretization of one of the fluid networks is as follows:
Aij＝S∫ΩNiNjdΩ；
wherein p is the pressure in a fluid network; a. theijIs an element in the matrix A, S is the water storage rate of the fluid network, NiAnd NjInterpolation functions corresponding to nodes i and j, respectively, and Ω is a three-dimensional space domain of the simulation calculation; cijIs the element in matrix C, k is the permeability of the fluid network, μ is the viscosity of the fluid; piIs the element in the vector P, s represents the transmission between different fluidic networks, α is the Biot-Wi of a fluidic networkThe coefficient of the llis is such that,is the strain rate, and q is the effect on the boundary Γ in the Neumann boundary condition2Of flow rate of (gamma)2Is the boundary acted upon by the specified traffic q.
After the spatial discretization is completed, the continuous equation after the spatial discretization can be discretized in a time domain through a weighted residue method (implicit post-difference), and the continuous equation after the time discretization is as follows:
where Δ t is the time step, θ is 1, n is the previous time step, and n +1 is the current time step.
In the embodiment of the application, based on the mechanical balance for generating elastic deformation, the conservation of mass in the fluid network and the darcy's law for describing fluid flow, the balance equation and the continuity equation of the quadruple fluid network can be determined according to the multi-network pore medium elastic mechanical model, the conservation of momentum of the whole brain model and the conservation of mass of the quadruple fluid network are respectively expressed, and discretization is performed on the balance equation and the continuity equation, so that the brain environment parameters with higher accuracy are obtained.
Further, after generating the calculation domain of the MPET and performing the simulation calculation of the MPET, the brain environment parameters of the subject can be solved. Referring to fig. 4, fig. 4 is a flowchart of a method for determining brain environment parameters according to an embodiment of the present application, where the method for determining brain environment parameters includes the following steps:
step S401: brain boundary conditions, brain parameters, and whole brain model data of the subject are obtained.
Step S402: and determining a control equation corresponding to the data of the whole brain model according to the multi-network pore medium elastomechanics model.
Step S403: and (3) bringing the brain parameters and the whole brain model data into a control equation, and carrying out iterative calculation by taking the brain boundary condition as a constraint condition until the control equation is converged to obtain the brain environment parameters of the subject.
Illustratively, a whole brain model of the subject is obtained in the MPET computational domain generation method in the above-described embodiment. Since the computational domain of MPET is defined by two surfaces: the outer boundary is the cortical surface and the inner boundary is the ventricular system surface, both of which can be given the boundary conditions of a solid phase and four fluid networks, please refer to table 1, which lists ten boundary conditions in the examples of the present application:
TABLE 1 brain boundary conditions
Among these, the blood supply to the brain environment is mainly provided by two pairs of arteries: the internal carotid and vertebral arteries, whose blood supply is transformed in the calculation into the boundary condition of the cortical surface of the brain (Neumann boundary condition), are embodied in the form of pulsatile waveforms. Wherein, because of the influence of the pulse, the calculation result has periodic variation, and a cycle corresponds to a pulse, and the comparison of the calculation results of different cycles shows that, after calculating about 50 cycles (i.e. 50 pulses), the fluctuation of the calculation result in the cycle can be ignored, and can be considered as representing the steady state. Therefore, the numerical simulation runs for 50 cycles to reach a steady state, and the finally output data is a steady-state calculation result.
Referring to table 2, table 2 lists the theoretical parameters of elasticity of the porous media used in the examples of the present application:
TABLE 2 theoretical parameters of elasticity of porous media
| Parameter(s) | Value taking | Unit of | Parameter(s) | Value taking | Unit of |
| αa，c | 0.25 | Sv | 1.5×10-5 | m2N-1 | |
| αe | 0.49 | ka，e，v | 1.0×10-10 | m2 | |
| αv | 0.01 | kcg | 1.0×10-8 | m2 | |
| λg | 505 | Pa | kcw | 1.0×10-10 | m2 |
| Gg | 216 | Pa | ωac | 1.5×10-7 | m2N-1s-1 |
| λw | 1010 | Pa | ωcv | 1.5×10-7 | m2N-1s-1 |
| Gw | 432 | Pa | ωev | 1.0×10-6 | m2N-1s-1 |
| pbp | 650 | Pa | ωce | 1.0×10-8 | m2N-1s-1 |
| Sa，c | 2.9×10-4 | m2N-1 | R | 8.5×1013 | m-3 |
| Se | 3.9×10-4 | m2N-1 | Qp | 5.8×10-9 | m3-1 |
In the embodiments of the present application, the manner of acquiring the brain boundary condition, the brain parameter, and the whole brain model data of the subject is not particularly limited, and those skilled in the art can select an appropriate manner to acquire the brain boundary condition, the brain parameter, and the whole brain model data of the subject according to the conventional technical means in the art. For example, data stored in the cloud server may be read, or data stored in the cloud server in advance may be acquired.
The specific implementation of step S402 has been described in detail in the above embodiments, and is not described herein again.
In the process of determining the brain environment parameters, as shown in fig. 5, fig. 5 is a flowchart of a method for iteratively solving the control equation provided in the embodiment of the present application. Firstly, inputting brain boundary conditions, brain parameters and whole brain model data of a subject, solving from 1 time step to the last time step in sequence, bringing initial pressure into a dispersed equilibrium equation and a continuous equation for solving, and updating displacement data. And then carrying out iterative calculation on the balance equation and the continuous equation after the last dispersion, and finally outputting data when the balance equation and the continuous equation after the dispersion converge to be used as the brain environment parameters of the subject.
As an embodiment, the brain environment parameters output in the embodiment of the present application may include: the flow rate of Darcy corresponding to the four fluid networks, the fluid pressure corresponding to the four fluid networks, the fluid volume change, the brain tissue displacement and the brain tissue expansion and volume strain corresponding to the four fluid networks. The researcher can comprehensively analyze and research the brain environment condition of the subject according to the fourteen data output.
In the embodiment of the application, the multi-network pore medium elastomechanics model is used for simulating the transfer condition and tissue deformation among a plurality of fluids in the human intracranial brain environment, determining the control equation of the whole brain model, and iteratively solving the control equation to obtain the brain environment parameters when the control equation is converged. Because the penetration of different fluids is considered in the calculation process, the brain environment parameters have higher accuracy, and can better show the physical and physiological characteristics of the brain environment, so that researchers can better research the whole brain of a human body according to the brain environment parameters.
Referring to fig. 6, fig. 6 is a block diagram of a brain environment parameter determining apparatus according to an embodiment of the present application, where the brain environment parameter determining apparatus 600 includes: a first obtaining module 601, configured to obtain a brain boundary condition, a brain parameter, and whole brain model data of a subject; a determining module 602, configured to determine a control equation corresponding to the data of the whole brain model according to a multi-network pore medium elastomechanics model; wherein the governing equation is used for describing momentum conservation and mass conservation of the whole brain; a calculating module 603, configured to bring the brain parameters and the whole brain model data into the control equation, perform iterative calculation with the brain boundary condition as a constraint condition until the control equation converges, and obtain brain environment parameters of the subject.
In the embodiment of the application, the multi-network pore medium elastomechanics model is used for simulating the transfer condition and tissue deformation among a plurality of fluids in the human intracranial brain environment, determining the control equation of the whole brain model, and iteratively solving the control equation to obtain the brain environment parameters when the control equation is converged. Because the penetration of different fluids is considered in the calculation process, the brain environment parameters have higher accuracy, and can better show the physical and physiological characteristics of the brain environment, so that researchers can better research the whole brain of a human body according to the brain environment parameters.
Further, the brain environment parameter determination apparatus 600 further includes: a second acquisition module for acquiring a whole brain nuclear magnetic resonance image of the subject; a model construction module for constructing a whole brain model of the subject from the whole brain nuclear magnetic resonance image; and the meshing module is used for meshing and marking meshes of the whole brain model so as to obtain the whole brain model data.
In the embodiment of the application, the whole brain nuclear magnetic resonance image of the subject is utilized to construct the whole brain model of the subject, and the mesh division is carried out on the whole brain model to achieve the purpose of discretization, so that a computer can process discrete data, and meanwhile, due to the fact that the mechanical properties of different substances in the brain are different, the whole brain model is subjected to mesh marking to distinguish different substances in different areas, and therefore the accuracy of the brain environment parameters obtained through solving is improved.
Further, the meshing module is further configured to: carrying out mesh division on the whole brain model by utilizing the mechanical property of fluid to obtain a quadruple fluid network; wherein the quadruple fluid network comprises an arterial vascular network, an arteriolar and capillary network, a cerebrospinal fluid and interstitial fluid network, and a venous vascular network.
In the embodiment of the application, the whole brain model after grid division comprises four fluid networks, so that the penetration conditions of the four different fluid networks are considered in the process of solving the brain environment parameters, and the brain environment parameters with higher accuracy are obtained.
Further, the determining module 602 is further configured to: determining a balance equation and a continuous equation of the quadruple fluid network according to the multi-network pore medium elastic mechanical model; wherein the equilibrium equation represents conservation of momentum for the whole brain model and the continuity equation represents conservation of mass for the quadruple fluid network; the brain environment parameter determination apparatus 600 further includes: and the discrete module is used for carrying out discretization processing on the balance equation and the continuous equation.
In the embodiment of the application, based on the mechanical balance for generating elastic deformation, the conservation of mass in the fluid network and the darcy's law for describing fluid flow, the balance equation and the continuity equation of the quadruple fluid network can be determined according to the multi-network pore medium elastic mechanical model, the conservation of momentum of the whole brain model and the conservation of mass of the quadruple fluid network are respectively expressed, and discretization is performed on the balance equation and the continuity equation, so that the brain environment parameters with higher accuracy are obtained.
Further, the balance equation is:
wherein u is the displacement of brain tissue, piIs the pressure in each fluid network, G is the shear modulus, λ is the Lame constant, ε is the expansion strain, αiIs the Biot-Willis coefficient of each fluid network, satisfies phi ≦ αa+αc+αe+αvLess than or equal to 1, phi is the total porosity, αaIs the Biot-Willis coefficient of the arterial vascular network, αcIs the Biot-Willis coefficient of the arteriole and capillary network, αeIs the Biot-Willis coefficient of the cerebrospinal fluid and interstitial fluid networks, αvIs the Biot-Willis coefficient of the venous vascular network.
Further, the discretized equilibrium equation is:
Ku-∑Qipi＝F；
wherein u is the displacement of brain tissue, piIs the pressure in the ith fluid network, K is the stiffness matrix:
K＝∫ΩBTDBdΩ；
wherein, B is a strain matrix, D is an elastic constant matrix, and omega is a three-dimensional space domain of simulation calculation;
Qiis the load contributed to the solid phase by the ith fluid network:
Qi＝∫ΩαiBThdΩ；
wherein h is a mapping vector;
f is the external force load:
where N is the interpolation function matrix, tNActing on the boundary gammaNExternal force on, gammaNIs acted by an external force tNThe boundary of (2).
Further, the continuous equation is:
wherein S isiIs the water storage rate, k, of each fluid networkiIs the permeability, μ, of each networkiIs the viscosity of each fluid, sjiGreater than 0 indicates fluid inflow, sjiLess than 0 indicates fluid outflow.
Further, the determining module 602 is further configured to: discretizing the continuous equation in a spatial domain to obtain a spatially discretized continuous equation:
Aij＝S∫ΩNiNjdΩ；
where p is the pressure in a fluid network, AijIs an element of the matrix A, S is the water storage rate of the fluid network, NiAnd NjInterpolation functions corresponding to nodes i and j, respectively, omega is the three-dimensional space domain of the simulation calculation, CijIs the element in matrix C, k is the permeability of the fluid network, μ is the viscosity of the fluid, PiIs the element in the vector P, s represents the transmission between the different fluidic networks, α is the Biot-Willis coefficient of the fluidic networks,
is the strain rate, and q is the effect on the boundary Γ in the Neumann boundary condition2Of flow rate of (gamma)2Is the boundary acted on by the specified flow q; discretizing the continuous equation after the space discretization in a time domain to obtain a continuous equation after the time discretization;
where Δ t is the time step, θ is 1, n is the previous time step, and n +1 is the current time step.
Referring to fig. 7, fig. 7 is a block diagram of an electronic device according to an embodiment of the present disclosure, where the electronic device includes: at least one processor 701, at least one communication interface 702, at least one memory 703 and at least one communication bus 704. Wherein the communication bus 704 is used for implementing direct connection communication of these components, the communication interface 702 is used for communicating signaling or data with other node devices, and the memory 703 stores machine readable instructions executable by the processor 701. When the electronic device is operated, the processor 701 communicates with the memory 703 through the communication bus 704, and the machine-readable instructions are called by the processor 701 to execute the above-mentioned method for determining the brain environment parameters.
The processor 701 may be an integrated circuit chip having signal processing capabilities. The processor 701 may be a general-purpose processor, including a Central Processing Unit (CPU), a Network Processor (NP), and the like; but also Digital Signal Processors (DSPs), Application Specific Integrated Circuits (ASICs), Field-Programmable Gate arrays (FPGAs) or other Programmable logic devices, discrete Gate or transistor logic devices, discrete hardware components. Which may implement or perform the various methods, steps, and logic blocks disclosed in the embodiments of the present application. A general purpose processor may be a microprocessor or the processor may be any conventional processor or the like.
The communication interface 702 couples various input/output devices to the processor 701, as well as to the memory 703. In some embodiments, the communication interface 702, the processor 701, and the memory 703 may be implemented in a single chip. In other examples, they may be implemented separately from the individual chips.
The Memory 703 may include, but is not limited to, a Random Access Memory (RAM), a Read Only Memory (ROM), a Programmable Read Only Memory (PROM), an Erasable Read Only Memory (EPROM), an electrically Erasable Read Only Memory (EEPROM), and the like.
It will be appreciated that the configuration shown in fig. 7 is merely illustrative and that the electronic device may include more or fewer components than shown in fig. 7 or have a different configuration than shown in fig. 7. The components shown in fig. 7 may be implemented in hardware, software, or a combination thereof. In this embodiment, the electronic device may be, but is not limited to, an entity device such as a desktop, a notebook computer, a smart phone, an intelligent wearable device, and a vehicle-mounted device, and may also be a virtual device such as a virtual machine. In addition, the electronic device is not necessarily a single device, but may also be a combination of multiple devices, such as a server cluster, and the like.
Embodiments of the present application further provide a computer program product comprising a computer program stored on a non-transitory computer readable storage medium, the computer program comprising program instructions, which when executed by a computer, the computer is capable of performing the steps of the method for determining brain environment parameters in the above embodiments, for example, including: acquiring brain boundary conditions, brain parameters and whole brain model data of a subject; determining a control equation corresponding to the data of the whole brain model according to a multi-network pore medium elastic mechanics model; wherein the governing equation is used for describing momentum conservation and mass conservation of the whole brain; and substituting the brain parameters and the whole brain model data into the control equation, and performing iterative calculation with the brain boundary condition as a constraint condition until the control equation is converged to obtain the brain environment parameters of the subject.
In the embodiments provided in the present application, it should be understood that the disclosed apparatus and method may be implemented in other ways. The above-described embodiments of the apparatus are merely illustrative, and for example, the division of the units is only one logical division, and there may be other divisions when actually implemented, and for example, a plurality of units or components may be combined or integrated into another system, or some features may be omitted, or not executed. In addition, the shown or discussed mutual coupling or direct coupling or communication connection may be an indirect coupling or communication connection of devices or units through some communication interfaces, and may be in an electrical, mechanical or other form.
In addition, units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of the embodiment.
Furthermore, the functional modules in the embodiments of the present application may be integrated together to form an independent part, or each module may exist separately, or two or more modules may be integrated to form an independent part.
In this document, relational terms such as first and second, and the like may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions.
The above description is only an example of the present application and is not intended to limit the scope of the present application, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, improvement and the like made within the spirit and principle of the present application shall be included in the protection scope of the present application.
Claims (10)
1. A brain environment parameter determination apparatus, comprising:
the first acquisition module is used for acquiring brain boundary conditions, brain parameters and whole brain model data of a subject;
the determining module is used for determining a control equation corresponding to the whole brain model data according to the multi-network pore medium elastic mechanical model; wherein the governing equation is used for describing momentum conservation and mass conservation of the whole brain;
and the calculation module is used for substituting the brain parameters and the whole brain model data into the control equation, performing iterative calculation with the brain boundary condition as a constraint condition until the control equation is converged, and obtaining the brain environment parameters of the subject.
2. The brain environment parameter determination apparatus according to claim 1, further comprising:
a second acquisition module for acquiring a whole brain nuclear magnetic resonance image of the subject;
a model construction module for constructing a whole brain model of the subject from the whole brain nuclear magnetic resonance image;
and the meshing module is used for meshing and marking meshes of the whole brain model so as to obtain the whole brain model data.
3. The brain environment parameter determination apparatus according to claim 2, wherein the meshing module is further configured to:
carrying out mesh division on the whole brain model by utilizing the mechanical property of fluid to obtain a quadruple fluid network; wherein the quadruple fluid network comprises an arterial vascular network, an arteriolar and capillary network, a cerebrospinal fluid and interstitial fluid network, and a venous vascular network.
4. The brain environment parameter determination apparatus according to claim 3, wherein the determination module is further configured to:
determining a balance equation and a continuous equation of the quadruple fluid network according to the multi-network pore medium elastic mechanical model; wherein the equilibrium equation represents conservation of momentum for the whole brain model and the continuity equation represents conservation of mass for the quadruple fluid network;
the brain environment parameter determination apparatus further includes:
and the discrete module is used for carrying out discretization processing on the balance equation and the continuous equation.
5. The brain environment parameter determination device according to claim 4, wherein the balance equation is:
wherein u is the displacement of brain tissue, piIs the pressure in each fluid network, G is the shear modulus, λ is the Lame constant, ε is the expansion strain, αiIs the Biot-Willis coefficient of each fluid network, satisfies phi ≦ αa+αc+αe+αvLess than or equal to 1, phi is the total porosity, αaIs the Biot-Willis coefficient of the arterial vascular network, αcIs the arteriole andBiot-Willis coefficient of capillary network, αeIs the Biot-Willis coefficient of the cerebrospinal fluid and interstitial fluid networks, αvIs the Biot-Willis coefficient of the venous vascular network.
6. The brain environment parameter determination apparatus according to claim 5, wherein the discretized equilibrium equation is:
Ku-∑Qipi＝F；
wherein u is the displacement of brain tissue, piIs the pressure in the ith fluid network, K is the stiffness matrix:
K＝∫ΩBTDBdΩ；
wherein, B is a strain matrix, D is an elastic constant matrix, and omega is a three-dimensional space domain of simulation calculation;
Qiis the load contributed to the solid phase by the ith fluid network:
Qi＝∫ΩαiBThdΩ；
wherein h is a mapping vector;
f is the external force load:
where N is the interpolation function matrix, tNActing on the boundary gammaNExternal force on, gammaNIs acted by an external force tNThe boundary of (2).
7. The brain environment parameter determination device according to claim 4, wherein the continuous equation is:
wherein S isiIs the water storage rate, k, of each fluid networkiIs the permeability, μ, of each networkiIs the viscosity of each fluid, sjiA value greater than 0 is indicative of fluid inflow,sjiless than 0 indicates fluid outflow.
8. The brain environment parameter determination apparatus according to claim 7, wherein the determination module is further configured to:
discretizing the continuous equation in a spatial domain to obtain a spatially discretized continuous equation:
Aij＝S∫ΩNiNjdΩ；
where p is the pressure in a fluid network, AijIs an element of the matrix A, S is the water storage rate of the fluid network, NiAnd NjInterpolation functions corresponding to nodes i and j, respectively, omega is the three-dimensional space domain of the simulation calculation, CijIs the element in matrix C, k is the permeability of the fluid network, μ is the viscosity of the fluid, PiIs the element in the vector P, s represents the transmission between the different fluidic networks, α is the Biot-Willis coefficient of the fluidic networks,
is the strain rate, and q is the effect on the boundary Γ in the Neumann boundary condition2Of flow rate of (gamma)2Is the boundary acted on by the specified flow q;
discretizing the continuous equation after the space discretization in a time domain to obtain a continuous equation after the time discretization;
where Δ t is the time step, θ is 1, n is the previous time step, and n +1 is the current time step.
9. A method for determining a brain environment parameter, comprising:
acquiring brain boundary conditions, brain parameters and whole brain model data of a subject;
determining a control equation corresponding to the data of the whole brain model according to a multi-network pore medium elastic mechanics model; wherein the governing equation is used for describing momentum conservation and mass conservation of the whole brain;
and substituting the brain parameters and the whole brain model data into the control equation, and performing iterative calculation with the brain boundary condition as a constraint condition until the control equation is converged to obtain the brain environment parameters of the subject.
10. A non-transitory computer-readable storage medium storing computer instructions which, when executed by a computer, cause the computer to perform the brain environment parameter determination method of claim 9.
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