CN110533758A - A kind of asymmetric reconstructing method of brain fiber based on the hydrodynamics differential equation - Google Patents

A kind of asymmetric reconstructing method of brain fiber based on the hydrodynamics differential equation Download PDF

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CN110533758A
CN110533758A CN201910680865.XA CN201910680865A CN110533758A CN 110533758 A CN110533758 A CN 110533758A CN 201910680865 A CN201910680865 A CN 201910680865A CN 110533758 A CN110533758 A CN 110533758A
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voxel
ftd
continuity
fiber
function
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CN110533758B (en
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冯远静
李茂�
何建忠
陈余凯
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Zhejiang University of Technology ZJUT
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
    • G06F17/13—Differential equations
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T15/00—3D [Three Dimensional] image rendering
    • G06T15/08—Volume rendering
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

Abstract

A kind of asymmetric reconstructing method of brain fiber based on the hydrodynamics differential equation, regards fibre bundle as a fluid stream, is modeled by the related notion being introduced into hydrodynamics to fiber reconstruct；Continuity of the fiber in voxel described with the divergence concept in hydrodynamics；The Space Consistency of fibre bundle is described by extending concept of the divergence between voxel；Asymmetric brain fiber microstructure reconstruct is calculated by the two straint optimations.Experiment compares on simulation MR data and actual clinical data with currently a popular fiber reconstructing method respectively, and the results show method proposed by the present invention improves the accuracy of fiber reconstruct.

Description

A kind of asymmetric reconstructing method of brain fiber based on the hydrodynamics differential equation
Technology neighborhood
The present invention relates to medical imaging, the Nervous System Anatomy neighborhood under computer graphics, especially a kind of brain fiber is micro- Structural remodeling method.
Background technique
Brain is that the control mankind carry out the movable synthesizers of sophisticated functions such as logical thinking, learning and memory, movement and emotion Official, to human brain working mechanism probe into be contemporary scientific research forward position and hot spot.Brain white matter integrity reconfiguration technique will be by that will have There is the brain fibre space Microstructure Information of Anatomical significance to be imaged, is the fibr tissue micro-structure in living body brain at present Unique non-intruding non-invasive methods are imaged, it has also become brain Mechanism of Cognition is probed into, neural class disease pathology is analyzed and brain surgery The important technical of the brain sciences researchs such as navigation.
The reconstruct of brain fiber microstructure is the basic steps of brain fiber imaging, provides accurate machine direction for fibre bundle tracking Estimation.Conventional reconstruction method often only relies on the micro-structure reconstruct that monomer prime information carries out voxel, and the type of model is essentially Centrosymmetrical model limits the accuracy of machine direction reconstruct.It is proposed new more accurate brain fiber microstructure reconstruct Model is the hot spot of research.
Summary of the invention
In order to overcome existing brain fiber microstructure reconstructing method lower for dependence, the precision of monomer prime information and mould Symmetrical problem centered on type, the present invention proposes a kind of neighborhood information of combination voxel, based on the non-of the hydrodynamics differential equation Symmetric form brain fiber microstructure reconstructing method.
The technical solution adopted by the present invention to solve the technical problems is:
A kind of asymmetric reconstructing method of brain fiber based on the hydrodynamics differential equation, includes the following steps:
Step 1: asymmetry fiber track is distributed (fiber trajectory distribution, FTD) function:
Regard fibre bundle as a fluid stream, a fluid stream constitutes S={ s by a series of streamline seti, i=1, n }, space The streamline tangent line at any point (x, y, z) is the flow field of the point, and the machine direction at any point in voxel is indicated with flow field:
FTD is indicated with the Flow Field Distribution in entire voxel, is come in approximate voxel using one group of ternary quadratic multimonial FTD:
υ (x, y, z)=AC (x, y, z) (2)
Wherein, coefficient matrices A is defined as follows:
C (x, y, z)=[x is indicated with C2,y2,z2,xy,xz,yz,x,y,z,1]T；
Step 2: spatial continuity of the binding fiber beam on neighborhood, process are as follows:
2.1, in voxel FTD continuity constraint
Assuming that diffusion displacement of the hydrone in same fibre bundle keeps continuity, managed using continuous incompressible fluid By describing the spatial continuity of fiber track by introducing the diverging concept of fiber stream in diffusion tensor vector field:
When FTD is not belonging to the starting or termination area of nerve fibre bundle, div Ω meets following formula:
Ω=0 div (5)
Simultaneous formula (2), (3), (4), (5) obtain:
Although spatial continuity constraint formula (6) 2.2, between FTD voxel can guarantee that the FTD in voxel meets continuity, But cannot indicate the fibre bundle continuity between voxel, same fibre bundle is consistent between adjacent voxels, i.e., corresponding FTD is answered Meet the continuity between voxel, proposes the compatibility function between a kind of FTD voxel to characterize fibre bundle between adjacent voxels Continuity, it is assumed that voxel is unit cube, with Nc=(c0,c1,…,c5) indicate six adjacent voxels of center voxel c, with Ac =(A0,A1,…,A5) indicate neighboring voxels FTD coefficient, for a fluid stream pass through adjacent voxels c and ci, cross surface arbitrary point Continuity function div Γ (x, y, z) be defined as follows:
Wherein Γ is the adjacent voxels joint face that a fluid stream passes through, and S is a fluid stream, υ and υiRespectively c and ciFTD, by ciWith c The same coordinate system is mapped to obtain:
Wherein ajkWithRespectively A and AiIn element, on entire surface Γ Continuity function div Ψ be div Γ (x, y, z) Line Integral:
There are six the neighboring voxels that connect for each voxel, and continuity function is the continuity of six joint faces between the voxel of voxel The sum of function:
Joint type (2)-formula (9):
Wherein ajkIndicate the element in the FTD coefficient matrices A of center voxel,Indicate the FTD system of i-th of voxel of neighborhood Matrix number AiIn element；
Step 3: the calculating of FTD
By minimize voxel between voxel continuity function calculate FTD be intended to so that fiber track be distributed it is most proper in Machine direction distribution function (fiber orientation distribution, FOD), the coefficient matrices A in FTD can be by most Optimize following cost function to calculate:
Wherein Φ (υ (x, y, z)) is FOD in the probability of point (x, y, z), and to simplify the calculation, we take the 26 of center voxel Neighborhood C=[c1,c2,…,c26] in FOD peak value P=[p1,p2,…,p26] it is used as the approximation of Φ (υ (x, y, z)), such formula (11) it is simplified as:
After flow field coefficient A is acquired, that is, acquire the FTD of voxel.
The invention has the benefit that improving the accuracy of fiber reconstruct.
Detailed description of the invention
Fig. 1 is the schematic diagram of center voxel and neighboring voxels.
Specific embodiment
The present invention will be further described with reference to the accompanying drawing.
Referring to Fig.1, a kind of asymmetric reconstructing method of brain fiber based on the hydrodynamics differential equation, includes the following steps:
Step 1: asymmetry fiber track is distributed (fiber trajectory distribution, FTD) function:
Regard fibre bundle as a fluid stream, a fluid stream constitutes S={ s by a series of streamline seti, i=1, n }, space The streamline tangent line at any point (x, y, z) is the flow field of the point, and the machine direction at any point in voxel is indicated with flow field:
FTD is indicated with the Flow Field Distribution in entire voxel, is come in approximate voxel using one group of ternary quadratic multimonial FTD:
υ (x, y, z)=AC (x, y, z) (2)
Wherein, coefficient matrices A is defined as follows:
C (x, y, z)=[x is indicated with C2,y2,z2,xy,xz,yz,x,y,z,1]T；
Step 2: spatial continuity of the binding fiber beam on neighborhood,
Since during dMRI data acquisition, cerebral nerve fiber can regard constant form as, correspond to hydrodynamics In related notion, i.e., regard a fluid stream as incompressible steady flow；Process is as follows:
2.1, in voxel FTD continuity constraint
Assuming that diffusion displacement of the hydrone in same fibre bundle keeps continuity, managed using continuous incompressible fluid By describing the spatial continuity of fiber track by introducing the diverging concept of fiber stream in diffusion tensor vector field:
When FTD is not belonging to the starting or termination area of nerve fibre bundle, div Ω meets following formula:
Ω=0 div (5)
Simultaneous formula (2), (3), (4), (5) obtain:
Although spatial continuity constraint formula (6) 2.2, between FTD voxel can guarantee that the FTD in voxel meets continuity, But cannot indicate the fibre bundle continuity between voxel, same fibre bundle is consistent between adjacent voxels, i.e., corresponding FTD is answered Meet the continuity between voxel, proposes the compatibility function between a kind of FTD voxel to characterize fibre bundle between adjacent voxels Continuity, it is assumed that voxel is unit cube, with Nc=(c0,c1,…,c5) indicate six adjacent voxels of center voxel c, with Ac =(A0,A1,…,A5) indicate neighboring voxels FTD coefficient, for a fluid stream pass through adjacent voxels c and ci, cross surface arbitrary point Continuity function div Γ (x, y, z) be defined as follows:
Wherein Γ is the adjacent voxels joint face that a fluid stream passes through, and S is a fluid stream, υ and υiRespectively c and ciFTD, by ciWith c The same coordinate system is mapped to obtain:
Wherein ajkWithRespectively A and AiIn element, on entire surface Γ Continuity function div Ψ be div Γ (x, y, z) Line Integral:
There are six the neighboring voxels that connect for each voxel, and continuity function is the continuity of six joint faces between the voxel of voxel The sum of function:
Joint type (2)-formula (9):
Wherein ajkIndicate the element in the FTD coefficient matrices A of center voxel,Indicate the FTD system of i-th of voxel of neighborhood Matrix number AiIn element；
Step 3: the calculating of FTD
By minimize voxel between voxel continuity function calculate FTD be intended to so that fiber track be distributed it is most proper in Machine direction distribution function (fiber orientation distribution, FOD), the coefficient matrices A in FTD can be by most Optimize following cost function to calculate:
Wherein Φ (υ (x, y, z)) is FOD in the probability of point (x, y, z), and to simplify the calculation, we take the 26 of center voxel Neighborhood C=[c1,c2,…,c26] in FOD peak value P=[p1,p2,…,p26] it is used as the approximation of Φ (υ (x, y, z)), such formula (11) it is simplified as:
After flow field coefficient A is acquired, that is, acquire the FTD of voxel.

Claims (1)

1. a kind of asymmetric reconstructing method of brain fiber based on the hydrodynamics differential equation, which is characterized in that the method includes Following steps:
Step 1: asymmetry fiber track is distributed FTD function:
Regard fibre bundle as a fluid stream, a fluid stream constitutes S={ s by a series of streamline seti, i=1 ..., n }, space any point The streamline tangent line of (x, y, z) is the flow field of the point, and the machine direction at any point in voxel is indicated with flow field:
FTD is indicated with the Flow Field Distribution in entire voxel, carrys out the FTD in approximate voxel using one group of ternary quadratic multimonial:
υ (x, y, z)=AC (x, y, z) (2)
Wherein, coefficient matrices A is defined as follows:
C (x, y, z)=[x is indicated with C2,y2,z2,xy,xz,yz,x,y,z,1]T；
Step 2: spatial continuity of the binding fiber beam on neighborhood, process are as follows:
2.1, in voxel FTD continuity constraint
Assuming that diffusion displacement of the hydrone in same fibre bundle keeps continuity, and it is theoretical using continuous incompressible fluid, lead to The diverging concept of fiber stream in introducing diffusion tensor vector field is crossed to describe the spatial continuity of fiber track:
When FTD is not belonging to the starting or termination area of nerve fibre bundle, div Ω meets following formula:
Ω=0 div (5)
Simultaneous formula (2), (3), (4), (5) obtain:
2.2, the spatial continuity constraint between FTD voxel
Although formula (6) can guarantee that the FTD in voxel meets continuity, the fibre bundle continuity between voxel cannot be indicated, Same fibre bundle is consistent between adjacent voxels, i.e., corresponding FTD should meet the continuity between voxel, proposes a kind of FTD Compatibility function between voxel characterizes continuity of the fibre bundle between adjacent voxels, it is assumed that voxel is unit cube, with Nc =(c0,c1,…,c5) indicate six adjacent voxels of center voxel c, with Ac=(A0,A1,…,A5) indicate neighboring voxels FTD Coefficient, the adjacent voxels c and c passed through for a fluid streami, continuity function div Γ (x, y, the z) definition of cross surface arbitrary point is such as Under:
Wherein Γ is the adjacent voxels joint face that a fluid stream passes through, and S is a fluid stream, υ and υiRespectively c and ciFTD, by ciIt is mapped with c It is obtained to the same coordinate system:
Wherein ajkWithRespectively A and AiIn element, the company on entire surface Γ Continuous property function div Ψ is the Line Integral of div Γ (x, y, z):
There are six the neighboring voxels that connect for each voxel, and continuity function is the continuity function of six joint faces between the voxel of voxel The sum of:
Joint type (2)-formula (9):
Wherein ajkIndicate the element in the FTD coefficient matrices A of center voxel,Indicate the FTD coefficient square of i-th of voxel of neighborhood Battle array AiIn element；
Step 3: the calculating of FTD
By minimizing, continuity function calculating FTD is intended to so that fiber track distribution is most proper in fiber between voxel in voxel Coefficient matrices A in direction distribution function FOD, FTD is calculated by optimizing following cost function:
Wherein Φ (υ (x, y, z)) is FOD in the probability of point (x, y, z), takes 26 neighborhood C=[c of center voxel1,c2,…,c26] Peak value P=[the p of middle FOD1,p2,…,p26] it is used as the approximation of Φ (υ (x, y, z)), such formula (11) is simplified as:
After flow field coefficient A is acquired, that is, acquire the FTD of voxel.
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112489220A (en) * 2020-10-23 2021-03-12 浙江工业大学 Nerve fiber continuous tracking method based on flow field distribution

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US20140294270A1 (en) * 2011-03-15 2014-10-02 University Of Pittsburgh - Of The Commonwealth System Of Higher Education Directional diffusion fiber tracking

Patent Citations (4)

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US20060281987A1 (en) * 2005-04-11 2006-12-14 Alberto Bartesaghi Systems, devices, and methods for bundle segmentation in diffusion tensor magnetic resonance imaging
US20060273792A1 (en) * 2005-04-25 2006-12-07 Kholmovski Evgueni G Systems and methods for image reconstruction of sensitivity encoded MRI data
US20070086058A1 (en) * 2005-10-14 2007-04-19 Erik Ordentlich Method and system for denoising pairs of mutually interfering signals
US20140294270A1 (en) * 2011-03-15 2014-10-02 University Of Pittsburgh - Of The Commonwealth System Of Higher Education Directional diffusion fiber tracking

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Publication number Priority date Publication date Assignee Title
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