CN101872385A - Fast-marching fiber tracking method based on topology preservation - Google Patents
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- 238000011478 gradient descent method Methods 0.000 claims abstract description 3
- 238000012423 maintenance Methods 0.000 claims description 7
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- 238000002598 diffusion tensor imaging Methods 0.000 abstract description 13
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- 238000001727 in vivo Methods 0.000 description 2
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- 230000009286 beneficial effect Effects 0.000 description 1
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Abstract
The invention belongs to the field of resonance diffusion imaging, in particular to a fast-marching fiber tracking method based on topology preservation, comprising the steps of: reading DTI (Diffusion Tensor Imaging) data; manually selecting a seed point and initializing; evoluting from the seed point to peripheral neighbor points by using a fast-marching method and adopting a curvature weighting speed function, recording topology information in an evolution process, i.e. a source node of each evoluting point; calculating all paths by adopting a time gradient descent method; and selecting a real fiber path by a link matrix. The invention has the advantages of more according with the real fiber path by fiber tracking and reducing urious positive branches; and the obtained fiber is smooth and better reflects the fiber direction.
Description
Technical Field
The invention belongs to the field of magnetic resonance diffusion tensor imaging, and relates to a fast marching fiber tracking method based on topology maintenance.
Background
Diffusion Tensor Imaging (DTI) is a new non-invasive imaging method developed on the basis of Magnetic Resonance Imaging (MRI), and the method utilizes the principle of water molecule free thermal motion anisotropy in tissues to detect the microstructure of the tissues so as to achieve the purpose of researching human body functions. At present, diffusion tensor imaging is the only noninvasive imaging method capable of displaying white matter fiber tracts in living bodies, so that the evaluation of the tissue structure and the connectivity of the white matter fiber tracts becomes possible, the method has incomparable superiority compared with general MRI examination, and opens up a new broad prospect for neuroimaging.
In recent years, an important advance of DTI research has been to apply it to visualization of white matter fibers, where fiber tracking or white matter fiber imaging is a hotspot of research in DTI visualization. In the white matter fibers, water molecules diffusing along the long axis direction thereof diffuse faster due to smaller resistance, while water molecules diffusing perpendicular to the long axis direction thereof diffuse slower due to larger resistance. The fiber tracking uses a continuous curve to represent the trend and the distribution of the fibers, a three-dimensional continuous white matter tissue structure can be obtained by a fiber tracking method, and the details of the white matter fibers can be displayed. At present, the reconstruction of the white matter nerve fibers is the research focus in the magnetic resonance diffusion imaging field, the research on the trend and the connection of the white matter fibers is beneficial to obtaining the information of brain structure and function connection, and effective information can be provided for disease diagnosis caused by fiber loss or structural abnormality. The method not only helps to deeply understand the structure of the human brain fibers, but also has great value in clinic.
In DTI, the diffusion tensor is a 3 x 3 symmetric matrix with 6 components. Diagonalizing this matrix can yield 3 eigenvalues and their corresponding eigenvectors. The direction of the eigenvector (principal vector) corresponding to the maximum eigenvalue is the main direction of water molecule diffusion, and is generally considered as the direction of the fiber in the voxel (a volume unit representing a three-dimensional space with a certain thickness is referred to as a voxel) in which the tensor is located. There are many fiber tracking methods available today, which can be roughly divided into two categories: tensor domain based and global energy minimization methods. The fiber tracking algorithm based on the tensor domain mainly utilizes local tensor information to track fibers, DTI can generate the preferential diffusion direction of each voxel, and the arrangement of each point tensor in space is called the tensor domain. The initial fiber tracking is started from a certain point on a fiber, the advancing direction of the point is calculated, the distance is tracked along the direction of the vector, and then the tracked fiber can be displayed by connecting a new point on the track as a starting point. The key point of the tensor domain-based fiber tracking algorithm is determination of diffusion direction of a current point, but the tensor domain-based fiber tracking algorithm has a defect that fiber bifurcation and intersection cannot be processed, and the algorithm is often stopped at a bifurcation area and intersection. And the method based on global energy minimization can process the bifurcation and the crossing fiber, the method increases the consideration of fiber uncertainty and randomness, and seeks an optimal path by minimizing a cost function, wherein the path with the minimum cost corresponds to a real path. The fast-marching fiber tracking algorithm based on level set (a numerical technique for interface tracking and shape modeling) is a global energy minimization based method, which controls the surface evolution by defining a velocity function, and seeks the optimal path by detecting all possible paths with surrounding neighbor points during each iteration of the evolution. But too many false positive branches were introduced in the evolution process and are not clearly described for fiber orientation.
Fiber tracking provides a method to study white matter organization and connectivity, but fiber tracking has certain limitations. The evaluation of the results of the in vivo fiber tracking is still lack of gold standard. DTI is the only method for displaying the track of nerve fiber bundles in vivo, because the microstructure of a tissue specimen inevitably changes in the processes of dissection, freezing, dehydration, fixation, slicing, dissolution and the like, so that geometric deformation is generated, and the application of a histological method to in vitro verification of the tracking result of the living body has great difficulty. At present, no algorithm can be generally accepted by a large family, so that the proposal of a reliable, effective and rapid fiber tracking algorithm is a research focus in the current research field.
Disclosure of Invention
The invention provides a Fast Marching fiber tracking method based on topology maintenance, aiming at the problems that the algorithm of Fast Marching (FM) based on global energy minimization has more false positive branches and unobvious fiber trend and the like. Therefore, the invention adopts the following technical scheme:
a topology-preserving fast-traveling fiber tracking method, comprising the steps of:
the first step is as follows: processing DTI data;
the second step is that: seed point selection and initialization
(4) An initial activity point, namely a seed point r', is designated as an initial position of the evolution of the curved surface;
(5) determining a speed function
Wherein,
r ' is the active point, n (r ') represents the evolution direction from the curved surface to r ', n (r) represents the evolution direction from the curved surface to r, e1(r) denotes the principal vector direction of r, e1(r ') denotes the principal vector direction of r ', the evolution direction n (r) is approximated using n (r) ═ r-r ' |, the fiber curvature n (r ') ═ r ' -r |;
(6) determining a narrow-band point and a far-away point, determining the arrival TIME T of the narrow-band point according to the following formula, wherein the arrival TIME of the far-away point is initially T ═ TIME _ MAXE, and establishing a minimum sequencing heap of the narrow-band point:
the third step: carrying out the curved surface evolution of topology maintenance by adopting a curvature weighted speed function;
(4) outputting a point r ' with the minimum arrival time T from the minimum sorting heap, marking the point r ' as an active point, and deleting the point r ' from the minimum sorting heap;
(5) inspecting the adjacent points r of the active points r ', and keeping the active points r' unchanged if the active points are all the adjacent points r; if the distance point is the distant point, the distance point is modified into a narrow-band point, the arrival time T (r) of the distance point is calculated, the parent node r' of the distance point is recorded and is put into a minimum sequencing heap; if the narrow-band point is the narrow-band point, recalculating the arrival time T (r), and if the arrival time T (r) is less than the arrival time of the last iteration, updating the arrival time of the point and the parent node r', and adjusting the minimum sequencing heap;
(6) if the curved surface evolution exceeds the volume range of the volume data, stopping iteration; setting a time threshold, and stopping iteration when the arrival time of the point exceeds the time threshold; or predefining iteration times, stopping when the iteration times are reached, ending the cycle, otherwise, turning to the step (1) and continuing to execute;
the third step: determining all fiber paths by adopting a time gradient descent method;
the fourth step: and selecting a real fiber path by using the communication matrix.
According to the fast-marching fiber tracking method, the topology maintenance model is added in the evolution process, the curvature is introduced into the speed function, and the bending energy is considered in the global energy range, so that the evolution process is better controlled, and the problem that the original fast-marching algorithm uses local similarity as unique measure is solved. The method provided by the invention can well reflect the bifurcation information of the fiber, accords with the model of the real fiber, keeps a good topological structure, and has the advantages of accurate fiber tracking result, less false positive branches, good noise robustness and the like compared with the prior art.
Drawings
FIG. 1 is a general flow chart of the present invention;
FIG. 2 is a flow chart of a fast marching algorithm employed by the present invention;
FIG. 3 is a schematic diagram of a fast marching algorithm employed by the present invention;
FIG. 4 is a schematic diagram of an evolution model for topology preservation as employed in the present invention;
FIG. 5 is a computer screen output resulting from processing a projected fiber radial crown using the method of the present invention;
FIG. 6 is an enlarged partial view of FIG. 5 of the computer screen output.
Detailed Description
Referring to fig. 1, the present invention provides a topology-preserving fast-forwarding fiber tracking method in view of the problems of the fast-forwarding fiber tracking method, including the following aspects:
DTI data processing
B. Seed point selection and initialization
C. Surface evolution for topology preservation using curvature weighted velocity function
D. Determining all paths using time gradient descent
E. Selecting true fiber paths using connectivity matrices
Referring to fig. 2, the topology preserving fast traveling fiber tracking method of the present invention and how it is utilized to achieve fiber tracking will be described in detail.
DTI data processing
The image is read and organized into three-dimensional data, and the medical image often contains noise due to electronic interference and the influence of the external environment in the imaging process, so that the noise is removed by using a filter.
Seed Point selection and initialization
The user specifies a seed point as the starting position of the curved surface evolution (i.e. the starting position of the fiber tracking), and then initializes:
1) moving points: the active point is a point with a known arrival time in the mesh, and is initially a seed point specified by a user, and the time T of the evolving surface passing through the point is 0.
2) Narrow band point: the time T of arrival of the neighborhoods of all the active points is 1/F, and the narrow-band points are placed in a minimum sorting pile, wherein F is a curvature weighted speed function which is an important function for controlling the evolution direction and speed of the curved surface, and the method is calculated according to a formula (2).
3) Far away from the point: the arrival TIME is at the point of infinity, T MAX TIME, the far point except the active point and the narrowband point.
Surface evolution with curvature weighted velocity function for topology preservation
1) The point r' with the minimum arrival time tmin is output from the minimum sorted heap, marked as the active point, and removed from the minimum sorted heap.
2) Examining the adjacent point of r', namely the neighbor point of the point on the space, as shown in fig. 3, if the adjacent point r is an active point, the adjacent point is not changed; if the distance point is the far point, the narrow-band point is modified, the arrival time of the narrow-band point is calculated according to the formula (1), and the parent node r' of the narrow-band point is recorded and put into the minimum sorting heap. If the point is a narrow-band point, the arrival time of the point is recalculated according to the formula (1), and if the arrival time T is less than the arrival time of the last iteration, the arrival time of the point and the parent node r' are updated, and the minimum sequencing heap is adjusted.
In each iteration, the curved surface evolves from a point r ' to r, r is a neighbor node of r ' and has a minimum arrival time in a narrow band, and similarly, r ' evolves from r ″, so that r → r ' → r are considered topological information in the evolution process in the evolution model, and r → r ' → r is on the fiber path, as shown in fig. 4.
Where T (r ') is the arrival time of r', F (r) is a function of velocity, ensuring that time T (r) proceeds from the seed point in the direction of n (r) at velocity F (r).
Wherein r ' is the active point, n (r ') represents the evolution direction from the curved surface to r ', n (r) represents the evolution direction from the curved surface to r, e1(r) denotes the principal vector direction of r, e1(r ') represents the principal vector direction of r'. The direction of evolution n (r) is approximated using n (r) ═ r-r ' |, the remaining topology n (r ') ═ r ' -r |, is the fiber curvature. When c (r) < 0, f (r) ═ 0, to ensure that the curved evolution always expands, without shrinking.
The curvature weighted velocity function is based on the following four considerations:
a. when the speeds of the moving points from the same moving point to different neighborhoods (different narrow-band points) are equal, the direction with the minimum curvature is selected to advance.
b. When arrival times of the nodes from different active points to the same neighborhood (same narrow-band point) are equal, the active point with smaller curvature is selected as a father node.
c. When the fiber orientation becomes less obvious and the vector field directions are not consistent, the direction with smaller curvature deflection is preferred, and the continuity and smoothness of the fiber are maintained.
d. The curved surface evolution is ensured to be along the extending direction of the fiber, and the X-shaped and T-shaped fiber paths are avoided.
Curvature weighted velocity function takes the bending energy into account, and when the evolving surface reaches a fiber boundary, an irregular vector field will be excluded because it causes the bending energy to become larger because of curvature limitations. Meanwhile, in the fiber bundle, the curvature weighted speed function can advance along the direction of a tensor field by minimizing bending energy in the fiber tracking process, and false positive branches are reduced.
3) If the curved surface evolution exceeds the volume range of the volume data, stopping iteration; defining a time threshold, when the arrival time of the point exceeds the threshold, considering that the point is relatively low in association degree with the seed point, and stopping iteration when no white matter fiber exists between the point and the seed point; or predefining iteration times, ending the loop when the iteration times are stopped, otherwise turning to 1), and continuing to execute.
Determination of all paths by time gradient descent
Assuming that a fibre γ is present and assuming a length L, τ is a point on γ, and time T is under the influence of speed F
The accumulated result of (1). The fast marching algorithm guarantees that the minimum path from seed point a to r occurs during the evolution and that t (r) is the minimum cost. If a to r there is a path then:
then from the end of the iteration, the shortest path from the wavefront location back to the seed point is calculated by time gradient descent, which is a fiber path.
Picking true fiber paths using connectivity matrices
After the iteration of the fast marching algorithm is finished, the point with any arrival time of T can be connected with the seed point through the minimum path algorithm, the judgment of the real path needs to pass through a link matrix phi, a phi threshold value is set, the most probable path with stronger connectivity with the seed point is selected through phi function mapping, and the fiber which does not meet the condition and is considered to be impossible to exist is deleted.
The rapid marching method of topology maintenance provided by the invention is adopted to reconstruct the white matter fibers, and the reconstruction algorithm starts from the seed point. The reconstructed data is from GE MEDICAL SYSTEMS, using an EP/SE sequence. The junction between the corpus callosum and the sagittal image is selected as the seed point, and fig. 5 shows the result obtained by using the topology preserving fast marching method of the invention to select the projection fiber radial crown, and the trend of different fibers is well distinguished in the image. As can be seen from fig. 6, the fiber path has a tree structure, well reflects the branching information of the fiber, conforms to the model of the real fiber, and maintains a good topological structure as a result.
Claims (1)
1. A topology-preserving fast-traveling fiber tracking method, comprising the steps of:
the first step is as follows: processing DTI data;
the second step is that: seed point selection and initialization
(1) An initial activity point, namely a seed point r', is designated as an initial position of the evolution of the curved surface;
(2) determining a speed function
Wherein,
r ' is the active point, n (r ') represents the evolution direction from the curved surface to r ', n (r) represents the evolution direction from the curved surface to r, e1(r) denotes the principal vector direction of r, e1(r ') denotes the principal vector direction of r ', the evolution direction n (r) is approximated using n (r) ═ r-r ' |, the fiber curvature n (r ') ═ r ' -r |;
(3) determining a narrow-band point and a far-away point, determining the arrival TIME T of the narrow-band point according to the following formula, wherein the arrival TIME of the far-away point is initially T ═ TIME _ MAXE, and establishing a minimum sequencing heap of the narrow-band point:
the third step: carrying out the curved surface evolution of topology maintenance by adopting a curvature weighted speed function;
(1) outputting a point r ' with the minimum arrival time T from the minimum sorting heap, marking the point r ' as an active point, and deleting the point r ' from the minimum sorting heap;
(2) inspecting the adjacent points r of the active points r ', and keeping the active points r' unchanged if the active points are all the adjacent points r; if the distance point is the distant point, the distance point is modified into a narrow-band point, the arrival time T (r) of the distance point is calculated, the parent node r' of the distance point is recorded and is put into a minimum sequencing heap; if the narrow-band point is the narrow-band point, recalculating the arrival time T (r), and if the arrival time T (r) is less than the arrival time of the last iteration, updating the arrival time of the point and the parent node r', and adjusting the minimum sequencing heap;
(3) if the curved surface evolution exceeds the volume range of the volume data, stopping iteration; setting a time threshold, and stopping iteration when the arrival time of the point exceeds the time threshold; or predefining iteration times, stopping when the iteration times are reached, ending the cycle, otherwise, turning to the step (1) and continuing to execute;
the third step: determining all fiber paths by adopting a time gradient descent method;
the fourth step: and selecting a real fiber path by using the communication matrix.
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Cited By (7)
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| CN103445780A (en) * | 2013-07-26 | 2013-12-18 | 浙江工业大学 | Diffusion-weighted magnetic resonance imaging multi-fiber reconstruction method |
| TWI509534B (en) * | 2014-05-12 | 2015-11-21 | Univ Nat Taiwan | Method of automatically calculating link strength of brain fiber tracts |
| CN105550498A (en) * | 2015-12-05 | 2016-05-04 | 中国航空工业集团公司洛阳电光设备研究所 | Moving least square method based ballistic curve fitting method |
| CN105631930A (en) * | 2015-11-27 | 2016-06-01 | 广州聚普科技有限公司 | DTI (Diffusion Tensor Imaging)-based cranial nerve fiber bundle three-dimensional rebuilding method |
| CN107463708A (en) * | 2017-08-21 | 2017-12-12 | 北京理工大学 | It is a kind of that joint visualization method is carried out to UKF Fiber tracks data |
| CN111369637A (en) * | 2019-08-08 | 2020-07-03 | 成都信息工程大学 | DWI fiber optimization reconstruction method and system fusing white matter function signals |
| 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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| CN107463708B (en) * | 2017-08-21 | 2019-10-18 | 北京理工大学 | A kind of pair of UKF Fiber track data carry out joint visualization method |
| CN111369637A (en) * | 2019-08-08 | 2020-07-03 | 成都信息工程大学 | DWI fiber optimization reconstruction method and system fusing white matter function signals |
| CN111369637B (en) * | 2019-08-08 | 2023-07-14 | 成都信息工程大学 | DWI fiber optimization reconstruction method and system for fusing white matter functional signals |
| 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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