Patent Publication Number: US-2017372195-A1

Title: System for Finding Shortest Pathway between Neurons in A Neural Network

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is a Continuation-in-Part of co-pending application Ser. No. 13/895,999, filed on May 16, 2013, for which priority is claimed under 35 U.S.C. §120; and this application claims priority of Application No. 101138827 filed in Taiwan on Oct. 19, 2012 under 35 U.S.C. §119; the entire contents of all of which are hereby incorporated by reference. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates to a system for establishing the connecting pathways between neurons within a neural network, and more particularly to a system and a method for finding shortest pathways between neurons through 3D neuron image data. 
     BACKGROUND OF THE INVENTION 
     Researches on brain function may be divided into several levels, from microscopic to macroscopic, such as gene expression, protein biochemistry, cellular morphology, brain neural network organizations and animal behavior. Molecular biology, flourished since the 1960s, allows gene manipulation to result in consequences at different scales. In other words, according to basic research in life science, researchers can now make use of technologies to identify genes involved in  Drosophila  memory and alter them to influence behaviors. Although scientists have a clear understanding of macro-scale biology such as animal behavior and micro-scale biology such as gene expression and perspectives of biology, meso-scale biological research remains under-studied owing to technical limitations including the difficulty to acquire the 3D structure of nerve cells and neural network&#39;s formation. Now, the integration of biofluorescent labeling and optical section scanning in confocal microscopy gives rise to the possibility of high-resolution digital images of the brain and its neural network. 
     Biologists often can not obtain images (information) of an organism&#39;s internal structure without damaging the organism itself. Furthermore, when acquiring biological images, physical limitations of laboratory equipment could only generate a serial of two-dimensional (2D) images instead of three dimensional images; as a result, the spatial information between organs is not immediately made available. While an invention in 2002, U.S. Pat. No. 6,472,216 presents a sample preparation solution which enables scientists to acquire images from a transparent whole mount samples. 
     Owing to the technological advances in the twentieth century, it is generally accepted that a completely modular brain model can depict its functional validity. Therefore, the interpretation of brain function can be analytically and anatomically described based on the interactions among different brain regions or even neurons. Accordingly, 3D image reconstruction technology can be applied to build models of major compartments of the brain, and at the same time, merge the anatomy of neuropils or neurons with the function of neural networks in the brain. 
     Although the information processing and transmission mechanism of the human brain fascinates scientists and are main research topics, owing to the fact that the human brain has 100 billion neurons, plus human&#39;s relatively long life span and the legal and moral restriction, human genes cannot be manipulated at will. Neuroscientists thus turn their investigation to other organisms, e.g. mice, zebrafish and  Drosophila . For instance, the  Drosophila  brain only has about 135,000 neurons, but can still exhibit complex memory and learning behaviors; consequently, it has become one of the most popular and important research targets in neuroscience. In addition,  Drosophila  genes have been entirely sequenced, and its short life cycle (approximately 60 days) further makes it a feasible research target. Transparent brain tissues of  Drosophila  may be prepared by utilizing tissue clearing solution invented by one of the inventors of the present application (U.S. Pat. No. 6,472,216 B1 and TW patent No. 594005), and a system is established to collect single neuron image in  Drosophila  brain (TW patent No. I291630 and U.S. Pat. No. 7,742,878 B2). Nowadays, there are nearly twenty thousand brain neurons collected in the  Drosophila  brain, which are arranged appropriately according to their related physiological locations and therefore can be utilized as the basis for the research of the structure and function of the brain (Current Biology 2011, vol: 21: p 1-11 Three-dimensional reconstruction of brain-wide wiring networks in  Drosophila  at single-cell resolution; Pacific Visualization Symposium (PacificVis), 2011 IEEE, 1-4 March: 35-42 The Neuron Navigator: Exploring the information pathway through the neural maze). 
     For brain function research, the message transmission pathways may facilitate to solve the puzzle of how the brain works. Once the shortest pathway between two neurons can be found, it may provide clues to facilitate simulation of the transmission and interpretation of neural signals. 
     The existing techniques can obtain high resolution images of neurons and acquire three dimensional stereoscopic models by utilizing three dimensional stereoscopic image reconstruction techniques. The interconnections among neuropils do not imply linkage neurons are directly connected because there are additional neurons with fibers tangled within each neuropil mediating signal transmissions. Thus, for the shortest pathway between two neurons, there is no method in the past to present the shortest pathway between neurons; especially each neuron possesses irregular shape and complicated terminal branches. Therefore, there is a demand for a new method which can solve the problems and visualize results, otherwise further study on the transmission pathways in the neural network is impossible. 
     SUMMARY OF THE INVENTION 
     One object of the present invention is to solve the problem of how to find the shortest pathway between every two neurons from the neuron images in three dimensional or higher dimensional neural networks. 
     To achieve the aforementioned object, the present invention provides a method for finding shortest pathways between neurons, with irregular shapes and complicated terminal branches, in a neural network. The method includes the following steps: establishing a neuron image database from three dimensional or higher dimensional neuron images by a processing device in a storage device, where the neuron images include a plurality of neurons stored within. Then, whether there is a connection between each of neurons and the other neurons in the three dimensional or higher dimensional neuron image database is determined by the processing device. Subsequently a shortest pathway table of all of the connected neurons is calculated via an All-pairs Shortest Paths algorithm and is temporarily or permanently stored in the storage device. Therefore, as long as any two connected neurons are selected from the three dimensional or higher dimensional neuron image database, the shortest pathway between the two neurons can be obtained in real-time by looking up the aforementioned shortest pathway table in the storage device. 
     In some embodiments of the present invention, the method described above may be performed by a local processing device. Alternatively, in other some embodiments of the present invention, the method described above may be performed by a processing device in a remote server which is connected to network. 
     In the aforementioned embodiments, the three dimensional or higher dimensional neural space database may be constructed from a plurality of unit voxels in the multi-dimensional neuron image space. 
     Furthermore, the determining step mentioned above includes establishing a connection matrix (CM) between the plurality of neurons from the three dimensional or higher dimensional neural space database, where CM(i, j)=1 denotes that there is a connection between a neuron n i  and a neuron n j ; CM(i, j)=0 denotes that there is no connection between the neuron n i  and the neuron n j . 
     A shortest pathway matrix (represented by SP) and a predecessor matrix (represented by Pred) are generated in the All-pairs Shortest Paths algorithm. When SP(i, j)=∞, it denotes that there is no connection between a neuron n i  and a neuron n j ; when Pred(i, j)=nil (i.e. empty set), it denotes that a shortest pathway between a node i and a node j is Edge(i, j); when Pred(i, j)=k, it denotes that the shortest pathway from the node i to the node j passes a node k, where the node k is the predecessor of the node j on the shortest pathway from the node i to the node j. The predecessor matrixes may be stored in the form of tables and the shortest pathway between any two nodes is established by looking up the predecessor table. The shortest pathway within all nodes needs not to be calculated repeatedly. 
     Based on the above description, neurology researchers may establish the database by employing the neural images interested via the aforementioned method and can then find out the shortest pathways between every two neurons in the database easily and rapidly through the method described in this invention, so as to facilitate the studies on neural functions and disease with persuasive anatomical descriptions. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  illustrates a flow chart of the method for finding the shortest pathways between neurons in neural network in accordance with the present invention; 
         FIG. 2  illustrates an architecture diagram of the system applied to perform the method for finding the shortest pathways between neurons in neural network in accordance with one embodiment of the present invention; 
         FIG. 3  illustrates an architecture diagram of the system applied to perform the method for finding the shortest pathways between neurons in neural network in accordance with another embodiment of the present invention; 
         FIG. 4  illustrates a diagram of a unit voxel utilized to construct the three dimensional neural space database in accordance with the present invention; 
         FIG. 5A  illustrates an architecture diagram of the manipulation interface applied in the present invention; 
         FIG. 5B  illustrates a diagram of the manipulation interface applied in the present invention in accordance with one embodiment; 
         FIG. 6  illustrates an architecture diagram of the system applied to perform the method for finding the shortest pathways between neurons in neural network in accordance with another embodiment of the present invention; 
         FIG. 7  illustrates an architecture diagram of the system applied to perform the method for finding the shortest pathways between neurons in neural network in accordance with yet another embodiment of the present invention; and 
         FIG. 8  illustrates a functional block diagram of the processing device applied to perform the method for finding the shortest pathways between neurons in neural network in accordance with one embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     The present invention will now be described with the embodiments and aspects taken together with the accompanying drawings and these descriptions interpret structure and procedures of the present invention only for illustrating but not for limiting the Claims of the present invention. As used herein, references to one or more “embodiments” are to be understood as describing a particular feature, structure, or characteristic included in at least one implementation of the invention. Thus, phrases such as “in one embodiment” or “in an alternate embodiment” appearing herein describe various embodiments and implementations of the invention, and do not necessarily all refer to the same embodiment. However, they are also not necessarily mutually exclusive. 
     The embodiments and details which will be described in detail below include descriptions in connection with the drawings. The description in connection with the drawings may be described in some embodiments or in all embodiments below as other potential embodiments or implementations of the invention concepts presented herein. The embodiments of the present invention are described in great detail below. Please refer to the drawings. 
     The present invention relates to a method for finding the shortest pathways between neurons in neural network through neuron image data. In other words, the method for finding the shortest pathways between neurons in neural network is utilized to receive information of two neurons (for example names or IDs), calculate the connecting neurons between the two neurons and output complete pathway information. 
     As shown in  FIG. 6 , it illustrates an architecture diagram of the system applied to perform the method for finding the shortest pathways between neurons in neural network in accordance with one embodiment of the invention. In this exemplary example, the system includes a micro-imaging device  600 , a neural image server  610 , a computing device  620  and a AR/VR display device  630 . The 3D (three dimensional) image is generated by inputting  Drosophila  neuronal image obtained from the micro-imaging device  600 . The 3D image is acquired from a fluorescent-labeled specimen scanned by a laser scanning microscope. During the scanning process, at least part of the sample is scanned by laser. The cross-section of different depths of the sample was scanned in accordance with a predetermined order; the resulting scanned images were numerous plane images at different depths. Images from different slices of the same stack were combined to form a complete image; and then the resulting 3D image consisting of different cross-sections was generated by a computer software. 
     The neural image server  610  includes a data receiving module  611 , a processing unit  612  and a transmission module  613 . The data receiving module  611  and the transmission module  613  are coupled to the processing unit  612 . The transmission module  613  may be a wireless transmission module or a wired transmission module. The micro-imaging device  600  may include a transmission module. The data retrieving module  635  of the computing device  200  is used for retrieving the 3D image data obtained from the micro-imaging device  600  in accordance with the retrieval condition, and followed by outputting the 3D image data to the computing device  620  via a transmission module. The data receiving module  611  of the neural image server  610  is used for receiving 3D neural space database, shortest pathway tables and predecessor matrix tables from the computing device  600  via a transmission module  613  and  632  in accordance with the receiving condition. It should be noted that the neural image server  610  may also include other auxiliary units, or necessary components which are not so relevant to the present invention. However, it should be easily appreciated by the person having ordinary skill in the art that the neural image server  610  may or may not include these components, which are therefore omitted herein. 
     In another embodiment, the data retrieving module  614  of the neural image server  610  is used for retrieving the 3D image data obtained from the micro-imaging device  600  in accordance with the retrieval condition, and followed by outputting the 3D image data to the neural image server  610  via a transmission module, shown in  FIG. 7 . The data receiving module  636  of the computing device  620  is used for receiving 3D neural space database, or shortest pathway tables and predecessor matrix tables from the neural image server  610  via a transmission module  613  and  632  in accordance with the receiving condition. 
     The computing device  620  includes a personal computer, such as a desktop or laptop computer, network server, or other similar device. Examples of a data link between the devices in the system include USB, USB X.0 (X=2, 3 . . . ), Ethernet, WiFi, or WiGig (Wireless Gigabit Alliance). The computing device  620  generally includes a processing unit  621 , an input unit  627 , a display unit  628 , a storage unit  629 , and a transmission module  632 , as shown in  FIG. 8 . The transmission module  613  is compatible with the transmission module  632  for facilitating data transfer. In this embodiment, the computing device  620  further includes a 3D neural space generating module  622 , a neurons connection determining module  623 , a neural shortest pathway tables generating module  624 , a neural shortest pathway searching module  625  and a manipulation interface  626 , as shown in  FIG. 8 . The above-mentioned modules and units are electrically coupled to the processing unit  621 . In one embodiment, the manipulation interface  626  is stored/disposed in the storage unit  629 . It should be noted that the computing device  620  may further include other auxiliary units or components which are not so relevant to the present invention. However, it should be easily appreciated by the person having ordinary skill in the art that the computing device  620  may or may not include these auxiliary units or components, which are therefore omitted herein. 
     The present invention provides the AR/VR (Augmented reality/Virtual reality) display device  630  capable of improving a stereoscopic feeling of the 3D neural image. 
     Please refer to  FIG. 1 , which is a flow chart of the method for finding the shortest pathways between neurons in neural network, taken together with  FIGS. 2 to 5 . 
     Firstly, the first step of the method for finding the shortest pathways between neurons through neuron image data disclosed by the present invention is to establish a three dimensional neural space database (also referred to as three dimensional neuron image database) which includes a plurality of neurons distributed within three dimensional neural space database (step  101 ). The three dimensional neural space database is generated by the 3D neural space generating module  622 . 
     It should be noted that although this embodiment is described with the three dimensional neural space database as an example, the present invention is not limited to the three dimensional neural space database but may be applied to higher dimensional neural space databases. 
     Please refer to  FIG. 2  first, which is an architecture diagram of the system applied to perform the method for finding the shortest pathways between neurons in neural network in accordance with one embodiment. In this example, the system  200  may be performed by a single processing device. The system (processing device)  200  may include a processing unit  201  to process the operation of the system (processing device)  200 ; and a storage device  203  to store data. Furthermore, the system  200  may also include a manipulation interface  205  connected to the processing unit  201  and the storage device  203  respectively. The storage device  203  includes storage spaces, and three dimensional neural space databases  2031 , shortest pathway table(s)  2033  and predecessor matrix table(s)  2035  (which will be described in detail below) may be stored in the storage spaces. In the present invention, the manipulation interface  205  and the storage spaces of the storage device  203  are connected to each other, such that the user can establish and manipulate the three dimensional neural space database  2031  through the manipulation interface  205 . Moreover, in this exemplary example, the system (processing device)  200  further includes an input unit  209  and a display unit  211 , both of which are electrically coupled to the processing unit  201 , such that the display unit  211  may display the pictures of the manipulation interface  205  in order for the user to view them, and the user may manipulate the manipulation interface  205  through the input unit  209 . 
     In some embodiments of this exemplary example, the system (processing device)  200  may be composed of a computer system, where the processing unit  201  may be performed by a central processing unit (CPU), and the storage device  203  may include any kinds of readable recording medium, such as magnetic storage device, optical storage device or volatile storage device, and shall not be limited thereto. Further, the input unit  209  may be performed by any kinds of components or devices for computer input, for instance mouse, keyboard, touch panel, etc, and shall not be limited thereto. The display unit  211  may also be performed by any kinds of components or device for display, for example liquid crystal display (LCD) device, etc. 
     Furthermore, please refer to  FIG. 3 , which is an architecture diagram of the system applied to perform the method for finding the shortest pathways between neurons in neural network in accordance with another embodiment. In this exemplary example, the system  300  may be composed of a processing device  310 , a server  320  and a network  330 . The processing device  310  generally includes a processing unit  311 , an input unit  313 , a display unit  315  and a storage unit  317 . The storage unit  317  is electrically coupled to the processing unit  311 , and a manipulation interface  319  is disposed therein. The input unit  313  and the display unit  315  are electrically coupled to the processing unit  311  respectively. It should be noted that the processing device  310  may further include other auxiliary units or components which are not so relevant to the present invention. However, it should be easily appreciated by the person having ordinary skill in the art that the processing device  310  may or may not include these auxiliary units or components, which are therefore omitted herein. 
     The server  320  generally includes a storage device  321 , and a three dimensional (3D) neural space database (DB)  3211  is established in the storage spaces of the storage device  321 . Similarly, the storage device  321  also stores shortest pathway tables  3213  and predecessor matrix tables  3215  (which will be described in detail below). 
     It should be noted that the server  320  may also include other auxiliary units, or necessary components which are not so relevant to the present invention. However, it should be easily appreciated by the person having ordinary skill in the art that the server  320  may or may not include these components, which are therefore omitted herein. 
     In this embodiment, the processing device  310  and the server  320  may connect to each other through a network. More specifically, the user can employ the manipulation interface  319  in the processing device  310  to connect with the three dimensional neural space database  3211  established in the storage device  321  in the remote server  320  through the network  330 , and can establish and manipulate the three dimensional neural space database  3211  via the manipulation interface  319 . 
     Similarly, in some embodiments of this exemplary example, the processing device  310 , the server  320  and the network  330  may be performed and operated by any kinds of existing processing devices, servers and networks, which are therefore omitted therein. 
     In the present invention, the establishment of the three dimensional neural space database (which may also be referred to as three dimensional neuron image database)  2031 ,  3211  is derived from the concept of spatial database management system (SDBMS). SDBMS is applied to geographic information system (GIS) initially, and is also utilized in different fields later. For instance, molecular biologists can employ SDBMS to search and compare the structures of different genes, and astronomers can also utilize SDBMS to search and analyze the constellations. Therefore, as long as all of the objects to be searched are located in the same coordinate space, SDBMS can be employed to sort and analyze them to help the researchers. 
     The method for establishing the three dimensional neural space database utilized in the present invention may refer to the disclosure in a Taiwan Patent Application Number 098115595, entitled “A METHOD FOR SEARCHING AND CONSTRUCTING 3D IMAGE DATABASE”. 
     The method for establishing the three dimensional neural space database (which may also be referred to as three dimensional neuron image database)  2031 ,  3211  may be generally divided into the preprocessing of three dimensional image and management of the neuron image. Each set of  Drosophila  brain neural images may be obtained, and each set of the obtained  Drosophila  brain neural images was warped and registered by employing the preprocessing steps and may be represented with tracing lines. The ends of the tracing lines may be the terminals of the neurons. These terminals represent the portions of the neurons which are responsible for information exchange. Thus, if the distance between the terminals of two neurons is less than a certain range, we assume that these two neurons are connected to each other, and the information exchanges happen between these two neurons. 
     Each neural image datum and each tracing line may be warped into a normalized  Drosophila  brain coordinate system, and the space occupied by neural images and each terminal have corresponding spatial coordinates. Thus, a Spatial Database Management System (SDBMS) may be employed to store and manage the information included in the  Drosophila  brain images, and the relationship querying function may be provided through the  Drosophila  neural image information stored in SDBMS. 
     In the present invention, the establishment of the three dimensional neural space database  2031 ,  3211  is described as follows: a unit voxel u (please refer to  FIG. 4 ) is defined in the space where all of the registered neural images are located (it is assumed that the dimensions of neuron image space in X, Y and Z directions are set to be Sx, Sy and Sz respectively), and the size of the unit voxel is set to be ux×uy×uz. The defined unit voxel u may be of different size, and the larger the unit voxel u is, the higher the fault tolerance will be. Dx, Dy and Dx denotes the number of the unit voxels which each dimension in this space can accommodate, i.e. Dx=Sx/ux, Dy=Sy/uy and Dz=Sz/uz. In other words, this neural space may include a number of Dx×Dy×Dz unit voxels. 
     In one embodiment of the present invention, the unit voxel may be 2×2×2 pixels, and the standard brain space may be 1944×1222×740 pixels, but is not limited thereto. 
     After the three dimensional neural space database  2031 ,  3211  which includes a plurality of neurons distributed therein is established, it is determined whether each neuron in the three dimensional neural space database  2031 ,  3211  is connected to the other neurons (step  103 ) by the neurons connection determining module  623 . 
     In the present invention, when the database  2031 ,  3211  is established, the connecting relationship between two neurons may be found by querying the database to know that if the terminals of these two neurons are located within the same unit voxel. There may be errors in the processing procedure of the neural images. Therefore, a threshold may be defined. In this embodiment, the size of a unit voxel is set as the threshold. Thus, if any one of terminals of one neuron and any one of terminals or part of the trace of another neuron are located within the same unit voxel, it is taken that a connection exists between the two neurons. That is, information is transmitted between the two neurons at such point. With reference to  FIG. 4 , the cube  405  represents a unit voxel, and the unit voxel  405  in which a terminal of a first neuron  401  is located has a second neuron  403  passing through. Thus, it may be considered that there is a connection between the first neuron  401  and the second neuron  403 . 
     Therefore, when the database  2031 ,  3211  is established, the database  2031 ,  3211  may be employed to find the neuron(s) connected with all other possible neurons. For instance, in order to find neuron(s) connected with a neuron n i , the first step is to find out all of the unit voxels through which the neuron n i  passes, and then all of the neurons which pass through these unit voxels can be found from the database  2031 ,  3211 . 
     In other word, for each unit voxel u in a number of Dx×Dy×Dz unit voxels, the neurons passing through the unit voxel u are found, and this related information is stored in the three dimensional neural space database (also referred to as three dimensional neuron image database)  2031 ,  3211  established in step  101 . The database  2031 ,  3211  mainly includes the location of the unit voxel (ux, uy, uz), and the content is the names of all of the neurons passing through this unit voxel (which may be represented by ID (identification number)). 
     Connection matrix (also referred to as adjacency matrix) between neurons may be built up via the aforementioned concepts. It is assumed first herein that there are m records stored in the database  2031 ,  3211 , i.e. there are m neurons. Thus, a m×m matrix, which is represented by CM, may be established. When CM(i, j)=1, it denotes that there is a connection between the neuron n i  and the neuron n j . Contrarily, when CM(i, j)=0, it denotes that there is no connection between the neuron n i  and the neuron n j . In such way, the values in the whole CM matrix are filled, and this CM matrix is the connection matrix showing the connecting relationship between neurons. 
     In the present invention, when the connection matrix between every two neurons is built up, the connection matrixes among all neurons may be converted into a undirected graph to represent them. Under this structure, each neuron is equivalent to a node. A connection between two neurons is equivalent to that there is a connecting edge between two nodes. Thus, if there is a connection between the neuron n i  and the neuron n j , i.e. CM(i, j)=1, it denotes that there is an edge with a weight of 1 between the node i and the node j. The algorithm of graph analysis in graph theory may then be applied to the neuron connection structure. In one exemplary example of the present invention, the neural images to be used are the neural images of  Drosophila  brain, which has about thirteen thousand neurons for now. Therefore, it is equivalent to that the shortest pathways have to be found from a graph with about thirteen thousand nodes. It&#39;s better to find out the shortest pathway in real-time. Traditionally, the shortest pathways are usually calculated by utilizing Dijkstra&#39;s algorithm, in which a certain node is utilized as a starting node, and the shortest pathways from the starting node to all of the other nodes are then calculated. If the traditional method is applied to the present system, the shortest connecting pathways between one node among ten thousand nodes and the other nodes among the ten thousand nodes have to be searched respectively. It is very difficult for the processing devices  200 ,  310  to find the shortest pathways in real-time. 
     In the present invention, all pairs shortest paths (APSP) may be calculated by employing Floyd-Washall Algorithm, which is also referred to as APSP algorithm. This calculating method can calculate the shortest pathways among all neurons which are connected to one another. Although there are thirteen thousand neurons in this embodiment and the computation is very time-consuming, i.e. the dimension of the connection matrix is around 13000×13000, the present invention calculates the shortest pathways among all connected neurons only one once and establishes shortest pathway matrix tables to store the shortest pathways (step  105 ) by the neural shortest pathway tables generating module  624 . The APSP algorithm is stored in the neural shortest pathway tables generating module  624 . 
     When the APSP algorithm is applied to the computation of the connection matrixes of the present invention, two matrixes will be generated, where one is the shortest path (SP) matrix, i.e. SP(i, j) is the distance of the short pathway from the node i to the node j, and the other is predecessor matrix (Pred). Thus, if SP(i, j)=∞, it denotes that there is no pathway to connect the node i and the node j. There are two situations for Pred(i, j) as follow: when Pred(i, j)=nil (i.e. an empty set), it represents that the shortest pathway between the node i and the node j is Edge(i, j); when Pred(i, j)=k, it represents that the shortest pathway from the node i to the node j may pass the node k, where the node k is the predecessor of the node j on the shortest pathway from the node i to the node j. The predecessor matrixes and the shortest pathway matrixes may be generated by the neural shortest pathway tables generating module  624 . 
     Therefore, in order to find the shortest pathway (Path(i, j)) between the neuron n i  and the neuron n j , the SP matrix needs to be checked first. If SP(i, j) is not ∞, it denotes that the shortest pathway exists. Then, the shortest pathway may be found from the Pred matrix. Moreover, if Pred(i, j)=k, the shortest pathway between the node i and the node j is Path(i, k) plus Path(k, j), such that the shortest pathway between the neuron n i  and the neuron n j  can be found. 
     The predecessor matrixes and the shortest pathway matrixes may be stored in the form of tables as the predecessor matrix table  2035 ,  3215  and the shortest pathway matrix table  2033 ,  3213  respectively. When the shortest pathway between any two neurons is to be searched, the pathway may be found directly by look-up-table (LUT) and the APSP algorithm needs not to be performed every time. 
     Thus, the shortest pathway tables (predecessor tables) may be formed through the aforementioned method (by the neural shortest pathway tables generating module  624 ) and may be then stored in the storage device  203 ,  321 . 
     After the shortest pathway tables are completed, as long as two neurons may be selected from the three dimensional neural space database  2031 ,  3211  (step  107 ), it can be determined whether the shortest pathway exists between the two neurons or not by looking up the aforementioned shortest pathway tables (step  109 ). The step  107  and the step  109  are performed by the neural shortest pathway searching module  625 . 
     When it is determined that the shortest pathway exists, the shortest pathway between the two neurons may be obtained (step  111 ). Otherwise, return to step  107  and reselect two neurons. 
     As described above, when the shortest pathway between any two neurons in the three dimensional neural space database (also referred to as three dimensional neuron image database)  2031 ,  3211  is to be searched, the step  109  may be utilized first to determine whether the shortest pathway exists or not. If yes, the shortest pathway between the two neurons may be found rapidly through the table formed from the predecessor matrixes. 
     In this embodiment, if the whole matrix cannot be loaded once due to the limitation of the system, the table may be split into several sub-pages and only the necessary sub-pages are loaded because the number of the nodes is about thirteen thousand and a 13000×13000 matrix includes a large amount of information. The loading and paging of sub-pages may be performed via the least recent used (LRU) method. 
     It should be noted that each step of the method for finding the shortest pathway between neurons disclosed by the present invention is performed by the system (processing device)  200  or the system  300 . The manipulation interface  205 ,  319  may be performed as the structure disclosed in  FIG. 5A . With reference to  FIG. 5B , which is a diagram of the manipulation interface applied in the present invention in accordance with one embodiment, the manipulation interface  205 ,  319  may include two portions, which are the user interface  510  and the visualization interface  520  respectively. 
     The user interface  510  may include the following several functions but be not limited thereto: a pathway searching interface (Path Query)  513  and a search target input field (Query)  511 , which enable the user to perform the manipulating action or the selecting action via the input unit  209 ,  313 . Furthermore, the visualization interface  520  may include the following several functions but be not limited thereto: mesh  521 , neuron  523 , semi-transparent effects  525  and two dimensional connectivity graphs  527 , which enable the user to recognize the neural images in a graphical way. Therefore, the user may manipulate the three dimensional neural space database  2031 ,  3211  via the manipulation interface  205 ,  319  mentioned above, and after the user inputs the shortest pathway search commands, the computation may be performed by the processing unit  201 ,  311 . 
     Based on the above description, neurology researchers may establish the database by employing the neural images interested via the aforementioned method and can then find out the shortest pathways between every two neurons in the database easily and rapidly through the method described in the present invention, so as to facilitate the studies on neural functions and disease with persuasive anatomical descriptions. 
     It should be appreciated that the embodiments and the attached drawings are described and illustrated for purposes of illustration only, not for limiting, and that numerous alterations and modifications may be practiced by those skilled in the art without departing from the spirit and scope of the present invention. It is intended that all such modifications and alterations are included insofar as they come within the scope of the present invention as claimed or the equivalents thereof.