Patent Publication Number: US-2022233122-A1

Title: Multi-sphere head model for dipole localization

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of copending U.S. application Ser. No. 16/353,536, filed Mar. 14, 2019, which is hereby incorporated by reference in its entirety. 
    
    
     BACKGROUND 
     Technical Field 
     This disclosure relates generally to generating multi-sphere head models, as may be used in dipole localization for magnetoencephalography (MEG). 
     Description of Related Art 
     In magnetoencephalography (MEG), the brain&#39;s electrical activity causes a magnetic field and this is captured by magnetic field sensors (MEG sensors) positioned at different locations around the brain. These signals can be analyzed for various purposes, such as diagnosing medical conditions, measuring brain function, and conducting research. They are especially well-suited for detecting temporal responses. In one common scenario, the subject undergoes different types of stimuli or performs different types of activity and the resulting MEG signals are reviewed for certain responses or characteristics. For example, if a known stimulus is presented to the subject, the MEG signals may be observed for a response of a certain frequency at a certain time delay after the stimulus. The presence or absence of that response may be an indication of a medical condition. Statistical analysis can also be performed across populations of subjects, for example between groups with and without a medical condition. 
     In many MEG applications, it is useful to have a multi-sphere model (aka overlapping sphere model) of a person&#39;s head. A multi-sphere model includes one sphere for each MEG sensor. The sphere is selected to match a local curvature of the brain surface in the area most relevant to the MEG sensor. These can then be used in the dipole localization step, which is a common step for many MEG processing pipelines. However, in many cases, the multi-sphere model generated using conventional approaches results in ghost spheres. In a ghost sphere, a significant percentage of the sphere&#39;s volume lies outside the brain. The use of ghost spheres results in models in which a large number of dipoles are located outside the brain, which does not match the physical reality. 
     Thus, there is a need for better approaches to generate overlapping sphere models, including for MEG and other encephalography applications. 
     SUMMARY 
     In one aspect, the present disclosure provides a computer-implemented method for correcting a multi-sphere head model used in dipole localization for a set of magnetic field sensors (MEG sensors) by replacing ghost spheres with replacement spheres that are not ghost spheres. One type of ghost sphere completely encloses the brain volume but is so large that a center of the sphere is outside the brain volume. Another type of ghost sphere lies entirely outside the brain volume. Various approaches for correcting ghost spheres are described below. 
     Other aspects include components, devices, systems, improvements, methods, processes, applications, computer readable mediums, and other technologies related to any of the above. The following examples use spheres as a basic shape, but other shapes may also be used, for example ellipsoids. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Embodiments of the disclosure have other advantages and features which will be more apparent from the following detailed description and the appended claims, when taken in conjunction with the examples in the accompanying drawings, in which: 
         FIG. 1  (prior art) is a flow diagram of a magnetoencephalography (MEG) forward model. 
         FIG. 2A  shows a single sphere head model. 
         FIG. 2B  shows an overlapping sphere (multi-sphere) head model. 
         FIGS. 3A and 3B  show two types of ghost spheres. 
         FIG. 4  is a flow diagram for correcting ghost spheres in a multi-sphere head model. 
         FIG. 5  shows a family of candidate replacement spheres. 
         FIG. 6A  shows different lines that may be used to define families of candidate replacement spheres. 
         FIG. 6B  shows an area that may be used to define a family of candidate replacement spheres. 
         FIGS. 7A and 7B  show volumes that may be used to define a family of candidate replacement spheres. 
         FIG. 8  shows different spheres that may be used to define a maximum diameter for a family of candidate replacement spheres. 
         FIG. 9  shows another family of candidate replacement spheres. 
         FIG. 10  shows a user interface for controlling the correction of ghost spheres. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     The figures and the following description relate to preferred embodiments by way of illustration only. It should be noted that from the following discussion, alternative embodiments of the structures and methods disclosed herein will be readily recognized as viable alternatives that may be employed without departing from the principles of what is claimed. 
       FIG. 1  (prior art) is a flow diagram of a magnetoencephalography (MEG) forward model. In MEG, magnetic field sensors are positioned at different locations around the brain. For example, the patient may position his head inside equipment with an array of MEG sensors or the patient may wear headgear containing an array of MEG sensors. The brain&#39;s electrical activity produces a magnetic field and the magnetic field at different locations is measured by the MEG sensors. The process in  FIG. 1  is a forward model, which estimates the magnetic field at each MEG sensor for a given pattern of brain activity. This forward model can then be used to solve the inverse problem: Given measurements of the magnetic field at each MEG sensor, estimate the electrical brain activity that produced the measured magnetic fields. 
     The process has three main steps. A model of the patient&#39;s head is generated  110 . A model of the sources of magnetic field in the brain is generated  120 . The source model  120  is applied to the head model  110  to estimate  130  the magnetic field at each of the MEG sensors. 
     In this example, assume that MRI slices of the patient&#39;s head are available. The head model  110  may be generated as follows. The MRI slices are first assembled into a three-dimensional volume model of the patient&#39;s head, for example a three-dimensional model that represents the patient&#39;s head as voxels  112 . A surface model  114  of the relevant structure is generated from the three-dimensional volume model. The surface model  114  is used to generate  116  the head model, for example a single sphere head model (SSM) or an overlapping sphere head model (OSM). In the following examples, the head model is based on spheres but other shapes may also be used, for example ellipsoids. 
       FIGS. 2A and 2B  illustrate the single sphere head model and the overlapping sphere head model (also known as a multi-sphere model). In both figures, MEG sensors  210  are positioned around the brain  220 . In the SSM ( FIG. 2A ), the patient&#39;s brain is represented by a single sphere  230  based on fit to the surface model. In the OSM ( FIG. 2B ), the patient&#39;s brain is represented by multiple overlapping spheres  240 A-F, one for each corresponding MEG sensor  210 A-F. Sphere  240 A corresponds to MEG sensor  210 A, sphere  240 B to MEG sensor  210 B, etc. The spheres  240  are chosen in part to match the local curvature of the brain&#39;s surface in the vicinity of the corresponding MEG sensor  210 . For convenience, the one sphere  230  in the SSM may be referred to as a global sphere because the same sphere is used for all MEG sensors  210 , and each of the spheres  240 A-F in the OSM may be referred to as local spheres. Returning to  FIG. 1 , the SSM/OSM  116  is used to model the propagation of magnetic fields from sources within the brain to the MEG sensors. 
     The sources within the brain are typically modelled  120  as dipole sources. The synaptic electrical activity in the brain may be modelled as current dipoles. The model includes a distribution  122  of dipoles throughout the volume of the brain. Given a dipole at a certain location of the brain and given the model of the brain volume (e.g., OSM or SSM), the magnetic field created by each dipole is simulated  124 . The contributions of all dipoles are aggregated  130  to estimate the total magnetic field at each MEG sensor. This is referred to as the lead field matrix. 
     Conventional approaches to generating the OSM (step  116  above) may result in local spheres that are “ghost spheres.” In conventional approaches, each local sphere  240  is generated based on the curvature of the brain&#39;s surface in the local vicinity of the corresponding MEG sensor  210 . However, if there is a sparsity of sample points for the brain&#39;s surface or if the points are excessively noisy or if the brain&#39;s surface has an unusual local curvature, the resulting sphere may not work well with later steps of MEG processing. 
       FIGS. 3A and 3B  show examples of two types of ghost spheres. In each figure, a local surface patch  314  of the brain closest to the MEG sensor  310  can be used to define outward and inward directions relative to the brain. The outward direction is the direction from the local surface patch  314  towards the MEG sensor  310 , and the inward direction is the direction from the local surface patch  314  away from the MEG sensor  310 . 
     In  FIG. 3A , the sphere  340 A with center  342 A was generated for MEG sensor  310 A. However, the surface model of the brain results in a sphere  340 A that is large compared to the brain. In this example, the center  342 A of the sphere is inwards of the local surface patch  314 A. That is, the center  342 A of the sphere and the MEG sensor  310 A are located on opposite sides of the local surface patch  314 A. Usually, this is desirable because the volume of the brain is located on the inward side of the local surface patch. However, the sphere has such a large diameter that the center  342 A of the sphere falls outside the brain volume. This may be problematic because fifty percent or more of the sphere&#39;s volume may lie outside the brain volume. If subsequent modeling places dipoles in this non-overlapping region, this is a large number of dipoles that physically do not exist. 
     In  FIG. 3B , the sphere  340 B has a center  342 B that is outwards of the local surface patch  314 B. That is, the center  342 B of the sphere and the MEG sensor  310 B are both located on the outward side of the local surface patch  314 B. This may occur, for example, if the sample points for the surface patch  314 B suggest that it is locally concave. In this example, the sphere  340 B typically is not overlapping with the brain volume. As in  FIG. 3A , this may also be problematic because dipoles located in the sphere  340 B will lie outside the brain volume. 
       FIG. 4  is a flow diagram for correcting a multi-sphere head model. Spheres in the OSM that are ghost spheres are identified  410 . This may be accomplished using the characteristics of ghost spheres described above. If a sphere&#39;s center lies outside the brain volume or if a significant fraction of a sphere falls outside the brain volume, it may be identified as a ghost sphere. The ghost spheres are not suitable for modeling dipole localization in the brain volume, typically because a significant fraction of the ghost sphere falls outside the brain volume. As a result, the ghost spheres are replaced  412  by other spheres that are not ghost spheres, resulting in a corrected OSM. 
     Various approaches to generate replacement spheres are described below. In one correction approach, ghost spheres are replaced by the global sphere generated for the single sphere model. This results in a hybrid approach. Some of the MEG sensors will use the local sphere generated for that sensor, and the rest of the MEG sensors will use the global sphere. In a variation, the global sphere may be generated based on only those MEG sensors that have ghost spheres, rather than based on all MEG sensors as is the case in a true SSM approach. 
     In another approach, the replacement sphere is selected from a family of candidate replacement spheres. For example, the family of candidate replacement spheres may all have centers that lie along a common line: the line defined by the MEG sensor and the point on the brain surface closest to the MEG sensor, or the line defined by the MEG sensor and the center of the global sphere described previously, or the line defined by the MEG sensor and the center of the brain volume. The family of candidate replacement spheres may also be constrained in diameter. For example, they may all have diameters that do not exceed a smallest diameter that completely encloses the brain volume. As another example, the family of candidate replacement spheres may all pass through the point on the brain surface closest to the MEG sensor. In one approach the replacement sphere is selected from the family of candidate replacement spheres based on a fit between the replacement sphere and the brain surface. 
       FIGS. 5-9  show some examples.  FIG. 5  shows a family of candidate replacement spheres  540  defined as follows. A line  548  is defined by the MEG sensor  510  and the point  514  on the brain surface that is closest to the MEG sensor. The centers of the replacement spheres  540  lie on line  548  on the inward side of point  514 . In addition, the replacement spheres  540  are constrained to include this surface point  514 . Increasing the diameter of the sphere yields the family of candidate replacement spheres  540 . In this example, the maximum diameter is also constrained by the smallest sphere that encloses the brain volume. 
     One of the candidate spheres is selected as the replacement sphere, typically based on a fit between the replacement sphere and the brain surface. The selection can be solved as an optimization problem. The family of candidate spheres can be parameterized as a function of the sphere diameter in a range of [ 0 , max diameter]. The problem is then to select the sphere diameter that optimizes a cost function. Examples of cost functions are based on local curvature fitting based on the L1 error, the L2 error, or using eigen-solvers (both analytical and approximation classes of sphere fitting the curvature of a local surface patch). 
     In  FIG. 5 , the centers of the candidate replacement spheres were constrained to lie along line  548 . Other lines could be selected, as shown in  FIG. 6A .  FIG. 6A  shows the following points: location  610  of the MEG sensor, the closest surface point  614  to the MEG sensor, the center  632  of the global sphere (from the SSM of  FIG. 2A ), and the center  622  of the brain volume. Different pairs of points define other lines: line  646  through the MEG sensor  610  and the SSM center  632 , line  647  through the MEG sensor  610  and the brain center  622 , line  648  through surface point  614  and the SSM center  632 , and line  649  through surface point  614  and the brain center  622 , for example. The lines through surface point  614  are dashed in order to more easily distinguish the lines from each other. Other families of candidate replacement spheres may be defined by requiring the center of the replacement sphere to lie on any of these lines. Other lines may also be used, for example lines that are normal to the surface of the brain. 
     The locus of possible locations for the sphere&#39;s center may also be an area or volume, rather than a line. For example, as shown in  FIG. 6B , it may be the triangle with vertices  610 - 632 - 622 , but considering only those points that are on the inward side of point  614 . The resulting locus of possible center points is the trapezoid  646 .  FIG. 7  shows another example where the location of the MEG sensor is defined by an area  710  rather than a point, and the closest surface patch is also defined by an area  714  rather than a point. The locus of possible center points is defined by a projection of area  710  through area  714 , which defines a three-dimensional volume  746 .  FIG. 7A  shows a more restrictive projection  746 A and  FIG. 7B  shows a more expansive projection  746 B. Volumes may also be defined by starting with a line or area and defining a volume that is within a certain distance of the line or area. 
     The region of interest, whether it is a line, area or volume, is typically defined by at least two of the following: (a) the location of the MEG sensor (whether defined as a point, area or volume), (b) the region of brain surface closest to the MEG sensor (which is typically a point or surface area), and (c) the location of the brain volume (e.g., the center of the SSM global sphere, or the centroid or center of mass of the brain volume). 
     The family of candidate replacement spheres may also be constrained to be smaller than a maximum size. The maximum diameter of the replacement sphere may be selected so that the replacement sphere is not a ghost sphere.  FIG. 8  shows the same situation as  FIG. 5  but also shows spheres of different maximum diameters, assuming that the center of the sphere lies along line  848  and the sphere includes surface point  814 . For sphere  840 A, the maximum diameter is defined by the largest sphere that is enclosed by the brain volume. For sphere  840 B, it is defined by the smallest sphere that encloses the brain volume (same as in  FIG. 5 ). For sphere  840 C, it is defined by requiring that the center  842 C of the sphere remains inside the brain volume. 
     In  FIG. 5 , the family of candidate replacement spheres is also constrained to include point  514 , which is the point closest to the MEG sensor. That is, every candidate replacement sphere  540  passes through point  514 . Other variations of this constraint are also possible. In  FIG. 9 , the candidate replacement spheres  940  are constrained to have centers that lie on line  948 , defined by the location  910  of the MEG sensor and the closest surface point  914 . However, the spheres are not required to all pass through the surface point  914 . Rather, each sphere  940  is located so that it makes a best fit to a local patch of the brain&#39;s surface. Thus, spheres  940  may be shifted slightly off of point  914 . 
     In some implementations, a user interface allows the user to control the correction process. In  FIG. 10 , the user interface shows a ghost sphere  1040  that lies outside the brain  1020 . The user is prompted  1070  whether correction should be attempted. The user responds by giving a user instruction whether to compute a replacement sphere for that particular ghost sphere. The next screen of the user interface could then show the computed replacement sphere and prompt the user whether to replace the ghost sphere with the calculated replacement sphere. The user interface displays the various spheres in relation to the brain so that the user can visualize the situation. 
     In yet another approach, rather than correcting ghost spheres, a multi-sphere head model is generated subject to constraints that prevent the generation of ghost spheres in the first place. For example, the centers of the spheres may be constrained to lie inside the brain volume. The diameters of the spheres may be constrained so that they do not exceed some maximum, for example the diameter of the smallest sphere that completely encloses the brain volume. The constraints described above for defining families of candidate replacement spheres may also be used as constraints to prevent the generation of ghost spheres in the first place. 
     As a final example, ghost spheres may result from fitting too few data points. To avoid this, the spheres may be fit to a set of points on the brain surface, but subject to the constraint that at least a predefined number of points are used to fit the sphere. 
     Although the detailed description contains many specifics, these should not be construed as limiting the scope of the invention but merely as illustrating different examples. It should be appreciated that the scope of the disclosure includes other embodiments not discussed in detail above. For example, ellipsoids or other shapes may be used instead of spheres. In that case, a multi-ellipsoid head model is developed in place of a multi-sphere head model and the concept of ghost spheres is replaced by ghost ellipsoids. Various other modifications, changes and variations which will be apparent to those skilled in the art may be made in the arrangement, operation and details of the method and apparatus disclosed herein without departing from the spirit and scope as defined in the appended claims. Therefore, the scope of the invention should be determined by the appended claims and their legal equivalents. 
     Alternate embodiments are implemented in computer hardware, firmware, software, and/or combinations thereof. Implementations can be implemented in a computer program product tangibly embodied in a computer-readable storage device for execution by a programmable processor; and method steps can be performed by a programmable processor executing a program of instructions to perform functions by operating on input data and generating output. Embodiments can be implemented advantageously in one or more computer programs that are executable on a programmable computer system including at least one programmable processor coupled to receive data and instructions from, and to transmit data and instructions to, a data storage system, at least one input device, and at least one output device. Each computer program can be implemented in a high-level procedural or object-oriented programming language, or in assembly or machine language if desired; and in any case, the language can be a compiled or interpreted language. Suitable processors include, by way of example, both general and special purpose microprocessors. Generally, a processor will receive instructions and data from a read-only memory and/or a random-access memory. Generally, a computer will include one or more mass storage devices for storing data files; such devices include magnetic disks, such as internal hard disks and removable disks; magneto-optical disks; and optical disks. Storage devices suitable for tangibly embodying computer program instructions and data include all forms of non-volatile memory, including by way of example semiconductor memory devices, such as EPROM, EEPROM, and flash memory devices; magnetic disks such as internal hard disks and removable disks; magneto-optical disks; and CD-ROM disks. Any of the foregoing can be supplemented by, or incorporated in, ASICs (application-specific integrated circuits), FPGAs and other forms of hardware.