Patent Publication Number: US-2021186405-A1

Title: System for and method of rapid peripheral nerve stimulation assessment of gradient coils

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is based on, claims priority to, and incorporates herein by reference in its entirety U.S. Ser. No. 62/946227 filed Dec. 10, 2019, and entitled “System for and Method of Rapid Peripheral Nerve Stimulation Assessment of 2D or 3D Gradient Coil Windings.” 
    
    
     STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH 
     This technology was made with government support under grants R00EB019482, U01EB025121 and U01EB025162 awarded by the National Institutes of Health. The government has certain rights in the technology. 
    
    
     FIELD 
     The present disclosure relates generally to assessing peripheral nerve stimulation (PNS) of a gradient coil and, in particular to a system and method for rapid assessment of PNS of a gradient coil based on a PNS predictor defined on a Huygens&#39; surface of a body model. 
     BACKGROUND 
     The ability to quickly assess Peripheral Nerve Stimulation (PNS) is becoming increasingly important for optimizing stimulation devices, as well as devices for which PNS is an unwanted side effect such as gradient coils in Magnetic Resonance Imaging (MM) or drive coils in Magnetic Particle Imaging (VIPI). In both cases, the device operator or designer must quickly assess if and where a candidate electrode or coil design induces action potentials (APs) in the body. Any insights into the device&#39;s PNS locations within the body and the onset PNS thresholds (i.e., the smallest stimulating electrode voltage or coil current amplitude inducing an action potential) can allow the device designer or operator to iteratively modify the device or change its position relative to the body to either increase or decrease the strength of the stimulation. 
     One process developed for PNS assessment of MRI gradient coils (e.g., estimating PNS thresholds) includes simulations of the titration process that incorporates a full neurodynamic model of the nerves in the body. The full neurodynamic model is a mathematical model of various ion population concentrations in the nerve cell and is coupled to an electromagnetic model of the human body to predict PNS. Specifically, this PNS simulation workflow starts with simulating the electric fields that an external coil induces in a body model. The electric fields are then projected onto the nerve fiber trajectories included in a nerve atlas of the body model (e.g., a detailed nerve atlas of the nerve fibers in the human body co-registered to the body model) and the projected electric fields are integrated to obtain the electric potential variations along the nerves (this is the driving function of PNS and the input to the neurodynamic model). Finally, this potential variation is fed into the neurodynamic model to predict the nerve&#39;s response. The output of the model is the intracellular potential changes along the nerve over the time-course of the applied coil current that may show induced action potentials if the nerve was stimulated. Although this process (i.e., a full electromagnetic plus neurodynamic model framework) is very useful when analyzing candidate coil designs during the design phase, it is not straightforward to incorporate it in the standard approach for numeric gradient winding optimization. The PNS metric from this PNS prediction process cannot be readily used as a linear constraint in a numeric optimization framework due to the non-linearity of the neurodynamic model. In addition, the electromagnetic and neurodynamic simulations are very time-consuming (both of which can take multiple hours up to several days), which does not permit the PNS metric to be computed repeatedly during a numerical optimization. 
     In order to convert the PNS metric to a form that is better suited to numerical optimization, a rapid linear PNS predictor or “oracle” was developed that can be used in gradient coil design optimization and is a surrogate for the full neurodynamic model. Accordingly, a PNS oracle allows the estimation or prediction of PNS thresholds without the need to simulate the complex neurodynamics of the nerve fibers using full neurodynamic modeling. The PNS oracle can estimate the PNS threshold of a nerve segment from the electric field using only linear operations (projection of the electric field onto the nerve to obtain the potential changes, finite differencing, convolution, and scaling). The PNS oracle assigns a value to every section of a nerve that inversely scales with the PNS threshold. The fact that the PNS oracle is linear in the electric field (and thus linear in the current fed to the coil that induces these E-fields) allows precomputing the PNS oracle for a large number of coil or wire pieces. The precomputed PNS oracle(s) may then be used to quickly assess arbitrary coil/wire configurations. The determination of PNS thresholds for the arbitrary coil/wire configurations using the pre-computed PNS oracle is very fast (milliseconds), rendering it adequate for numerical optimization that requires repeated evaluation of hundreds of PNS responses. In addition, the PNS oracle can be directly incorporated in the standard approach for the design of MRI gradient coils, namely the boundary element method stream function (BEM-SF) approach. In the BEM-SF approach, the PNS oracle can be pre-computed for each stream function basis. This precomputation step involves simulating the electric field (E-field) induced by a stream function basis. The E-field is then projected onto the nerve fiber path and integrated to obtain the electric potential changes. The PNS oracle can then be directly calculated from the electric potential changes. Combining PNS oracle contributions induced by all stream function basis in all nerve segments yields a so-called P-matrix that can be incorporated in the BEM-SF winding optimization as a linear PNS penalty matrix to enforce PNS-optimized coil layouts. However, the PNS oracle approach still requires the simulation of electric fields in the body model (from which the PNS oracles can be computed). In fact, to obtain the full P-matrix, the electric fields need to be simulated for every stream function basis individually to extract their PNS oracles. This process can take more than a week for a single gradient coil design shape. In addition, every modification of the coil former shape requires the re-computation of the P-matrix. 
     SUMMARY 
     In accordance with an embodiment, a method for assessing peripheral nerve stimulation (PNS) for a coil geometry includes retrieving a PNS Huygens&#39; P-matrix for a body model. The PNS Huygens&#39; P-matrix is defined on a Huygens&#39; surface enclosing the body model. The method further includes generating a coil specific PNS P-matrix for the coil geometry based on at least the PNS Huygens&#39; P-matrix for the body model, determining at least one PNS threshold for the coil geometry based on the coil specific PNS P-matrix, and storing the at least one PNS threshold in a storage device. 
     In accordance with another embodiment, a magnetic resonance imaging (MRI) system includes a magnet system configured to generate a polarizing magnetic field about at least a portion of a subject, a magnetic gradient system including a plurality of gradient coils configured to apply at least one gradient field to the polarizing magnetic field and a radio frequency (RF) system configured to apply an excitation field to the subject and to receive MR data from the subject using a coil array. The MRI system further includes a computer system that is programmed to retrieve a PNS Huygens&#39; P-matrix for a body model. The PNS Huygens&#39; P-matrix is defined on a Huygens&#39; surface enclosing the body model. The computer system is further programmed to generate a coil specific PNS P-matrix for a predetermined gradient coil geometry based on at least the PNS Huygens&#39; P-matrix for the body model, determine at least one PNS threshold for the gradient coil geometry based on the coil specific PNS P-matrix, and store the at least one PNS threshold in a storage device. 
     In accordance with another embodiment, a method for optimizing a design of a gradient coil geometry includes creating a current density distribution of the gradient coil geometry, determining the B-field generated by each stream function basis associated with the current density distribution and determining a coil specific PNS P-matrix for the gradient coil geometry based on at least a PNS Huygens&#39; P-matrix for a body model. The PNS Huygens&#39; P-matrix is defined on a Huygens&#39; surface enclosing the body model. The method further includes determining a current density pattern using an optimization process including the coil specific PNS P-matrix for the gradient coil geometry, and storing the current density pattern. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The present disclosure will hereafter be described with reference to the accompanying drawings, wherein like reference numerals denote like elements. 
         FIG. 1  illustrates a method for generating a PNS Huygens&#39; P-matrix for assessment of peripheral nerve stimulation in accordance with an embodiment; 
         FIG. 2  illustrates various steps of the method of  FIG. 1  for generating a PNS Huygens&#39; P-matrix in accordance with an embodiment; 
         FIG. 3  illustrates an example PNS Huygens&#39; P-matrix in accordance with an embodiment; 
         FIG. 4  illustrates a method for assessing peripheral nerve stimulation (PNS) for a coil geometry in accordance with an embodiment; 
         FIG. 5  illustrates a method for gradient coil design and optimization in accordance with an embodiment; 
         FIG. 6  is a block diagram of an example computer system in accordance with an embodiment; and 
         FIG. 7  is a block diagram of an example MRI system for use in accordance with an embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     The present disclosure describes systems and methods for assessing peripheral nerve stimulation of a gradient coil or magneto-stimulation (or magnetic stimulator) device using a coil specific PNS predictor that is generated using a linear PNS penalty matrix (P-matrix) defined on a Huygens&#39; surface of a body model (hereinafter referred to as a PNS Huygens&#39; P-matrix (P H )). The coil specific PNS predictor is also in the form of a linear PNS penalty matrix, is generated for a specific coil geometry (e.g., a coil winding pattern or a coil former shape) and is hereinafter referred to as a coil specific PNS P-matrix (P D ). The PNS Huygens&#39; P-matrix can be pre-computed and stored and, therefore, only needs to be generated once for each body model. For assessment of a specific gradient coil geometry (e.g., winding pattern, coil former shape), the PNS Huygens&#39; P-matrix may be translated to a coil specific PNS P-matrix associated with the coil geometry using a mapping matrix or a mapping vector. Accordingly, the PNS Huygens&#39; P-matrix may be mapped to individual coil shapes and winding patterns. The generation of the coil specific PNS P-matrices does not require the computation of electric fields and PNS predictor values for each different coil former shape or coil winding. A coil specific PNS P-matrix may be directly incorporated into a standard gradient winding optimization approach for gradient design, such as the boundary element method stream function (BEM-SF) approach. A coil specific PNS P-matrix may also be used to rapidly assess PNS (e.g., predict PNS thresholds) for discrete coil windings (e.g., existing or hypothetical gradient coils). In addition, coil specific PNS P-matrix may be used to rapidly assess PNS (e.g., predict PNS thresholds) for a magneto-stimulation (or magnetic stimulator) device, for example, consisting of an array of magnetic coils, that may be used for therapy and treatment applications. The system and methods for assessing PNS of gradient coils or magneto-stimulation devices may be used, for example, to design PNS optimized gradient coils, for online PNS monitoring on an MR Scanner for different patient positions and guided placement of magneto-stimulation devices (coil or coil array). 
       FIG. 1  illustrates a method for generating a PNS Huygens&#39; P-matrix for assessment of peripheral nerve stimulation in accordance with an embodiment and  FIG. 2  illustrates various steps of the method of  FIG. 1  for generating a PNS Huygens&#39; P-matrix in accordance with an embodiment. Referring to  FIGS. 1 and 2 , a body model  204  is selected at block  102 . In one embodiment, the body model  204  may be selected by a user via a user input of a computer system. At block  104 , an intermediate surface mesh (i.e., the Huygens&#39; surface)  202  is chosen so that the entire body model is enclosed with a minimum distance between the Huygens&#39; surface and the boundary of the body model (e.g., 5 cm) and the Huygens&#39; surface  202  is closely fitted to the body model  204 . In addition, the Huygens&#39; surface is chosen so that it smoothly encloses the entire body model. In  FIG. 2 , only a portion of the Huygens&#39; surface is shown enclosing a portion of the body model  204  for clarity and to illustrate the body model  204 . As mentioned, the Huygens&#39; surface will enclose the entire body model. The body model  204  also includes a nerve atlas. At block  106 , the Huygens&#39; surface  202  is densely populated with elements that serve as basis functions for the magnetic fields. In one embodiment, the basis elements are small current loops  206 , as shown in  FIG. 2 . The number and size of the loops can be chosen so as to yield a complete basis. In one example, approximately 3000 bases with a few millimeters in diameter may be used to densely populate the Huygens&#39; surface. In other embodiments, other basis elements (other than loops) may be added on the Huygens&#39; surface, for example, electric dipoles. However, current loops (i.e., magnetic dipoles) have been found to account for the vast majority of the EM variability achievable at the kHz frequencies relevant for PNS. At block  108 , magnetic field components (B x , B y , B z are simulated on the boundary of the body model  204  for every Huygens&#39; basis. At block  110 , a matrix B H  is created from the simulated magnetic fields induced by each Huygens&#39; basis. The matrix B H  has a size of b×n H  where b is the number of points on the boundary of the body model and n H  is the number of Huygens&#39; basis functions. The matrix B H  may be simulated, for example, using the fast Biot-Savart formulation, since MRI gradients and other coils relevant for PNS are operated in the low kHz frequency range. In an embodiment, the matrix B H  is pre-computed and only needs to be generated once for each body model. 
     At block  112 , the electric field that every Huygens&#39; basis function induces in the body model  204  is simulated. Diagram  208  illustrates an example electric field of Huygens&#39; basis. At block  114 , a PNS predictor value  212  is extracted along all nerves of the body model&#39;s nerve atlas, for example, as illustrated in diagram  210  in  FIG. 2 . In one embodiment, the PNS predictor (or oracle) values (PNSO) may be determined using: 
         PNSO ( r )= K ( D )/ m ( D )* V ( r−L )−2 V ( r )+ V ( r+L )/ L ( D ) 2    Eqn 1
 
     where V(r) is the extracellular potential along the nerve position r, L(D) is the distance between consecutive nodes of Ranvier (which is a function of the axon diameter D), K(D) is a spatial kernel, and m(D) is a calibration factor. At block  112 , the PNS Huygens&#39; P-matrix (P H ) is created by combining the PNS predictor values induced by all Huygens&#39; bases along all nerve segments. The PNS Huygens&#39; P-matrix is a linear P-matrix. The PNS Huygens&#39; P-matrix (P H ) has a size of p×n H  where p is number of nerve segments in the body model and n H  is the number of basis functions on the Huygens&#39; surface. At block  214 , PNS Huygens&#39; P-matrix (P H ) and the matrix B H  may be stored in a memory or data storage of, for example, an MRI system (e.g., MRI system  700  discussed below with respect to  FIG. 7 ) or other computer system (e.g., computer system  600  discussed below with respect to  FIG. 6 ). The PNS Huygens&#39; P-matrix (P H ) and matrix B H  may be obtained or retrieved from the memory or data storage 
       FIG. 3  illustrates an example PNS Huygens&#39; P-matrix  300  in accordance with an embodiment. The Huygens&#39; basis functions  306  (columns) are ordered from head to feet. In this embodiment, the nerve segments  302  (rows) are clustered into groups of the major anatomical nerves  308  which are also ordered from head to feet. Scale  304  shows the different PNS predictor values indicated in the matrix by shading. 
       FIG. 4  illustrates a method for assessing peripheral nerve stimulation (PNS) for a coil geometry in accordance with an embodiment. At block  402 , a body model is selected. At block  404 , a coil geometry, for example, a coil former shape or coil winding pattern, is selected for PNS assessment. As mentioned above, the coil geometry may be for a device such as a gradient coil or a magneto-stimulation device. In one embodiment, the body model and the coil geometry may be selected by a user via a user input of a computer system. At block  406 , a matrix of magnetic field components (B H  ) on a boundary of a body model is obtained or retrieved. In one embodiment, the matrix B H  may be generated for a set of Huygens&#39; surface bases as described above with respect to  FIG. 1 . In an embodiment, the matrix B H  may be pre-computed and stored in a memory or data storage. The matrix B H  may be obtained or retrieved from the memory or data storage. At block  408 , a PNS Huygens&#39; P-matrix (P H ) for the body model may be obtained or retrieved. The PNS Huygens&#39; P-matrix (P H ) facilitates the rapid determination or optimization of the response of peripheral nerves to any winding pattern (the sources) located beyond the Huygens&#39; surface. An example method for generating the PNS Huygens&#39; P-matrix (P H ) is described above with respect to  FIG. 1 . While generation of the PNS Huygens&#39; P-matrix is typically slow (approximately one month per body model), the PNS Huygens&#39; P-matrix only needs to be generated once per body model and is fixed for any arrangement of the sources located beyond the Huygens&#39; surface. Accordingly, in an embodiment, the PNS Huygens&#39; P-matrix (P H ) may be pre-computed and stored in a memory or data storage The PNS Huygens&#39; P-matrix (P H ) may be obtained or retrieved from the memory or data storage. 
     At block  410 , a B-field matrix (B D ) is determined for initial sources for the body model. The B-field matrix B D  is determined for the initial sources (located beyond the Huygens&#39; surface) by simulating the magnetic field component on the boundary of the body model for each initial source (similar to the B H  matrix of the Huygens&#39; basis functions). The resulting matrix B D  has a size b×n D  where b is the number of points on the body model boundary and n D  is the number of sources. The B-field matrix B D  may be stored in memory or data storage of, for example, an MRI system (e.g., MRI system  700  discussed below with respect to  FIG. 7 ) or other computer system (e.g., computer system  600  discussed below with respect to  FIG. 6 ). 
     At block  412 , a mapping matrix (M) or a mapping vector (m) is generated. In one embodiment, a mapping matrix (M) is generated if the coil specific PNS P-matrix P D  will be used for optimization of a gradient coil and will be directly incorporated into a standard gradient winding optimization approach (e.g., BEM-SF). In an embodiment, the mapping matrix M may be generated by solving a system of linear matrix equations including the matrices B H  and B D  (described above) using Tikhonov regularized pseudo-inverse: 
         M =( B   H   T   B   H +λ 2   I ) −1   B   H   T   B   D    Eqn. 2
 
     where B H  and B D  are the B-field matrices described above, I denotes the identity matrix, λ is the regularization strength and T denotes the transpose of the matrix. The mapping matrix M has a size of n H ×n D  where n H  is the number of Huygens&#39; basis functions and n D  is the number of basis functions on the design surface or the number of independently driven discrete coils (such as gradient coil axes or coils of a magnetic stimulator device). In other embodiments, other known approaches may be used to generate the mapping matrix M, such as directly solving the linear system for each basis function using linear optimization solvers. In another embodiment, a mapping vector m is generated if the coil specific PNS P-matrix P D  will be used to predict PNS thresholds for a single discrete coil winding (e.g., existing gradient coils). A mapping vector (m) may be used rather than the mapping matrix (M) in this embodiment because the coil corresponds to a single basis element. In this embodiment, the sources are discrete wires instead of stream functions. Generation of the mapping vector (m) may also performed using Eqn 2. The mapping matrix (M) and mapping vector (m) may be stored in memory or data storage of, for example, an MRI system (e.g., MRI system  500  discussed below with respect to  FIG. 5 ) or other computer system (e.g., computer system  400  discussed below with respect to  FIG. 4 ). Advantageously, in one example the generation of mapping matrix M or the mapping vector is very fast (e.g., only a few seconds). The mapping matrix M may be generated very quickly (seconds) because it only involves: 1) calculation of the magnetic field created by the sources beyond the Huygens&#39; surface (which only takes seconds), namely, the matrix B D  ; and 2) solving a system of linear equations. As mentioned above with respect to block  406 , the matrix B H  may be pre-computed for a set of Huygens&#39; surface bases and, for example, retrieved from a memory or storage device. 
     At block  414 , a coil specific PNS P-matrix (P D ) may be created using the PNS Huygens&#39; P-matrix (P H ) and either the mapping matrix (M) or the mapping vector (m). The coil specific PNS P-matrix is a linear P-matrix. In one embodiment, the coil specific PNS P-matrix P D  may be used for optimization of a gradient coil. In order to translate or map the general PNS Huygens&#39; P-matrix P H  to a coil specific PNS P-matrix P D , a projection operation of the initial sources (located beyond the Huygens&#39; surface) to the Huygens&#39; surface is performed and is expressed mathematically as: 
       P D =P H M   Eqn. 3
 
     The coil specific PNS P-matrix P D  assigns a value (a predictor value) to each section of a nerve that inversely scales with the PNS threshold. The PNS threshold may be given by the inverse of the maximum absolute PNS P-matrix P D , namely: 
       max{|P H M| −1 }  Eqn. 4
 
     In another embodiment, the coil specific PNS P-matrix P D  may be used to predict PNS thresholds for single discrete coil winding (e.g., an existing gradient coil). In this embodiment, the projection of the Huygens&#39; P H  matrix is achieved using a mapping vector m. As mentioned, above, a mapping vector (m) may be used in this embodiment rather than a mapping matrix (M), because the coil corresponds to a single basis element. The projection operation may be expressed as: 
       P D =P H m   Eqn. 5
 
     As mentioned above, the coil specific PNS P-matrix P D  assigns a value (a predictor value) to each section of a nerve that inversely scales with the PNS threshold. The PNS threshold may be given by the inverse of the maximum absolute PNS P-matrix P D , namely: 
       max{|P H m| −1 }  Eqn. 6
 
     At block  416 , PNS thresholds may be determined using the coil specific PNS P-matrix (P D ), for example, by determining the inverse of the coil specific PNS matrix PNS predictor values as given by Eqn 4 and 6. A PNS threshold is the smallest stimulating coil current amplitude inducing an action potential (AP). At block  418 , the PNS thresholds may be stored in memory or data storage of, for example, an MRI system (e.g., MRI system  700  discussed below with respect to  FIG. 7 ) or other computer system (e.g., computer system  600  discussed below with respect to  FIG. 6 ). In an embodiment, a report may be generated indicating the PNS thresholds (using, for example, a chart, graph or image) and provided to and shown on a display (e.g., display  618  shown in  FIG. 6  or display  704 ,  736  or  744 l shown in  FIG. 7 ). The report may also be stored in memory or data storage. 
     The PNS Huygens&#39; P-matrix (P H ) fully describes the body models&#39; electric fields (i.e., the electric fields induced in the body model) and their interaction with the nervous system. The PNS Huygens&#39; P-matrix is defined on the smooth Huygens&#39; surface enclosing the body model. Instead of re-computing electric fields and PNS predictor values for different coil windings or different coil former shapes within numeric coil winding optimization as required by prior PNS predictor tools, the systems and methods described herein facilitate the quick translation or mapping of the PNS Huygens&#39; P-matrix to arbitrary coil former surfaces and coil windings using the mapping matrix or mapping vector. As mentioned, the PNS Huygens&#39; P-matrix approach described herein may be applicable to both discrete coil winding patterns (e.g., existing or hypothetical MRI gradient coils) and continuous current density patterns (i.e., the coil specific PNS P-matrix can be directly incorporated into, for example, the standard BEM-SF approach for numeric gradient winding optimization). 
     In another embodiment the coil specific PNS P-matrix may be used to rapidly assess PNS (e.g., predict PNS thresholds) for a magneto-stimulation (or magnetic stimulator) device, for example, consisting of an array of magnetic coils, that may be used for therapy and treatment applications. In this embodiment, the coil specific PNS matrix (P D ) may be split into two matrices based on the desired nerves to be stimulated. In particular, a matrix P tar  may be created from a set of targeted nerves to be stimulated and a matrix P avd  may be created from the remaining nerves in the matrix P D  for which stimulation must be avoided. The matrices P tar  and P avd  may be used to identify a weight vector x opt  (denoting electric current or voltages of independently driven coils) that specifies the optimal weighting by which every element of the stimulation device needs to be driven. In other words, the weight vector x opt  maximally stimulates given target nerves while sparing all other nerves. In one embodiment, this can be expressed as: 
     
       
         
           
             
               
                 
                   
                     
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     where P tar  denotes the portion of the PNS matrix for the nerves to be stimulated, P avd  denoting the portion of the PNS matrix, for which stimulation must be avoided, and I max  and V max  denote the maximum current or voltage per independently driven coil used to perform the targeted stimulation. 
     As mentioned above, in another embodiment, a coil specific PNS P-matrix P D  may be used for optimization of a gradient coil and may be directly incorporated into a BEM-SF gradient winding optimization approach.  FIG. 5  illustrates a method for gradient coil design and optimization in accordance with an embodiment. At block  502 , a gradient coil geometry (e.g., a coil former shape or winding patterns). In one embodiment, the gradient coil geometry may be selected by a user via a user input of a computer system. At block  504 , a current density distribution representation of the gradient coil geometry is created on a coil former mesh (e.g., a cylinder mesh). Every vertex of the mesh carries a discrete current density element called a stream function basis. At block  506 , the B-field generated by each stream function basis is determined. For example, the B-field for each stream function basis may be pre-computed. At block  508 , a linear combination of each stream function&#39;s B-field is created as an expression of the total field. At block  510 , a coil specific PNS P-matrix (P D ) is determined using, for example, the method described above with respect to  FIG. 4 . As mentioned above, the coil specific PNS P-matrix is a linear P-matrix. At block  512 , a current density pattern (i.e., a set of weighted basis functions) is determined using a linear solver that incorporates the coil specific PNS P-matrix (P D ). As mentioned above, the coil specific PNS P-matrix (P D ) is incorporated in the optimization process to enforce PNS-optimized coil layouts. In an embodiment, the linear solver determines the current density pattern such that the total field matches the target field. At block  514 , the current density pattern may be stored in memory or data storage of, for example, an MRI system (e.g., MRI system  700  discussed below with respect to  FIG. 7 ) or other computer system (e.g., computer system  600  discussed below with respect to  FIG. 6 ). In an embodiment, a report may be generated indicating the current density pattern (using, for example, a chart, graph or image) and provided to and shown on a display (e.g., display  618  shown in  FIG. 6  or display  704 ,  736  or  744  shown in  FIG. 7 ). The report may also be stored in memory or data storage 
     The disclosed systems and methods may be implemented using a computer system.  FIG. 6  is a block diagram of an example computer system in accordance with an embodiment. Computer system  600  may be used to implement the methods described herein. In some embodiments, the computer system  600  may be a workstation, a notebook computer, a tablet device, a mobile device, a multimedia device, a network server, a mainframe, one or more controllers, one or more microcontrollers, or any other general-purpose or application-specific computing device. The computer system  600  may operate autonomously or semi-autonomously, or may read executable software instructions from the memory or storage device  616  or a computer-readable medium (e.g., a hard drive, a CD-ROM, flash memory), or may receive instructions via the input device  622  from a user, or any other source logically connected to a computer or device, such as another networked computer or server. Thus, in some embodiments, the computer system  600  can also include any suitable device for reading computer-readable storage media. 
     Data, such as data acquired with an imaging system (e.g., a CT imaging system, a magnetic resonance imaging (MM) system, etc.) may be provided to the computer system  600  from a data storage device  616 , and these data are received in a processing unit  602 . In some embodiment, the processing unit  602  includes one or more processors. For example, the processing unit  602  may include one or more of a digital signal processor (DSP)  604 , a microprocessor unit (MPU)  606 , and a graphics processing unit (GPU)  608 . The processing unit  602  also includes a data acquisition unit  610  that is configured to electronically receive data to be processed. The DSP  604 , MPU  606 , GPU  608 , and data acquisition unit  610  are all coupled to a communication bus  612 . The communication bus  612  may be, for example, a group of wires, or a hardware used for switching data between the peripherals or between any components in the processing unit  602 . 
     The processing unit  602  may also include a communication port  614  in electronic communication with other devices, which may include a storage device  416 , a display  418 , and one or more input devices  620 . Examples of an input device  620  include, but are not limited to, a keyboard, a mouse, and a touch screen through which a user can provide an input. The storage device  616  may be configured to store data, which may include data such as body models, coil geometries for gradient coils and magneto-stimulation devices, PNS Huygens&#39; P-matrices, coil specific PNS P-matrices, B-field matrices and mapping matrices/vectors whether these data are provided to, or processed by, the processing unit  602 . The display  618  may be used to display images and other information, such as magnetic resonance images, patient health data, and so on. 
     The processing unit  602  can also be in electronic communication with a network  622  to transmit and receive data and other information. The communication port  614  can also be coupled to the processing unit  602  through a switched central resource, for example the communication bus  612 . The processing unit can also include temporary storage  624  and a display controller  626 . The temporary storage  624  is configured to store temporary information. For example, the temporary storage  624  can be a random access memory. 
     In the embodiments, the disclosed systems and methods may be implemented using or designed to accompany a magnetic resonance imaging (“MRI”) system  100 , such as is illustrated in  FIG. 7 . The MRI system  700  includes an operator workstation  702 , which will typically include a display  704 , one or more input devices  706  (such as a keyboard and mouse or the like), and a processor  708 . The processor  708  may include a commercially available programmable machine running a commercially available operating system. The operator workstation  702  provides the operator interface that enables scan prescriptions to be entered into the MRI system  700 . In general, the operator workstation  702  may be coupled to multiple servers, including a pulse sequence server  710 ; a data acquisition server  712 ; a data processing server  714 ; and a data store server  716 . The operator workstation  702  and each server  710 ,  712 ,  714 , and  716  are connected to communicate with each other. For example, the servers  710 ,  712 ,  714 , and  716  may be connected via a communication system  740 , which may include any suitable network connection, whether wired, wireless, or a combination of both. As an example, the communication system  740  may include both proprietary or dedicated networks, as well as open networks, such as the internet. 
     The pulse sequence server  710  functions in response to instructions downloaded from the operator workstation  702  to operate a gradient system  718  and a radiofrequency (“RF”) system  720 . Gradient waveforms to perform the prescribed scan are produced and applied to the gradient system  718 , which excites gradient coils in an assembly  722  to produce the magnetic field gradients G x , G  y , G z  used for position encoding magnetic resonance signals. The gradient coil assembly  722  forms part of a magnet assembly  724  that includes a polarizing magnet  726  and a whole-body RF coil  728 . 
     RF waveforms are applied by the RF system  720  to the RF coil  728 , or a separate local coil (not shown in  FIG. 7 ), in order to perform the prescribed magnetic resonance pulse sequence. Responsive magnetic resonance signals detected by the RF coil  728 , or a separate local coil, are received by the RF system  720 , where they are amplified, demodulated, filtered, and digitized under direction of commands produced by the pulse sequence server  710 . The RF system  720  includes an RF transmitter for producing a wide variety of RF pulses used in MM pulse sequences. The RF transmitter is responsive to the scan prescription and direction from the pulse sequence server  710  to produce RF pulses of the desired frequency, phase, and pulse amplitude waveform. The generated RF pulses may be applied to the whole-body RF coil  728  or to one or more local coils or coil arrays. The RF system  720  also includes one or more RF receiver channels. Each RF receiver channel includes an RF preamplifier that amplifies the magnetic resonance signal received by the coil  728  to which it is connected, and a detector that detects and digitizes the I and Q quadrature components of the received magnetic resonance signal. The magnitude of the received magnetic resonance signal may, therefore, be determined at any sampled point by the square root of the sum of the squares of the I and Q components: 
         M =√   I   2   +Q   2     Eqn. 6
 
     and the phase of the received magnetic resonance signal may also be determined according to the following relationship: 
     
       
         
           
             
               
                 
                   ϕ 
                   = 
                   
                     
                       tan 
                       
                         - 
                         1 
                       
                     
                      
                     
                       ( 
                       
                         Q 
                         I 
                       
                       ) 
                     
                   
                 
               
               
                 
                   Eqn 
                   . 
                   
                       
                   
                    
                   7 
                 
               
             
           
         
       
     
     The pulse sequence server  710  also optionally receives patient data from a physiological acquisition controller  730 . By way of example, the physiological acquisition controller  730  may receive signals from a number of different sensors connected to the patient, such as electrocardiograph (“ECG”) signals from electrodes, or respiratory signals from a respiratory bellows or other respiratory monitoring device. Such signals are typically used by the pulse sequence server  710  to synchronize, or “gate,” the performance of the scan with the subject&#39;s heart beat or respiration. 
     The pulse sequence server  710  also connects to a scan room interface circuit  732  that receives signals from various sensors associated with the condition of the patient and the magnet system. It is also through the scan room interface circuit  732  that a patient positioning system  734  receives commands to move the patient to desired positions during the scan. 
     The digitized magnetic resonance signal samples produced by the RF system  720  are received by the data acquisition server  712 . The data acquisition server  712  operates in response to instructions downloaded from the operator workstation  702  to receive the real-time magnetic resonance data and provide buffer storage, such that no data is lost by data overrun. In some scans, the data acquisition server  712  does little more than pass the acquired magnetic resonance data to the data processor server  714 . However, in scans that require information derived from acquired magnetic resonance data to control the further performance of the scan, the data acquisition server  712  is programmed to produce such information and convey it to the pulse sequence server  710 . For example, during prescans, magnetic resonance data is acquired and used to calibrate the pulse sequence performed by the pulse sequence server  710 . As another example, navigator signals may be acquired and used to adjust the operating parameters of the RF system  720  or the gradient system  718 , or to control the view order in which k-space is sampled. In still another example, the data acquisition server  712  may also be employed to process magnetic resonance signals used to detect the arrival of a contrast agent in a magnetic resonance angiography (“MRA”) scan. By way of example, the data acquisition server  712  acquires magnetic resonance data and processes it in real-time to produce information that is used to control the scan. 
     The data processing server  714  receives magnetic resonance data from the data acquisition server  712  and processes it in accordance with instructions downloaded from the operator workstation  702 . Such processing may, for example, include one or more of the following: reconstructing two-dimensional or three-dimensional images by performing a Fourier transformation of raw k-space data; performing other image reconstruction techniques, such as iterative or back-projection reconstruction techniques; applying filters to raw k-space data or to reconstructed images; generating functional magnetic resonance images; calculating motion or flow images; and so on. 
     Images reconstructed by the data processing server  714  are conveyed back to the operator workstation  702 . Images may be output to operator display  712  or a display  736  that is located near the magnet assembly  724  for use by attending clinician. Batch mode images or selected real time images are stored in a host database on disc storage  738 . When such images have been reconstructed and transferred to storage, the data processing server  714  notifies the data store server  716  on the operator workstation  702 . The operator workstation  702  may be used by an operator to archive the images, produce films, or send the images via a network to other facilities. 
     The MRI system  700  may also include one or more networked workstations  742 . By way of example, a networked workstation  742  may include a display  744 , one or more input devices  746  (such as a keyboard and mouse or the like), and a processor  748 . The networked workstation  742  may be located within the same facility as the operator workstation  702 , or in a different facility, such as a different healthcare institution or clinic. The networked workstation  742  may include a mobile device, including phones or tablets. 
     The networked workstation  742 , whether within the same facility or in a different facility as the operator workstation  702 , may gain remote access to the data processing server  714  or data store server  716  via the communication system  740 . Accordingly, multiple networked workstations  742  may have access to the data processing server  714  and the data store server  716 . In this manner, magnetic resonance data, reconstructed images, or other data may exchange between the data processing server  714  or the data store server  716  and the networked workstations  742 , such that the data or images may be remotely processed by a networked workstation  742 . This data may be exchanged in any suitable format, such as in accordance with the transmission control protocol (“TCP”), the internet protocol (“IP”), or other known or suitable protocols. 
     Computer-executable instructions for assessing peripheral nerve stimulation (PNS) for gradient coils according to the above-described methods may be stored on a form of computer readable media. Computer readable media includes volatile and nonvolatile, removable, and non-removable media implemented in any method or technology for storage of information such as computer readable instructions, data structures, program modules or other data. Computer readable media includes, but is not limited to, random access memory (RAM), read-only memory (ROM), electrically erasable programmable ROM (EEPROM), flash memory or other memory technology, compact disk ROM (CD-ROM), digital volatile disks (DVD) or other optical storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other medium which can be used to store the desired instructions and which may be accessed by a system (e.g., a computer), including by internet or other computer network form of access 
     The present invention has been described in terms of one or more preferred embodiments, and it should be appreciated that many equivalents, alternatives, variations, and modifications, aside from those expressly stated, are possible and within the scope of the invention.