Method and device of brain's cartography implemented by interpolation

• US 4,957,116 A
• Filed: 01/19/1989
• Issued: 09/18/1990
• Est. Priority Date: 01/19/1988
• Status: Expired due to Fees

• Current Assignee: Institut National De La Sante Et De La Recherche Medicale (Inserm) (Allianz Global Investors GmbH)
• Original Assignee: Institut National De La Sante Et De La Recherche Medicale (Inserm) (Allianz Global Investors GmbH)
• Inventors: Pernier, Jacques, Perrin, Francois
• Primary Examiner(s): Jaworski, Francis
• Application Number:
  US07/299,153
• Time in Patent Office: 607 Days
• Field of Search: 128/731-732, 364/413.02, 364/413.05, 364/413.18, 364/577
• US Class Current: 600/544
• CPC Class Codes: A61B 5/372 Analysis of electroencephalograms
• CPC Class Codes: A61B 5/377 using evoked responses
• CPC Class Codes: G06F 2218/22 Source localisation; Inverse modelling

Abstract

This invention relates to a method of interpolation of an electric value Ut any point of a sphere, based on a finished number n of measures made at determined and known sites P_i.

This invention is also concerned with a device comprising processing circuits for the signals picked up at known acquisition sites, a central computer fitted with memorization and visualization means.

Applications: topography of present potentials, neurology.

Claims

1. A device for the determination of the value of an electrical quantity U_m (P) at any particular site P of a sphere, based on measurements Z_i of said electrical quantity made at known sites P_i on said sphere, said device comprising:

measuring means for measuring the values Z_i of said electrical quantity at n said sites P_i having polar coordinates (θ

_i, φ

_il ) and cartesian coordinates (x_i, y_i, z_i) with respect to X, Y and Z axes, respectively, where n is an integer, i is an integer between 1 and n, θ

_i is an angle formed with respect to said Z axis by a vector joining a center of said sphere with a site P_i, and φ

_i is an angle formed with respect to said X axis by a projection, into a projection plane containing said X and Y axes, of a vector joining said center of said sphere with said particular site P;

a storage memory for storing coordinates (θ

_i, φ

_i) and associated measured values Z_i of said electrical quantity;

a computer for

(1) calculating for the n sites P_i the values;

x_i =cos φ

_i

y_i =sin θ

_i ##EQU25## (2) calculating for all pairs of said n sites (P_i, P_j), where i and j are integers between 1 and n;

##EQU26## (3) generating a vector K of values k_ij of a function k_m (cosφ

_ij) for each of said pairs of sites (P_i, P_j) by reading out the value of the funtion k_m from a pre-computed table,

(4) constructing the matrix;

##EQU27## where E is a table (1,1, . . . .

     1)^t, (5) determining the value of coefficients P=(p_i, . . . p_n)^t and the value of a variable q by resolution of the matrix;

##EQU28## where Z is a table (Z₁, . . . Z_n)^t of measured values Z_i,

(6) computing, for all points P'"'"' of coordinate (X,Y) of said projection plane, the values, in the case of a radial type projection mode;

##EQU29## (7) determining the coefficient;

cos φ

(P,P_i) =1-d² /2 ##EQU30## (8) determining the variable k_m (cos φ

) by reading out the value of the function k_m from a pre-computed table, and

(9) calculating the value;

##EQU31## corresponding to the value of the electric signal at said particular point P; and

display means for displaying said calculated value of U_m (P).

2. A device according to claim 1, further comprising a second storage memory for storing the values of the function k_m (cos φ

) as pre-computed for cos φ

ranging from -1 to +1.

3. A device according to claim 2, characterized in that the computer further determines a value h_m (P, P_i) by reading out values of the function h_m from a pre-computed table and computes the radial component of the current density vector:

##EQU32##

4. A device according to claim 1, characterized in that the computer further determines a value h_m (P, P_i) by reading out the values of the function h_m from a pre-computed table and computes the radial component of the current density vector:

##EQU33##

5. A device for the display of the topography of the potential field representing an electroencephalographic parameter in accordance with measurements of electrical signals at various locations over a scalp, said device comprising:

processing circuits for processing signals Z_i picked up by a plurality of electrodes placed over the scalp at n sites P_i having polar coordinates (θ

_i, φ

_i) and cartesian coordinates (x_i, y_i, z_i) with respect to X, Y and Z axes, respectively, where n is an integer, i is an integer between 1 and n, θ

_i is an angle formed with respect to said Z axis by a vector joining a center of said sphere with a site P_i, and φ

_i is an angle formed with respect to said X axis by a projection, into a projection plane containing said X and Y axes, of a vector joining said center of said sphere with said particular site P;

a computer driven by a program for

(1) calculating for the n sites P_i the values;

x_i =cos φ

_i

y_i =sin θ

_i ##EQU34## (2) calculating for all pairs of said n site (P_i, P_j), where i and j are integers between 1 and n;

##EQU35## (3) generating a vector K of values k_ij of a function k_m (cosφ

_ij) for each of said pairs of sites (P_i, P_j) by reading out the value of the function k_m from a pre-computed table,

(4) constructing the matrix;

##EQU36## where E is a table (1,1, . . . .

     1)^t, (5) determining the value of coefficients P=(p_i, . . . p_n)^t and the value of a variable q by resolution of the matrix;

##EQU37## where Z is a table (Z₁, . . . Z_n)^t of measured values Z_i,

(6) computing for all points P'"'"' of coordinate (X,Y) of said projection plane of the values, in the case of a radial type projection mode;

##EQU38## (7) determining the coefficient;

##EQU39## (8) determining the variable k_m (cos φ

) by reading out the value of the function k_m from a pre-computed table, and

(9) calculating the value;

##EQU40## corresponding to the value of the electric signal at said particular point P; and

display means for displaying the topography of values U_m (P) determined by said computer on a plane projection of said scalp.

6. A device according to claim 5, characterized in that said computer further comprises a storage memory of the values of the function k_m (cos φ

) as pre-computed for cos φ

ranging from -1 to +1.

7. A device according to claim 5, characterized in that the computer further determines a value h_m (P, P_i) by reading out values of the function h_m from a pre-computed table and computes the radial component of the current density vector:

##EQU41##