Method for functional brain imaging from magnetoencephalographic data by estimation of source signal-to-noise ratio

• US 6,697,660 B1
• Filed: 08/24/1998
• Issued: 02/24/2004
• Est. Priority Date: 01/23/1998
• Status: Expired due to Term

• Current Assignee: VSM Medtech Systems Incorporated (VSM Medtech, Ltd.)
• Original Assignee: CTF Systems, Inc. (VSM Medtech, Ltd.)
• Inventors: Robinson, Stephen E.
• Primary Examiner(s): Lateef, Marvin M.
• Assistant Examiner(s): SHAW, SHAWNA JEANNINE
• Application Number:
  US09/138,826
• Time in Patent Office: 2,010 Days
• Field of Search: 600/409, 600/544, 600/407, 128/920, 128/922, 382/128, 324/248, 324/260, 324/244
• US Class Current: 600/409
• CPC Class Codes: A61B 5/242 Detecting biomagnetic fields, e.g. magnetic fields produced by bioelectric currents
• CPC Class Codes: A61B 5/245 specially adapted for magnetoencephalographic [MEG] signals
• CPC Class Codes: A61B 5/246 using evoked responses
• CPC Class Codes: A61B 5/4094 Diagnosing or monitoring seizure diseases, e.g. epilepsy
• CPC Class Codes: G06F 2218/22 Source localisation; Inverse modelling

Abstract

An improved method, termed “statistical synthetic aperture magnetometry” (SSAM) of transforming magnetoencephalographic (MEG) measurements into corresponding three-dimensional images of the electrophysiological activity within the brain. The computed images are static, representing the time-integrated brain activity over a selected period. By selecting the time periods and frequency bands of interest, the SSAM method selectively images brain activity relating to different types of brain pathology or to cognitive events. Unlike prior art methods, the SSAM method compensates for the growth of ionic signal source strength estimates with depth into the head, resulting, in part, from the declining sensitivity of the MEG sensors. This is achieved by computing and displaying functions of the ratio of source strength to its noise for each element comprising the image. That is, a functional image is determined by an array of voxels where each voxel is based upon a function of source signal-to-noise ratio (SNR) rather than the source strength, alone. By using functions of SNR to represent source activity, the SSAM method achieves more accurate and higher resolution source localization. Each voxel is represented as a function of the ratio of a source power estimate to a source noise variance estimate. Such functions are found to be maximum at the true locations of sources, whereas plots of source power alone (as in prior art methods), show maxima which appear deeper and more diffuse in the brain than they in fact are.

Claims

1. A method of making a functional image of a subject'"'"'s brain from magnetoencephalographic measurements, said method comprising the steps of:

(a) simultaneously collecting a plurality of magnetoencephalographic data signals from a plurality of sensors surrounding said brain;

(b) selecting an array of voxels relative to said plurality of sensors, said voxels defining a region of interest within said brain;

(c) determining one of a correlation matrix and a covariance matrix for said data signals;

(d) determining an uncorrelated noise variance matrix for said sensors;

(e) determining, for each of said sensors, a predicted signal value attributable to a theoretical source of unit strength at each of said voxels;

(f) determining, for each of said voxels, by inverse solution of said matrices and said predicted signal values, a source power, being the mean-square source current dipole moment;

(g) determining, for each of said voxels, an uncorrelated noise variance;

(h) determining, for each of said voxels, a function of said voxel source power and said voxel uncorrelated noise variance;

(i) for each of said voxels, converting said function into a false-color or gray-scale functional image of source activity;

(j) coregistering said functional image with a predefined anatomical image; and

,

(k) displaying said coregistered images.

2. A method as defined in claim 1, further comprising after said step 1(a), frequency domain filtering said collected magnetoencephalographic data signals to exclude therefrom signal frequencies outside a selected frequency range.

3. A method as defined in claim 2, wherein said selected frequency range is characteristic of a selected brain activity.

4. A method as defined in claim 1, further comprising after said step 1(b), selecting time segmented portions of said magnetoencephalographic signals.

5. A method as defined in claim 4, wherein said time segmented portions are characteristic of a selected brain activity.

6. A method as defined in claim 1, wherein said array of voxels are distributed over a curvilinear surface having a shape conforming to the shape of said subject'"'"'s cerebral cortex.

7. A method as defined in claim 1, wherein said array of voxels are distributed over a regular equidistant Cartesian three-dimensional grid encompassing said subject'"'"'s head.

8. A method as defined in claim 1, wherein said step 1(d) further comprises eigendecomposition of said one of said correlation matrix and said covariance matrix.

9. A method as defined in claim 1, further comprising, after said step 1(g), deriving a corrected estimate of said source power by subtracting said uncorrelated noise variance from said mean-square source current dipole moment, for each of said voxels.

10. A method as defined in claim 1, further comprising determining a z-statistic representation of said function.

11. A method as defined in claim 10, wherein said z-statistic representation is a square root of said function.

12. A method as defined in claim 1, further comprising the steps of:

(a) performing said steps 1(a) through 1(h) to determine an active source power to noise variance ratio ^(a)ρ

_θ

while said brain performs an activity task;

(b) performing said steps 1(a) through 1(h) to determine a control source power to noise variance ratio ^(c)ρ

_η

while said brain performs a control task;

(c) for each of said voxels, deriving a ratio of said active and control source power to noise variance ratios;

${\text{\hspace{1em}<br><br>}}^{\left(a;<br><br>c\right)}<br><br>{\mathrm{\eta <br><br>}}_{\mathrm{\theta <br><br>}}=\frac{{\text{\hspace{1em}<br><br>}}^{\left(a\right)}<br><br>{\mathrm{\rho <br><br>}}_{\mathrm{\theta <br><br>}}}{{\text{\hspace{1em}<br><br>}}^{\left(c\right)}<br><br>{\mathrm{\rho <br><br>}}_{\mathrm{\theta <br><br>}}};<br><br>$

(d) converting said ratio of said active and control source power to noise variance ratios into a false-color or gray-scale functional image of source activity;

(e) coregistering said functional image with a predefined anatomical image; and

,

(f) displaying said coregistered images.

13. A method as defined in claim 1, further comprising the steps of:

(a) performing said steps 1(a) through 1(h) to determine an active source power and an active noise variance while said brain performs an activity task;

(b) performing said steps 1(a) through 1(h) to determine a control source power and a control noise variance while said brain performs a control task;

(c) for each of said voxels, deriving a function containing the ratio of the difference between said active and control source powers to the sum of their noise variance ratios;

${\text{\hspace{1em}<br><br>}}^{\left(a-c\right)}<br><br>T_{\mathrm{\theta <br><br>}}={\left[\frac{n<br><br>{<br><br>}^{\left(a\right)}<br><br>S_{\mathrm{\theta <br><br>}}^2-{\hspace{0.17em}<br><br>}^{\left(c\right)}<br><br><br><br>S_{\mathrm{\theta <br><br>}}^2<br><br><br><br>}{{\text{\hspace{1em}<br><br>}}^{\left(a\right)}<br><br>{\mathrm{\sigma <br><br>}}_{\mathrm{\theta <br><br>}}^2+{\hspace{0.17em}<br><br>}^{\left(c\right)}<br><br><br><br>{\mathrm{\sigma <br><br>}}_{\mathrm{\theta <br><br>}}^2}\right]}^{1/2};<br><br>$

(d) converting said function containing said ratio into a false-color or gray-scale functional image of source activity;

(e) coregistering said functional image with a predefined anatomical image; and

,

(f) displaying said coregistered images.

14. A method of making a functional image of a subject'"'"'s brain from magnetoencephalographic measurements, said method comprising the steps of:

(a) simultaneously collecting a plurality of magnetoencephalographic data signals from a plurality of M sensors surrounding said subject'"'"'s brain;

(b) selecting K time-sampled portions of said collected magnetoencephalographic data signals;

(c) deriving a covariance matrix C of elements C_ij, where;

(i) $C_{\mathrm{ij}}=\frac{1}{K}<br><br>\underset{k=1}{\overset{K}{\sum <br><br>}}<br><br>\left[m_{\mathrm{ik}}-{\stackrel{\_}{m}}_i\right]<br><br>\text{\hspace{1em}<br><br>}\left[m_{\mathrm{jk}}-{\stackrel{\_}{m}}_j\right];<br><br>$

(ii ) i,j=1,2,3, . . . , M;

(iii) k=1,2,3, . . . , K;

(iv) m_ik is the response of the i^th sensor during time sample k;

(v) m_jk is the response of the j^th sensor during time sample k;

(vi) ${\stackrel{\_}{m}}_i=\frac{1}{K}<br><br>\underset{k=1}{\overset{K}{\sum <br><br>}}<br><br>m_{\mathrm{ik}}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{and}<br><br>\text{\hspace{1em}<br><br>}<br><br>{\stackrel{\_}{m}}_j=\frac{1}{K}<br><br>\underset{k=1}{\overset{K}{\sum <br><br>}}<br><br>m_{\mathrm{jk}};<br><br>$

(d) selecting an array of voxels defining a region of interest within said brain;

(e) determining an uncorrelated noise variance value for each of said sensors;

(f) determining a weighting coefficient $W_{\mathrm{\theta <br><br>}}=\frac{{\left[C+\mathrm{\mu <br><br>}\sum <br><br>\right]}^{-1}<br><br>G_{\mathrm{\theta <br><br>}}}{{G_{\mathrm{\theta <br><br>}}^T<br><br>\left[C+\mathrm{\mu <br><br>}\sum <br><br>\right]}^{-1}<br><br>G_{\mathrm{\theta <br><br>}}}$

 

for each of said voxels, where G is Green'"'"'s function, μ

is a regularization parameter, and T denotes the matrix transpose;

(g) determining, for each of said voxels, at a selected target θ

, the mean-square source moment S_θ

²=[G_θ

^T(C+μ

Σ

)<sup>−

1</sup>G_θ

]<sup>−

1</sup>;

(h) determining, for each of said voxels, at said respective targets θ

, a noise variance σ

_θ

²=W_θ

^TΣ

W_θ

;

(i) determining a function of source power and said noise variance for each of said voxels;

(j) converting said function into a false-color or gray-scale functional image of source activity;

(k) coregistering said functional image with a predefined anatomical image; and

,

(l) displaying said coregistered images.

15. A method as defined in claim 14, further comprising before said step 14(b), frequency domain filtering said collected magnetoencephalographic data signals to exclude therefrom signal frequencies outside a selected frequency range.

16. A method as defined in claim 15, wherein said selected frequency range is characteristic of a selected brain activity.

17. A method as defined in claim 14, wherein said selecting step 14(b) further comprises selecting time segmented portions of said magnetoencephalographic signals.

18. A method as defined in claim 17, wherein said time segmented portions are characteristic of a selected brain activity.

19. A method as defined in claim 14, wherein M≧

64.

20. A method as defined in claim 14, wherein said array of voxels are distributed over a curvilinear surface having a shape conforming to the shape of said subject'"'"'s cerebral cortex.

21. A method as defined in claim 14, wherein said array of voxels are distributed over a regular equidistant Cartesian three-dimensional grid encompassing said subject'"'"'s head.

22. A method as defined in claim 14, wherein said step 14(e) further comprises eigendecomposition of said covariance matrix.

23. A method as defined in claim 14, wherein said step 14(e) further comprises applying an eigendecomposition C=USV^T to said covariance matrix C, where S is a matrix of singular values representing signal power for each of the spatial modes of C, and U and V are orthogonal matrices containing spatial modes of C.

24. A method as defined in claim 14, wherein said function is a ratio determined as ${\rho }_{}$

θ

=Sθ

2σ

θ

2.

25. A method as defined in claim 24, further comprising, after said step 14(h), deriving a corrected estimate of source power by subtracting said noise variance from said mean-square source moment, for each of said voxels.

26. A method as defined in claim 25, further comprising determining a z-statistic representation of said function.

27. A method as defined in claim 26, wherein said z-statistic representation is z_θ

=[ρ

_θ

]^½

.

28. A method as defined in claim 14, further comprising the steps of:

(a) performing said steps 14(a) through 14(h) to determine an active source power to noise variance ratio ^(a)ρ

_θ

while said subject'"'"'s brain performs an activity task;

(b) performing said steps 14(a) through 14(h) to determine a control source power to noise variance ratio ^(c)ρ

_θ

while said subject'"'"'s brain performs a control task;

(c) for each of said voxels, deriving a ratio of said active and control source power to noise variance ratios;

${\text{\hspace{1em}<br><br>}}^{\left(a;<br><br>c\right)}<br><br>{\mathrm{\eta <br><br>}}_{\mathrm{\theta <br><br>}}=\frac{{\text{\hspace{1em}<br><br>}}^{\left(a\right)}<br><br>{\mathrm{\rho <br><br>}}_{\mathrm{\theta <br><br>}}}{{\text{\hspace{1em}<br><br>}}^{\left(c\right)}<br><br>{\mathrm{\rho <br><br>}}_{\mathrm{\theta <br><br>}}};<br><br>$

(d) converting said ratio of said active and control source power to noise variance ratios into a false-color or gray-scale functional image of source activity;

(e) coregistering said functional image with a predefined anatomical image; and

,

(f) displaying said coregistered images.

29. A method as defined in claim 14, further comprising the steps of:

(a) performing said steps 14(a) through 14(h) to determine an active source power and an active noise variance ratio while said subject'"'"'s brain performs an activity task;

(b) performing said steps 14(a) through 14(h) to determine a control source power and a control noise variance ratio while said subject'"'"'s brain performs a control task;

(c) for each of said voxels, deriving a function of the ratio of said active and control source power difference to the active and control noise variance sum;

${\text{\hspace{1em}<br><br>}}^{\left(a-c\right)}<br><br>T_{\mathrm{\theta <br><br>}}={\left[\frac{n<br><br>{<br><br>}^{\left(a\right)}<br><br>S_{\mathrm{\theta <br><br>}}^2-{\hspace{0.17em}<br><br>}^{\left(c\right)}<br><br><br><br>S_{\mathrm{\theta <br><br>}}^2<br><br><br><br>}{{\text{\hspace{1em}<br><br>}}^{\left(a\right)}<br><br>{\mathrm{\sigma <br><br>}}_{\mathrm{\theta <br><br>}}^2+{\hspace{0.17em}<br><br>}^{\left(c\right)}<br><br><br><br>{\mathrm{\sigma <br><br>}}_{\mathrm{\theta <br><br>}}^2}\right]}^{1/2};<br><br>$

(d) converting said function of said active and control source power and noise variances into a false-color or gray-scale functional image of source activity;

(e) coregistering said functional image with a predefined anatomical image; and

,

(f) displaying said coregistered images.