Abstract

A method for constructing visualizations of current distributions with magnetic field measurements of biological current is presented. Two uses are discussed: SQUID tomography and longitudinal region-of-interest reconstruction.

© 1985 Optical Society of America

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References

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  1. G. M. Baule, R. McFee, “Detection of Magnetic Fields of the Heart,” Am. Heart J. 66, 95 (1963).
    [CrossRef]
  2. J. E. Zimmerman, P. Thieme, J. T. Harding, “Design and Operation of Stable rf-Biased Superconducting Point-Contact Quantum Devices, and a Note on the Properties of Perfectly Clean Contacts,” J. Appl. Phys. 41, 1572 (1970).
    [CrossRef]
  3. B. N. Cuffin, D. Cohen, “Magnetic Fields Produced by Models of Biological Current Sources,” J. Appl. Phys. 48, 3971 (1977).
    [CrossRef]
  4. J. L. Harris, “Diffraction and Resolving Power,” J. Opt. Soc. Am. 54, 931 (1964); C. L. Byrne, R. M. Fitzgerald, M. A. Fiddy, T. J. Hall, A. M. Darling, “Image Restoration and Resolution Enhancement,” J. Opt. Soc. Am. 73, 1481 (1983).
    [CrossRef]
  5. H. C. Andrews, B. R. Hunt, Digital Image Restoration (Prentice-Hall, Englewood Cliffs, N.J., 1977), p. 87.

1977 (1)

B. N. Cuffin, D. Cohen, “Magnetic Fields Produced by Models of Biological Current Sources,” J. Appl. Phys. 48, 3971 (1977).
[CrossRef]

1970 (1)

J. E. Zimmerman, P. Thieme, J. T. Harding, “Design and Operation of Stable rf-Biased Superconducting Point-Contact Quantum Devices, and a Note on the Properties of Perfectly Clean Contacts,” J. Appl. Phys. 41, 1572 (1970).
[CrossRef]

1964 (1)

1963 (1)

G. M. Baule, R. McFee, “Detection of Magnetic Fields of the Heart,” Am. Heart J. 66, 95 (1963).
[CrossRef]

Andrews, H. C.

H. C. Andrews, B. R. Hunt, Digital Image Restoration (Prentice-Hall, Englewood Cliffs, N.J., 1977), p. 87.

Baule, G. M.

G. M. Baule, R. McFee, “Detection of Magnetic Fields of the Heart,” Am. Heart J. 66, 95 (1963).
[CrossRef]

Cohen, D.

B. N. Cuffin, D. Cohen, “Magnetic Fields Produced by Models of Biological Current Sources,” J. Appl. Phys. 48, 3971 (1977).
[CrossRef]

Cuffin, B. N.

B. N. Cuffin, D. Cohen, “Magnetic Fields Produced by Models of Biological Current Sources,” J. Appl. Phys. 48, 3971 (1977).
[CrossRef]

Harding, J. T.

J. E. Zimmerman, P. Thieme, J. T. Harding, “Design and Operation of Stable rf-Biased Superconducting Point-Contact Quantum Devices, and a Note on the Properties of Perfectly Clean Contacts,” J. Appl. Phys. 41, 1572 (1970).
[CrossRef]

Harris, J. L.

Hunt, B. R.

H. C. Andrews, B. R. Hunt, Digital Image Restoration (Prentice-Hall, Englewood Cliffs, N.J., 1977), p. 87.

McFee, R.

G. M. Baule, R. McFee, “Detection of Magnetic Fields of the Heart,” Am. Heart J. 66, 95 (1963).
[CrossRef]

Thieme, P.

J. E. Zimmerman, P. Thieme, J. T. Harding, “Design and Operation of Stable rf-Biased Superconducting Point-Contact Quantum Devices, and a Note on the Properties of Perfectly Clean Contacts,” J. Appl. Phys. 41, 1572 (1970).
[CrossRef]

Zimmerman, J. E.

J. E. Zimmerman, P. Thieme, J. T. Harding, “Design and Operation of Stable rf-Biased Superconducting Point-Contact Quantum Devices, and a Note on the Properties of Perfectly Clean Contacts,” J. Appl. Phys. 41, 1572 (1970).
[CrossRef]

Am. Heart J. (1)

G. M. Baule, R. McFee, “Detection of Magnetic Fields of the Heart,” Am. Heart J. 66, 95 (1963).
[CrossRef]

J. Appl. Phys. (2)

J. E. Zimmerman, P. Thieme, J. T. Harding, “Design and Operation of Stable rf-Biased Superconducting Point-Contact Quantum Devices, and a Note on the Properties of Perfectly Clean Contacts,” J. Appl. Phys. 41, 1572 (1970).
[CrossRef]

B. N. Cuffin, D. Cohen, “Magnetic Fields Produced by Models of Biological Current Sources,” J. Appl. Phys. 48, 3971 (1977).
[CrossRef]

J. Opt. Soc. Am. (1)

Other (1)

H. C. Andrews, B. R. Hunt, Digital Image Restoration (Prentice-Hall, Englewood Cliffs, N.J., 1977), p. 87.

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Equations (28)

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× H = 4 π c J × H = J ,
· B = 0 · H = 0 .
ρ × H ˜ = J ˜ ,
ρ · H ˜ = 0 ,
H = U + V .
H ˜ = U ˜ + V ˜ .
V = V ( r ) S ( r ) ,
J = J ( r ) T ( r ) .
V ˜ ( ρ ) = m V ˜ ( m ) S ( ρ m )
J ˜ ( ρ ) = m J ˜ ( m ) T ˜ ( ρ m )
C ˜ ( ρ ) = ρ × U ˜ ( ρ ) = m { [ ρ × V ˜ ( m ) ] S ˜ ( ρ m ) + J ˜ ( m ) T ˜ ( ρ m ) } ,
D ( ρ ) = ρ · U ˜ ( ρ ) = m { [ ρ · V ˜ ( m ) ] S ˜ ( ρ m ) } .
G ( ρ ) = m M ( ρ , m ) F ( m ) ,
G ( ρ ) = [ C ˜ x ( ρ ) , C ˜ x ( ρ + Δ ρ ) , C ˜ y ( ρ ) , C ˜ y ( ρ + Δ ρ ) , D ˜ ( ρ ) ] , F ( m ) = [ V ˜ x ( m ) , V ˜ y ( m ) , V ˜ z ( m ) , J ˜ x ( m ) , J ˜ y ( m ) ] .
S ˜ ( ρ m ) = δ ( ρ x m x δ ( ρ y m y σ ˜ ( ρ z m z ) , T ˜ ( ρ m ) = δ ( ρ x m x ) δ ( ρ y m y ) τ ˜ ( ρ z m z ) , }
C x n = m [ σ ˜ ( n m ) ( ρ y V z m n V ˜ y m ) + τ ˜ ( n m ) J ˜ x m ] , C y n = m [ σ ˜ ( n m ) ( n V ˜ x m ρ x V ˜ z m ) + τ ˜ ( n m ) J ˜ y m ] , D ˜ n = m [ σ ˜ ( n m ) ( ρ x V ˜ x m + ρ y V ˜ y m + n V ˜ z m ) ] .
A ˜ n = ( ρ y C ˜ x n + n D ˜ n ρ x C ˜ y n ) = m [ σ ˜ ( n m ) ( ρ x 2 + ρ y 2 + n 2 ) V ˜ z m ] + ( n m ) ( ρ y J ˜ x m ρ x J ˜ y m ) ]
G = M F ,
G n = ( A ˜ n , A ˜ n + Δ n ) , F m = [ V ˜ z m , ( ρ y J ˜ x m ρ x J ˜ y m ) ] ,
M n m = [ σ ˜ ( n m ) [ ρ x 2 + ρ y 2 + n 2 ] τ ˜ ( n m ) , σ ˜ ( n + Δ n m ) [ ρ x 2 + ρ y 2 + ( n + Δ n ) 2 τ ˜ ( n + Δ n m ) ] ] .
τ ˜ ( ρ z ) = 1 .
A ˜ n = m [ σ ˜ ( n m ) ( ρ x 2 + ρ y 2 + n 2 ) V ˜ z m + ( ρ y J ˜ x m ρ x J ˜ y m ) ] ,
A ˜ n + Δ n A ˜ n = m [ σ ˜ ( n m ) ( ρ x 2 + ρ y 2 ) ] σ ˜ ( n + Δ n m ) [ ρ x 2 + ρ y 2 + ( n + Δ n ) 2 ] V ˜ z m ,
G = M F , G n = A n + Δ n A n , F m = V ˜ z m , M n m = σ ˜ ( n m ) ( ρ x 2 + ρ y 2 + n 2 ) σ ˜ ( n + Δ n m ) [ ρ x 2 + ρ y 2 + ( n + Δ n ) 2 ] .
M n m = ( ρ x 2 + ρ y 2 + n 2 ) ρ x 2 + ρ y 2 + ( n + Δ n ) 2 = Δ n ( 2 n + Δ n ) ,
V ˜ z 0 = A ˜ n + Δ n A ˜ n Δ n ( 2 n + Δ n ) .
ρ x 2 = ρ y 2 + 32 ; σ ˜ ( m ) = 3 π 2 4 sin c ( m 4 ) ; sin c ( x ) = sin ( π x ) π x , m = 4,0,4 ; n = 4,0,4 ; Δ n = 2 ; σ ˜ ( m ) = σ ˜ ( m ) , σ ˜ ( 0 ) = 3 π 2 4 σ ˜ ( + 4 ) = 0 , σ ˜ ( 1 ) = 3 σ ˜ ( + 5 ) = 3 5 , σ ˜ ( 2 ) = 3 2 2 σ ˜ ( 6 ) = 2 2 , σ ˜ ( 3 ) = 1 σ ˜ ( 7 ) = 3 7 ,
83.58 25.46 28.58 , 76.37 30.26 48.08 , 25.46 76.37 15.69 ,

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