Current density impedance imaging (CDII)

US 20050054911A1
Filed: 09/03/2004
Published: 03/10/2005
Est. Priority Date: 09/04/2003
Status: Active Grant

First Claim

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1. A method of non-invasive imaging of electrical impedance of an object, comprising the steps of:

a) making measurements of at least two current density vector fields, J₁and J₂, within a region of interest in an object; and

b) calculating the logarithmic gradient of local conductivity, ∇

ln σ

(x, y, z), using a formula $\begin{matrix} \nabla \ln σ = \frac{(\nabla \times J_{2}) \cdot (J_{1} \times J_{2})}{{\langle J_{1} \times J_{2} \rangle}^{2}} J_{1} + \frac{(\nabla \times J_{1}) \cdot (J_{2} \times J_{1})}{{\langle J_{1} \times J_{2} \rangle}^{2}} J_{2} + \frac{(\nabla \times J_{1}) \cdot J_{2}}{{\langle J_{1} \times J_{2} \rangle}^{2}} J_{1} \times J_{2} & (1) \end{matrix}$ where {right arrow over (J)}₁(x,y,z) and {right arrow over (J)}₂(x,y,z), are the pair of measured nonparallel current densities at point (x,y,z) and ∇

denotes the gradient operator.

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Abstract

A method for non-invasive mapping (imaging) of the electrical impedance of an object. The present invention provides a method, current density impedance imaging (CDII) which produces an impedance image of object by measuring current density distributions and directly calculating the local impedance values. The method includes making measurements of at least two current density vector fields, J₁and J₂, within a region of interest in an object and then calculating the logarithmic gradient of local conductivity, ∇ In σ(x, y, z), using a formula $\begin{matrix} \begin{matrix} \nabla \ln σ = \frac{(\nabla \times J_{2}) \cdot (J_{1} \times J_{2})}{{\langle J_{1} \times J_{2} \rangle}^{2}} J_{1} + \\ \frac{(\nabla \times J_{1}) \cdot (J_{2} \times J_{1})}{{\langle J_{1} \times J_{2} \rangle}^{2}} J_{2} + \\ \frac{(\nabla \times J_{1}) \cdot J_{2}}{{\langle J_{1} \times J_{2} \rangle}^{2}} J_{1} \times J_{2} \end{matrix} & (1) \end{matrix}$
where {right arrow over (J)}₁(x,y,z) and {right arrow over (J)}₂(x,y,z), are the pair of measured nonparallel current densities at point (x,y,z) and ∇ denotes the gradient operator.

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27 Claims

1. A method of non-invasive imaging of electrical impedance of an object, comprising the steps of:
- a) making measurements of at least two current density vector fields, J₁and J₂, within a region of interest in an object; and
  
  b) calculating the logarithmic gradient of local conductivity, ∇
  
  ln σ
  
  (x, y, z), using a formula $\begin{matrix} \nabla \ln σ = \frac{(\nabla \times J_{2}) \cdot (J_{1} \times J_{2})}{{\langle J_{1} \times J_{2} \rangle}^{2}} J_{1} + \frac{(\nabla \times J_{1}) \cdot (J_{2} \times J_{1})}{{\langle J_{1} \times J_{2} \rangle}^{2}} J_{2} + \frac{(\nabla \times J_{1}) \cdot J_{2}}{{\langle J_{1} \times J_{2} \rangle}^{2}} J_{1} \times J_{2} & (1) \end{matrix}$ where {right arrow over (J)}₁(x,y,z) and {right arrow over (J)}₂(x,y,z), are the pair of measured nonparallel current densities at point (x,y,z) and ∇
  
  denotes the gradient operator.
- View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11)
- - 2. The method according to claim 1 including calculating a relative conductivity $σ$
    - R ⁡
      
      ( x , y , z ) = σ
      
      ⁡
      
      ( x , y , z ) σ
      
      ⁡
      
      ( x 0 , y 0 , z 0 ) , between any two points (x,y,z) and (x₀,y₀,z₀) from ∇
      
      ln σ
      
      (x,y,z) by integration along any path joining the two points along which ∇
      
      ln σ
      
      (x,y,z) has been determined, using a formula for σ
      
      _R(x,y,z) given by $\begin{matrix} σ_{R} (x, y, z) = \exp (\int_{(x_{0}, y_{0}, z_{0})}^{(x, y, z)} \nabla \ln σ) . & (2) \end{matrix}$
  - 3. The method according to claim 2 including using the resulting image, σ
    - _R(x,y,z) to display a conductivity weighted image of the object by selecting an initial point (x₀,y₀,z₀) in the formula (2) and assigning it a conductivity of 1.
  - 4. The method according to claim 1 including calculating the conductivity image of the object using a convolution formula given by $σ$
    - ⁡
      
      ( r ) = σ
      
      0 ⁢
      
      exp ⁢
      
      { ∫
      
      V
      
      ⁢
      
      ∇
      
      r ′
      
      ⁢
      
      G ⁡
      
      ( r , r ′
      
      ) ·
      
      ∇
      
      ⁢
      
      ln ⁢
      
      ⁢
      
      σ
      
      ⁡
      
      ( r ′
      
      ) ⁢
      
      d 3 ⁢
      
      r ′
      
      } ⁢
      
      when the conductivity is a known constant value at the boundary of the region of interest, wherein G denotes the free space Green'"'"'s function for the Laplacian.
  - 5. The method according to claim 2 including determining an absolute value of conductivity σ
    - (x,y,z), by the steps of determining an absolute value of conductivity, σ
      
      (x₀,y₀,z₀) at some point in the region of interest, and calculating said absolute conductivity using an equation given by $σ (x, y, z) = \exp (\int_{(x_{0}, y_{0}, z_{0})}^{(x, y, z)} \nabla \ln σ) \times σ (x_{0}, y_{0}, z_{0}) .$
  - 6. The method according to claim 5 wherein the step of determining an absolute value of conductivity, σ
    - (x₀,y₀,z₀) at some point in the region of interest includes derivation from either an a priori knowledge of the object, an introduction of an external agent with known conductivity into the object or a surface measurement of potentials.
  - 7. The method according to claim 5 wherein the object is a mammal, and wherein the step of introduction of an external agent with known conductivity into the object includes the mammal swallowing a pill containing a substance of known conductivity prior to imaging.
  - 8. The method according to claim 1 wherein the step of making measurements of at least two current density vector fields, J₁and J₂, within a region of interest in an object) includes a) affixing a sufficient number of current conducting electrodes to a surface of the object so that at least two sets of current distribution are created inside the object, the current conducting electrodes being connected to a current generator;
    - b) placing the object inside a magnetic field generated by a magnetic resonance (MR) imager magnet;
      
      c) during the MR imaging, inducing current flow in an interior of the object by applying current between a first pair of current conductors synchronously with an effective current imaging sequence which encodes a strength of the magnetic field arising from the current flow induced inside the object, the extra magnetic field component being encoded as a part of a complex MR image;
      
      d) acquiring the resulting complex MR images through the use of a typical MR imaging sequence and transferring the resulting complex MR images to a computer;
      
      e) processing the complex MR images to calculate the current density vector field J₁; and
      
      f) repeating steps c), d) and e) at least once more to measure the current density vector field J₂for at least one other combination of current electrodes.
  - 9. The method according to claim 8 wherein the current applied between the electrodes attached to the surface of the object is direct current (DC).
  - 10. The method according to claim 8 wherein the current applied between the electrodes attached to the surface of the object is alternating current (AC).
  - 11. The method according to claim 1 wherein the step of making measurements of at least two current density vector fields, J₁and J₂, within a region of interest in the object includes a) locating a pre-selected number of current inducing coils at pre-selected locations in close proximity to the object, the current inducing coils being connected to a current source, wherein applying electrical current through the current inducing coils induces at least two sets of current flow distribution inside the object;
    - b) placing the object inside a magnetic field generated by a magnetic resonance (MR) imager magnet;
      
      c) during the MR imaging, inducing current flow in an interior of the object by applying current to a first of the pre-selected number of current inducing coils synchronously with an effective current imaging sequence which encodes a strength of the magnetic field arising from the current flow induced inside the object, the extra magnetic field component being encoded as a part of a complex MR image;
      
      d) acquiring the resulting complex MR images through the use of a typical MR imaging sequence and transferring the resulting complex MR images to a computer;
      
      e) processing the complex MR images to calculate the current density vector field J₁; and
      
      f) repeating steps c), d) and e) at least once more to measure the current density vector field J₂for at least one other of the pre-selected number of current inducing coils.

12. A method of non-invasive imaging of electrical impedance of an object, comprising the steps of:
- a) making measurements of the derivatives of at least two current density vector fields, J₁and J₂, in one direction d within a region of interest in an object when a condition ∂
  
  _d∇
  
  σ
  
  =0 is satisfied; and
  
  b) calculating the logarithmic gradient of local conductivity, ∇
  
  ln σ
  
  (x, y, z), at that point, using a formula $\begin{matrix} \nabla \ln σ = \frac{(\nabla \times \partial_{d} J_{2}) \cdot (\partial_{d} J_{1} \times \partial_{d} J_{2})}{{\langle \partial_{d} J_{1} \times \partial_{d} J_{2} \rangle}^{2}} \partial_{d} J_{1} + \frac{(\nabla \times \partial_{d} J_{1}) \cdot (\partial_{d} J_{2} \times \partial_{d} J_{1})}{{\langle \partial_{d} J_{1} \times \partial_{d} J_{2} \rangle}^{2}} \partial_{d} J_{2} + \frac{(\nabla \times \partial_{d} J_{1}) \cdot \partial_{d} J_{2}}{{\langle \partial_{d} J_{1} \times \partial_{d} J_{2} \rangle}^{2}} \partial_{d} J_{1} \times \partial_{d} J_{2} & (3) \end{matrix}$ where ∂
  
  _ddenotes the directional derivative in the direction d, where ∂
  
  _dJ₁and ∂
  
  _dJ₂are the pair of measured derivatives of the current density vector fields in the direction d at point (x,y,z), and Vdenotes the gradient operator.
- View Dependent Claims (13, 14, 15, 16, 17, 18)
- - 13. The method according to claim 12 including calculating a relative conductivity $σ$
    - R ⁡
      
      ( x , y , z ) = σ
      
      ⁡
      
      ( x , y , z ) σ
      
      ⁡
      
      ( x 0 , y 0 , z 0 ) , between any two points (x,y,z) and (x₀,y₀,z₀) from ∇
      
      ln σ
      
      (x,y,z) by integration along any path joining the two points along which ∇
      
      ln σ
      
      (x,y,z) has been determined, using a formula for σ
      
      _R(x,y,z) given by $\begin{matrix} σ_{R} (x, y, z) = \exp (\int_{(x_{0}, y_{0}, z_{0})}^{(x, y, z)} \nabla \ln σ) . & (2) \end{matrix}$
  - 14. The method according to claim 13 including using the resulting image, σ
    - _R(x,y,z) to display a conductivity weighted image of the object by selecting an initial point (x₀,y₀,z₀) in the formula (2) and assigning it a conductivity of 1.
  - 15. The method according to claim 12 including calculating the conductivity image of the object using a convolution formula given by $σ$
    - ⁡
      
      ( r ) = σ
      
      0 ⁢
      
      exp ⁢
      
      { ∫
      
      V
      
      ⁢
      
      ∇
      
      r ′
      
      ⁢
      
      ⁢
      
      G ⁡
      
      ( r , r ′
      
      ) ·
      
      ∇
      
      ln ⁢
      
      ⁢
      
      σ
      
      ⁡
      
      ( r ′
      
      ) ⁢
      
      d 3 ⁢
      
      r ′
      
      } when the conductivity is a known constant value at the boundary of the region of interest, wherein G denotes the free space Green'"'"'s function for the Laplacian.
  - 16. The method according to claim 13 including determining an absolute value of conductivity σ
    - (x,y,z), by the steps of determining an absolute value of conductivity, σ
      
      (x₀,y₀,z₀) at some point in the region of interest, and calculating said absolute conductivity using an equation given by $σ (x, y, z) = \exp (\int_{(x_{0}, y_{0}, z_{0})}^{(x, y, z)} \nabla \ln σ) \times σ (x_{0}, y_{0}, z_{0}) .$
  - 17. The method according to claim 16 wherein the step of determining an absolute value of conductivity, σ
    - (x₀,y₀,z₀) at some point in the region of interest includes derivation from either an a priori knowledge of the object, an introduction of an external agent with known conductivity into the object, or surface measurement of potentials.
  - 18. The method according to claim 16 wherein the object is a mammal, and wherein the step of introduction of an external agent with known conductivity into the object includes the mammal swallowing a pill containing a substance of known conductivity prior to imaging.

19. A method of non-invasive imaging of electrical impedance of an object, comprising the steps of:
- a) affixing a sufficient number of current conducting electrodes to a surface of the object so that at least two sets of current distribution are created inside the object, the current conducting electrodes being connected to a current generator;
  
  b) placing the object inside a magnetic field generated by a magnetic resonance (MR) imager magnet;
  
  c) during the MR imaging, inducing current flow in an interior of the object by applying current between a first pair of current conductors synchronously with an effective current imaging sequence which encodes a strength of the magnetic field arising from the current flow induced inside the object, the extra magnetic field component being encoded as a part of a complex MR image;
  
  d) acquiring the resulting complex MR images through the use of a typical MR imaging sequence and transferring the resulting complex MR images to a computer;
  
  e) processing the complex MR images to calculate the current density vector field J₁;
  
  f) repeating steps c), d) and e) at least once more to measure the current density vector field J₂for at least one other combination of current electrodes; and
  
  g) calculating the logarithmic gradient of local conductivity, ∇
  
  ln σ
  
  (x, y, z), using a formula $\begin{matrix} \nabla \ln σ = \frac{(\nabla \times J_{2}) \cdot (J_{1} \times J_{2})}{{\langle J_{1} \times J_{2} \rangle}^{2}} J_{1} + \frac{(\nabla \times J_{1}) \cdot (J_{2} \times J_{1})}{{\langle J_{1} \times J_{2} \rangle}^{2}} J_{2} + \frac{(\nabla \times J_{1}) \cdot J_{2}}{{\langle J_{1} \times J_{2} \rangle}^{2}} J_{1} \times J_{2} & (1) \end{matrix}$ where {right arrow over (J)}₁(x,y,z) and {right arrow over (J)}₂(x,y,z), are a pair of measured nonparallel current densities at point (x,y,z) and ∇
  
  denotes the gradient operator.
- View Dependent Claims (20, 22, 23, 24, 25, 26, 27)
- - 20. The method according to claim 19 including calculating a relative conductivity $σ$
    - R ⁡
      
      ( x , y , z ) = σ
      
      ⁡
      
      ( x , y , z ) σ
      
      ⁡
      
      ( x 0 , y 0 , z 0 ) , between any two points (x,y,z) and (x₀,y₀,z₀) from ∇
      
      ln σ
      
      (x,y,z) by integration along any path joining the two points along which ∇
      
      ln σ
      
      (x,y,z) has been determined, using a formula for σ
      
      _R(x,y,z) given by $\begin{matrix} σ_{R} (x, y, z) = \exp (\sum_{(x_{0}, y_{0}, z_{0})}^{(x, y, z)} \nabla \ln σ) . & (2) \end{matrix}$
  - 22. The method according to claim 19 including calculating the conductivity image of the object using a convolution formula given by $σ$
    - ⁡
      
      ( r ) = σ
      
      0 ⁢
      
      exp ⁢
      
      { ∫
      
      V ⁢
      
      ∇
      
      r , G ⁡
      
      ( r , r ′
      
      ) ·
      
      ∇
      
      ln ⁢
      
      ⁢
      
      σ
      
      ⁡
      
      ( r ′
      
      ) ⁢
      
      ⅆ
      
      3 ⁢
      
      r ′
      
      } when the conductivity is a known constant value at the boundary of the region of interest, wherein G denotes the free space Green'"'"'s function for the Laplacian.
  - 23. The method according to claim 20 including determining an absolute value of conductivity σ
    - (x,y,z), by the steps of determining an absolute value of conductivity, σ
      
      (x₀,y₀,z₀) at some point in the region of interest, and calculating said absolute conductivity using an equation given by $σ (x, y, z) = \exp (\sum_{(x_{0}, y_{0}, z_{0})}^{(x, y, z)} \nabla \ln σ) \times σ (x_{0}, y_{0}, z_{0}) .$
  - 24. The method according to claim 23 wherein the step of determining an absolute value of conductivity, σ
    - (x₀,y₀,z₀) at some point in the region of interest includes derivation from either an a priori knowledge of the object, an introduction of an external agent with known conductivity into the object or a surface measurement of potentials.
  - 25. The method according to claim 23 wherein the object is a mammal, and wherein the step of introduction of an external agent with known conductivity into the object includes the mammal swallowing a pill containing a substance of known conductivity prior to imaging.
  - 26. The method according to claim 19 wherein the current applied between the electrodes attached to the surface of the object is direct current (DC).
  - 27. The method according to claim 19 wherein the current applied between the electrodes attached to the surface of the object is alternating current (AC).

21. The method according to claim 21 including using the resulting image, σ
- _R(x,y,z) to display a conductivity weighted image of the object by selecting an initial point (x₀,y₀,z₀) in the formula (2) and assigning it a conductivity of 1.

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Current Assignee
Adrian Nachman, Karshi F. Hasanov, Michael L.G. Joy, Richard S. Yoon
Original Assignee
Adrian Nachman, Karshi F. Hasanov, Michael L.G. Joy, Richard S. Yoon
Inventors
Nachman, Adrian, Joy, Michael L. G., Yoon, Richard S., Hasanov, Karshi F.

Granted Patent

US 7,603,158 B2
Time in Patent Office

Days
Field of Search
US Class Current

600/411
CPC Class Codes

A61B 5/0536 Impedance imaging, e.g. by ...

Current density impedance imaging (CDII)

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Current density impedance imaging (CDII)

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