Electrical Impedance Tomography Method and Device

• US 20100007357A1
• Filed: 09/26/2007
• Published: 01/14/2010
• Est. Priority Date: 09/28/2006
• Status: Abandoned Application

• Current Assignee: Centre National De La Recherche Scientifique
• Original Assignee: Centre National De La Recherche Scientifique
• Inventors: Capdebscq, Yves, Bonnetier, Eric, Ammari, Habib, Fink, Mathias, Tanter, Mickael
• Application Number:
  US12/443,138
• Publication Number:
  US 20100007357A1
• Time in Patent Office: Days
• US Class Current: 324/649
• CPC Class Codes: A61B 5/0536 Impedance imaging, e.g. by tomography
• CPC Class Codes: A61B 5/4064 Evaluating the brain A61B5/031, A61B5/369, A61B5/14553 take precedence
• CPC Class Codes: A61B 8/485 involving measuring strain or elastic properties

Abstract

Electrical impedance tomography method comprising: an electrical measurement step during which pre-determined electrical conditions are imposed on the surface of a medium to be imaged, while generating a mechanical disturbance at predefined points of the medium by locally modifying the impedance of the medium and an electrical parameter is measured at several points on the surface of the medium; and a calculation step during which the electrical impedance is determined at several points in the internal volume of the medium, taking into account the measurements carried out during the disturbance, as a function of a law for modification of the electrical impedance by this disturbance.

Claims

1. An electrical impedance tomography method for imaging a medium having a certain internal volume delimited by an external surface, this method comprising:

at least one electrical measurement step during which;

predetermined electrical conditions are imposed on the surface of the medium by an electrical measurement apparatus controlled by a central unit, said electrical measurement apparatus having electrodes on the surface of the medium;

and at least one electrical parameter is measured by said electrical measurement apparatus at several points on the surface of the medium while generating a mechanical disturbance at predefined points of the medium by a mechanical disturbance generating apparatus controlled by said central unit, thus locally modifying the impedance of the medium,

and at least one calculation step during which at least one parameter, linked to the electrical impedance, is determined at several points in the internal volume of the medium, wherein during the calculation step, said parameter linked to electrical impedance is determined taking into account the measurements carried out during said disturbance, using a predetermined law for modification of the electrical impedance by said disturbance.

2. The method according to claim 1, in which the electric conditions imposed include at least one current imposed at least one point on the surface of the medium, and said measured electrical parameter is an electrical potential.

3. The method according to claim 1, in which said parameter linked to the electrical impedance is the conductivity.

4. The method according to claim 1, in which the mechanical disturbance is a wave focussed on at least one point of the medium.

5. The method according to claim 4, in which the wave is an acoustic wave.

6. The method according to claim 5, in which the acoustic wave is an ultrasonic wave.

7. The method according to claim 6, in which the wave corresponds to an amplitude-modulated signal at a modulation frequency suitable for generating an ultrasound radiation force resulting in a local displacement of the medium.

8. The method according to claim 4, in which the wave is an elastic wave.

9. The method according to, claim 4, in which the wave corresponds to an encoded signal.

10. The method according to claim 4, in which, during the calculation step, the following equation is solved:

$\begin{array}{cc}\mathrm{\gamma <br><br>}<br><br>\left(z\right)=\frac{E^k<br><br>\left(z\right)}{A<br><br>\nabla <br><br>u^k<br><br>\left(z\right)·<br><br>\nabla <br><br>u^k<br><br>\left(z\right)}& \left(8\right)\end{array}$

for any point z of the medium to be imaged,

where;

k is an index denoting a set of at least one electric current j_i^k at the surface of the medium, i being an index denoting each current of this set,

E^k(z) is an energy corresponding to the disturbance produced by the wave during the application of the set of electric currents j_i^k at the surface of the medium,

u^k(z) is the electrical potential at the point z of the medium,

and A is a matrix representative of the shape of a focal spot produced by the wave about the point on which it is focussed.

11. The method according to claim 10, in which the focal spot is spherical and A is the identity matrix.

12. The method according to claim 10, in which during the calculation step, said energy is determined as a function of said law for modification of the electrical impedance by said disturbance.

13. The method according to claim 10, in which said energy is calculated by the formula:

$\begin{array}{cc}{E}^k<br><br>\left(z\right)=\underset{i}{\sum <br><br>}<br><br>D_i^k<br><br>\left(z\right)<br><br>j_i^k,& \left(6\right)\end{array}$

where;

z denotes a point situated in the medium,

D_i^k(z) is a value representative of the electrical disturbance measured at an index point i on the surface (3) of the medium and generated by the wave during the application of the set of electric currents j_i^k at the points i.

14. The method according to claim 13, in which D_i^k(z) corresponds to the following formula:

D_i^k(z)=γ

A∇

u^k(z)·

∇

G(z,i), 

 

(3)

where γ

is the conductivity and G(z,i) the Neumann function of the medium.

15. The method according to claim 13, in which the D_i^k(z) values are calculated from the measurements carried out, using waves corresponding to different signals S_l(t), l being an index comprised between l and L.

16. The method according to claim 15, in which L is equal to 2 and two signals are used, S_l(t)=S_l.s(t) and S₂(t)=S₂.s(t) of respective amplitudes S_l and S₂, the D_i^k(z) values being calculated, when the shape of the focal spot is a disc or a sphere, by the formula:

$\begin{array}{cc}{D}_i^k<br><br>\left(z\right)=\frac{\left(u_i^{k,1}<br><br>\left(z\right)-u_i^k\right)<br><br>\left(u_i^{k,2}<br><br>\left(z\right)-u_i^k\right)<br><br>\left(S_1-S_2\right)}{d<br><br>\left(S_2<br><br>u_i^{k,1}<br><br>\left(z\right)-S_2<br><br>u_i^k-S_1<br><br>u_i^{k,2}<br><br>\left(z\right)+S_1<br><br>u_i^k\right)<br><br><br><br>V<br><br>}.& \left(4\right)\end{array}$

where;

d is either equal to 2 for two-dimensional imaging, or equal to 3 for three-dimensional imaging,

|V| is either the area of the focal spot for two-dimensional imaging, or the volume of the focal spot for three-dimensional imaging.

17. The method according to claim 15, in which the wave is an ultrasonic wave, L is equal to 2 and two signals are used, S_l(t)=S_l.s(t) and S₂(t)=S₂.s(t) of respective amplitudes S_l and S₂, s(t) being an amplitude-modulated signal at a modulation frequency suitable for generating an ultrasound radiation force resulting in a local displacement of the medium, the D_i^k(z) values being calculated, when the shape of the focal spot is a disc or a sphere, by the formula:

$\begin{array}{cc}{D}_i^k<br><br>\left(z\right)=\frac{\left(u_i^{k,1}<br><br>\left(z\right)-u_i^k\right)<br><br>\left(u_i^{k,2}<br><br>\left(z\right)-u_i^k\right)<br><br>\left(S_1^2-S_2^2\right)}{d<br><br>\left(S_2^2<br><br>u_i^{k,1}<br><br>\left(z\right)-S_2^2<br><br>u_i^k-S_1^2<br><br>u_i^{k,2}<br><br>\left(z\right)+S_1^2<br><br>u_i^k\right)<br><br><br><br>V<br><br>}.& \left(4^{\mathrm{\prime <br><br>}}\right)\end{array}$

where;

d is either equal to 2 for two-dimensional imaging, or equal to 3 for three-dimensional imaging,

|V| is either the area of the focal spot for two-dimensional imaging, or the volume of the focal spot for three-dimensional imaging.

18. The method according to claim 10, in which, during the calculation step, starting from a supposed conductivity γ

the following sub-steps are repeated;

a) the following equation is solved numerically;

$\begin{array}{cc}\{\begin{array}{cc}\mathrm{div}<br><br>\left(\mathrm{\gamma <br><br>}<br><br>\nabla <br><br>u^k\right)=0& \begin{array}{c}\mathrm{at}<br><br><br><br>\mathrm{any}<br><br><br><br>\mathrm{point}<br><br><br><br>z<br><br><br><br>\mathrm{of}<br><br><br><br>\mathrm{the}<br><br><br><br>\mathrm{medium}<br><br><br><br>\mathrm{on}\\ \mathrm{the}<br><br><br><br>\mathrm{external}<br><br><br><br>\mathrm{surface},\end{array}<br><br>\\ \mathrm{\gamma <br><br>}<br><br><br><br>\nabla <br><br>u^k·<br><br>\stackrel{\to <br><br>}{n}=j_k& \end{array}& \left(9\right)\end{array}$

γ

being a previously estimated conductivity value,

b) an estimated error e^k in the conductivity is calculated,

c) the following equation is solved;

$\begin{array}{cc}\{\begin{array}{cc}\mathrm{div}<br><br>\left(\mathrm{\gamma <br><br>}<br><br>\nabla <br><br>v^k\right)=-\mathrm{div}<br><br>\left(e^k<br><br>\nabla <br><br>u^k\right)& \begin{array}{c}\mathrm{at}<br><br><br><br>\mathrm{any}<br><br><br><br>\mathrm{point}<br><br><br><br>z<br><br><br><br>\mathrm{of}<br><br><br><br>\mathrm{the}<br><br><br><br>\mathrm{medium}\\ \mathrm{on}<br><br><br><br>\mathrm{the}<br><br><br><br>\mathrm{external}<br><br><br><br>\mathrm{surface},\end{array}\\ \mathrm{\gamma <br><br>}<br><br>\nabla <br><br>u^k·<br><br>\stackrel{\to <br><br>}{n}=0& \end{array}& \left(11\right)\end{array}$

d) the conductivity is updated by the formula;

$\begin{array}{cc}{\mathrm{\gamma <br><br>}}_k=-\mathrm{\gamma <br><br>}\left(2<br><br>\frac{A^{\frac{1}{2}}<br><br>\nabla <br><br>u^k·<br><br>\nabla <br><br>v^k}{{<br><br>A^{\frac{1}{2}}<br><br>\nabla <br><br>u^k<br><br>}^2}\right)+e^k,& \left(12\right)\end{array}$

where v^k is the solution of the equation (11) and u_k is the solution of the equation (9),

and γ

_k is used as a new conductivity value γ

, with another set of currents j_i^k generating current lines not parallel to those generated by the set of currents j_i^k in at least one zone of the medium, the sub-steps a) to d) being reiterated until a stop criterion is satisfied.

19. The method according to claim 18, in which, during sub-step b), an estimated error e^k in the conductivity is calculated by the formula:

e^k=E^k/A∇

u^k·

∇

u^k−

γ

. 

 

(10)

20. The method according to claim 18, in which, during sub-step b), an estimated error e^k in the conductivity is calculated by the formula:

$\begin{array}{cc}{e}^k=\frac{\left(E^k/A<br><br>\nabla <br><br>u^k·<br><br>\nabla <br><br>u^k-\mathrm{\gamma <br><br>}\right)}{\left(<br><br>E^k/A<br><br>\nabla <br><br>u^k·<br><br>\nabla <br><br>u^k-\mathrm{\gamma <br><br>}<br><br>+1\right)}.& \left({10}^{\mathrm{\prime <br><br>}}\right)\end{array}$

21. The method according to claim 18, in which, during sub-step (d):

for each point z of the medium, it is sought what index k of electric conditions corresponds to the greatest energy

${<br><br>A^{\frac{1}{2}}<br><br>\nabla <br><br>u^k<br><br>}^2$

which gives a function k(z),

the conductivity is updated as follows;

${\mathrm{\gamma <br><br>}}_{k<br><br>\left(z\right)}=-\mathrm{\gamma <br><br>}\left(2<br><br>\frac{A^{\frac{1}{2}}<br><br>\nabla <br><br>u^{k<br><br>\left(z\right)}·<br><br>\nabla <br><br>v^{k<br><br>\left(z\right)}}{{<br><br>A^{\frac{1}{2}}<br><br>\nabla <br><br>u^{k<br><br>\left(z\right)}<br><br>}^2}\right)+e^{k<br><br>\left(z\right)},$

and γ

_k(z) is used as a conductivity value γ

.

22. The method according to claim 1, in which the medium to be imaged is a biological tissue.

23. The method according to claim 22, in which the medium to be imaged is a human organ.

24. The method according to claim 1, in which the medium to be imaged is the terrestrial subsoil.

25. An electrical impedance tomography device for imaging a medium having a certain internal volume delimited by an external surface, said device comprising:

a central unit;

an electrical measurement apparatus having electrodes, said electrical measurement apparatus being controlled by said central unit for imposing predetermined electrical conditions on said electrodes on the surface of the medium and for measuring at least one electrical parameter through at least part of said electrodes on the surface of the medium,

a mechanical disturbance generating apparatus controlled by said central unit for generating a mechanical disturbance at predefined points of the medium by locally modifying the impedance of the medium while measuring said electrical parameter;

calculating means for determining at least one parameter, linked to the electrical impedance, at several points in the internal volume of the medium, said calculating means being adapted to determine said parameter taking into account the measurements carried out during said disturbance, using a predetermined law for modification of the electrical impedance by said disturbance.

26. The electrical impedance tomography device as claimed in claim 25, in which the mechanical disturbance generating apparatus is adapted to generate a wave focussed on at least one point of the medium.