Method and device for determining and presenting surface charge and dipole densities on cardiac walls

Abstract

The invention discloses a method, a system, a computer program and a device for determining the surface charge and/or dipole densities on heart walls. Using the foregoing, a table of dipole densities ?(P, t) and/or a table of surface charge densities ?(P, t) of a given heart chamber can be generated.

Claims

1. A cardiac activity mapping system, comprising: one or more electrodes configured to record electrical potential data V.sub.e of a heart chamber; a display apparatus; and a special purpose computer configured to: generate a map of a distribution of at least one of dipole density data and/or surface charge density data based on the recorded electrical potential data V.sub.e, wherein the special purpose computer is configured to transform the recorded electrical potential data V.sub.e into cellular membrane data over a series of sequential time periods to produce the at least one of dipole density data and/or surface charge density data; and display the map on the display apparatus.

2. The system of claim 1, wherein the map includes a distribution of dipole density data and not surface charge density data.

3. The system of claim 1, wherein the map includes a distribution of surface charge density data and not dipole density data.

4. The system of claim 1, wherein the map includes a distribution of dipole density data and a distribution of surface charge density data.

5. The system of claim 1, wherein the special purpose computer is further configured to display the map in conjunction with a three-dimensional geometry of the heart chamber.

6. The system of claim 1, wherein the special purpose computer is further configured to display the map in conjunction with anatomical data from at least one or more computed tomography (CT) scans or magnetic resonance imaging (MRI) scans.

7. The system of claim 6, wherein the special purpose computer is further configured to display the map in conjunction with a three-dimensional geometry of the heart chamber.

8. The system of claim 1, wherein the special purpose computer further comprises an interface to a probe system configured to measure electrical potentials V.sub.P, and wherein the special purpose computer is configured to calculate the electrical potential data V.sub.e based on the electrical potentials V.sub.P.

9. The system of claim 8, wherein the special purpose computer is further configured to calculate the electrical potential data V.sub.e based on the measured potentials V.sub.P according to the equation:
V.sub.e=TV.sub.P, where T is a linear matrix transformation.

10. The system of claim 9, wherein the measured potentials V.sub.P are stored as a linear, finite element matrix.

11. The system of claim 8, wherein the probe system includes a catheter configured to measure the electrical potentials V.sub.P using contact mapping.

12. The system of claim 11, wherein the probe system includes at least one electrode configured to contact at least a portion of a wall of the heart chamber.

13. The system of claim 11, wherein the catheter includes a multi-electrode array configured to be disposed within the heart chamber.

14. The system of claim 13, wherein the multi-electrode array includes a basket electrode array.

15. The system of claim 8, wherein the probe system includes one or more probe electrodes configured to measure the electrical potentials V.sub.P using non-contact mapping.

16. The system of claim 15, wherein the special purpose computer is further configured to calculate the electrical potential data V.sub.e based on a shape or shapes of the one or more probe electrodes.

17. The system of claim 16, wherein the one or more probe electrodes includes one or more electrodes having a spherical shape, an ellipsoidal shape, or combinations thereof.

18. The system of claim 8, wherein the special purpose computer further comprises: at least one a/d-converter configured to convert the measured electric potentials V.sub.P into digital data; at least one memory configured to save the digital data; and at least one processor unit configured to transform the digital data into digital surface charge density and/or dipole density data.

19. The system of claim 1, wherein the special purpose computer is further configured to transform the recorded electrical potential data V.sub.e into cellular membrane data as a distribution across an area of an endocardial surface of the heart chamber.

20. The system of claim 1, wherein the map displayed by the special purpose computer comprises a time-dependent sequence of images.

Description

DRAWINGS

(1) FIG. 1 is an exemplary embodiment of a mapping system, according to aspect of the present invention;

(2) FIG. 2 is an exemplary embodiment of a computer architecture forming part of the mapping system of FIG. 1;

(3) FIG. 3 is an example embodiment of a method of determining and storing surface charge densities, in accordance with aspects of the present invention; and

(4) FIG. 4 is an example embodiment of a method of determining and storing dipole densities, in accordance with aspects of the present invention.

DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

(5) Research has indicated that the use of the surface charge densities (i.e. their distribution) or dipole densities (i.e. their distribution) to generate distribution map(s) will lead to a more detailed and precise information on electric ionic activity of local cardiac cells than potentials. Surface charge density or dipole densities represent a precise and sharp information of the electric activity with a good spatial resolution, whereas potentials resulting from integration of charge densities provide only a diffuse picture of electric activity. The electric nature of cardiac cell membranes comprising ionic charges of proteins and soluble ions can be precisely described by surface charge and dipole densities. The surface charge densities or dipole densities cannot be directly measured in the heart, but instead must be mathematically and accurately calculated starting from measured potentials. In other words, the information of voltage maps obtained by current mapping systems can be greatly refined when calculating surface charge densities or dipole densities from these.

(6) The surface charge density means surface charge (Coulombs) per unit area (cm.sup.2). A dipole as such is a neutral element, wherein a part comprises a positive charge and the other part comprises the same but negative charge. A dipole might represent the electric nature of cellular membranes better, because in biological environment ion charges are not macroscopically separated.

(7) In order to generate a map of surface charge densities (surface charge density distribution) according to the present invention, the geometry of the given heart chamber must be known. The 3D geometry of the cardiac chamber is typically assessed by currently available and common mapping systems (so-called locator systems) or, alternatively, by integrating anatomical data from CT/MRI scans. FIG. 1 shows an example embodiment of a mapping system 100 that can be used to map a heart 12 of a human 10. Mapping system 100 can include a computer 110 having known types of input devices and output devices, such as a display 120 and printer 130, and a probe system 140. For the measurement of potentials the non-contact mapping method a probe electrode 142 will be used, which is connected to the computer 110 via a cable and forms part of probe system 140. The probe electrode 142 may be a multi-electrode array with elliptic or spherical shape. The spherical shape has certain advantages for the subsequent data analysis. But also other types or even several independent electrodes could be used to measure V.sub.e. For example, when considering, for example, the ventricular cavity within the endocardium and taking a probe electrode with a surface S.sub.P, which is located in the blood, it is possible to measure the potential V(x,y,z) at point x,y,z on the surface S.sub.P. In order to calculate the potential at the endocardial surface S.sub.e the Laplace equation:

(8) $\begin{array}{cc}?V=\left(\frac{{?}^2}{?x^2}+\frac{{?}^2}{?y^2}+\frac{{?}^2}{?z^2}\right)V=0& \left(1\right)\end{array}$
needs to be solved, wherein V is the potential and x,y,z denote the three dimensional coordinates. The boundary conditions for this equation are V(x,y,z)=V.sub.P(x,y,z) on S.sub.P, wherein V.sub.P is the potential on surface of the probe.

(9) The solution is an integral that allows for calculating the potential V(xyz) at any point xyz in the whole volume of the heart chamber that is filled with blood. For calculating said integral numerically a discretisation of the cardiac surface is necessary and the so called boundary element method (BEM) has to be used.

(10) The boundary element method is a numerical computational method for solving linear integral equations (i.e. in surface integral form). The method is applied in many areas of engineering and science including fluid mechanics, acoustics, electromagnetics, and fracture mechanics.

(11) The boundary element method is often more efficient than other methods, including the finite element method. Boundary element formulations typically give rise to fully populated matrices after discretisation. This means, that the storage requirements and computational time will tend to grow according to the square of the problem size. By contrast, finite element matrices are typically banded (elements are only locally connected) and the storage requirements for the system matrices typically grow quite linearly with the problem size.

(12) With the above in mind, all potentials V.sub.P (x1,y1,z1) on the surface of the probe can be measured. To calculate the potential V.sub.e on the wall of the heart chamber, the known geometry of the surface of the heart chamber must be divided in discrete parts to use the boundary element method. The endocardial potentials V.sub.e are then given by a linear matrix transformation T from the probe potentials V.sub.P: V.sub.e=T V.sub.P.

(13) After measuring and calculating one or more electric potential(s) V.sub.e of cardiac cells in one or more position(s) P(x,y,z) of the at least one given heart chamber at a given time t. The surface charge density and the dipole density is related to potential according to the following two Poisson equations:

(14) $\begin{array}{cc}?V_e=?\left(P\right){?}_{S_e}\left(P\right)& \left(2\right)\\ ?V_e=\frac{?}{?n}\left(v{?}_{S_e}\left(P\right)\right)& \left(3\right)\end{array}$
wherein ?(P) is the surface charge density in position P=x,y,z, ?.sub.S.sub.e(P) is the delta-distribution concentrated on the surface of the heart chamber S.sub.e and ? is the dipole density.

(15) There is a well known relationship between the potential V.sub.e on the surface of the wall of the heart chamber and the surface charge (4) or dipole densities (5).

(16) $\begin{array}{cc}{V}_e\left(P\right)=-\frac{1}{4?}{?}_{S_e}\frac{?\left(P^{}\right)}{\left|P^{}-P\right|}d?\left(P^{}\right)& \left(4\right)\\ V_e\left(P\right)=\frac{1}{4?}{?}_{S_e}?\left(P^{}\right)\frac{?}{?n_{P^{}}}\frac{1}{\left|P^{}-P\right|}d?\left(P^{}\right)& \left(5\right)\end{array}$
(For a review see Jackson J D. Classical Electrodynamics, 2.sup.nd edition, Wiley, N.Y. 1975.)

(17) The boundary element method again provides a code for transforming the potential V.sub.e in formulas 4 and 5 into the desired surface charge densities and dipole densities, which can be recorded in the database.

(18) In another embodiment of the method of the present invention the electric potential(s) V.sub.e is (are) determined by contact mapping. In this case the steps for calculating the electric potential V.sub.e are not necessary, because the direct contact of the electrode to the wall of the heart chamber already provides the electric potential V.sub.e.

(19) In a preferred embodiment of the method of the present invention the probe electrode comprises a shape that allows for calculating precisely the electric potential V.sub.e and, thus, simplifies the calculations for transforming V.sub.e into the desired charge or dipole densities. This preferred geometry of the electrode is essentially ellipsoidal or spherical.

(20) In order to employ the method for determining a database table of surface charge densities of at least one given heart chamber in the context of the present invention, it is preferred to use a system comprising at least: a) one unit for measuring and recording electric potentials V at a given position P(x,y,z) on the surface of a given heart chamber (Contact mapping) or a probe electrode positioned within the heart, but without direct wall contact (noncontact mapping) b) one a/d-converter for converting the measured electric potentials into digital data, c) one memory to save the measured and/or transformed data, and d) one processor unit for transforming the digital data into digital surface charge density or dipole density data.

(21) It is noted that numerous devices for localising and determining electric potentials of cardiac cells in a given heart chamber by invasive and non-invasive methods are well known in the art and have been employed by medical practitioners over many years. Hence, the method, system, and devices of the present invention do not require any particular new electrodes for implementing the best mode for practicing the present invention. Instead, the invention provides a new and advantageous processing of the available data that will allow for an increase in precision, accuracy and spatial resolution of cardiac activation mapping when compared to prior art systems based on electric surface potentials in the heart only. In the near future, the present invention will allow for providing superior diagnostic means for diagnosing cardiac arrhythmias and electric status of heart cells including metabolic and functional information.

(22) FIG. 2 provides an example embodiment of a computer architecture 200 that can form part of mapping system 100. Architecture 200 includes standard interface modules 210 for probe system 140 (and electrode 142) and standard interface modules 220 for interfacing with output devices 120, 130. The computer includes at least one processor 240 and at least one computer memory 250. The foregoing are generally known, however the present invention further includes an electrical potential to surface charge density and/or dipole density converter module 230. Module 230 includes instructions necessary for caring out the methods described herein, when executed by processor 240, wherein the results of such processing are stored in memory 250as would be understood by one skilled in the art having the benefit of this disclosure.

(23) FIG. 3 and FIG. 4 summarize methods for determining and storing surface charge densities and dipole densities in accordance with aspects of the present invention, respectively, which have been described in detail above.

(24) In method 300 of FIG. 3, in step 302, mapping system 100 is used to measure and/or calculate one or more electric potential(s) V.sub.e into one or more position(s) P within a heart chamber at a given time t. In step 304, V.sub.e is transformed into a surface charge density ?(P,t). In step 306, the surface charge density ?(P,t) is stored in a database table. The method is repeated if there is another P, in step 308.

(25) In method 400 of FIG. 4, in step 402, mapping system 100 is used to measure and/or calculate one or more electric potential(s) V.sub.e in one or more position(s) P within a heart chamber at a given time t. In step 404, V.sub.e is transformed into said dipole density ?(P,t) by using an algorithm suitable for transforming an electric potential into surface charge density. In step 406, the dipole density ?(P,t) is stored in a database table. The method is repeated if there is another P, in step 408.

(26) While the foregoing has described what are considered to be the best mode and/or other preferred embodiments, it is understood that various modifications may be made therein and that the invention or inventions may be implemented in various forms and embodiments, and that they may be applied in numerous applications, only some of which have been described herein. It is intended by the following claims to claim that which is literally described and all equivalents thereto, including all modifications and variations that fall within the scope of each claim.