Abstract:
A method of acquiring and mapping physiological data in a heart chamber includes inserting a catheter having an electrode into the heart chamber. Physiological data in the heart chamber is acquired with the electrode. The position of the electrode is determined, and the location of the acquired physiological data is determined using the position of the electrode. The acquired physiological data is integrated with the location of the acquired physiological data. Information related to the three-dimensional geometry of at least a portion of the heart chamber is received, and a continuous three-dimensional color-coded map of the physiological data is created and superimposed on a geometrical representation of the three-dimensional geometry information. The map is then utilized to deliver ablation therapy.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS  
       [0001]     This application is a divisional of U.S. patent application Ser. No. 10/375,752, filed Feb. 26, 2003, which is a divisional of U.S. patent application Ser. No. 09/588,930, filed Jun. 7, 2000, now U.S. Pat. No. 6,603,996, which is a divisional of U.S. patent application Ser. No. 08/387,832, filed May 26, 1995, now U.S. Pat. No. 6,240,307, which is a national stage application of PCT/US93/09015, filed Sep. 23, 1993, which in turn claims priority to U.S. patent application Ser. No. 07/950,448, filed Sep. 23, 1992, now U.S. Pat. No. 5,297,549 and U.S. patent application Ser. No. 07/949,690, filed Sep. 23, 1992, now U.S. Pat. No. 5,311,866, each of which is incorporated by reference herein in its entirety. 
     
    
     BACKGROUND OF THE INVENTION  
       [0002]     1. Technical Field  
         [0003]     The invention discloses the apparatus and technique for forming a three-dimensional electrical map of the interior of a heart chamber, and a related technique for forming a two-dimensional subsurface map at a particular location in the endocardial wall.  
         [0004]     2. Background Art  
         [0005]     It is common to measure the electrical potentials present on the interior surface of the heart as a part of an electrophysiologic study of a patient&#39;s heart. Typically such measurements are used to form a two-dimensional map of the electrical activity of the heart muscle. An electrophysiologist will use the map to locate centers of ectopic electrical activity occurring within the cardiac tissues. One traditional mapping technique involves a sequence of electrical measurements taken from mobile electrodes inserted into the heart chamber and placed in contact with the surface of the heart. An alternative mapping technique takes essentially simultaneous measurements from a floating electrode array to generate a two-dimensional map of electrical potentials.  
         [0006]     The two-dimensional maps of the electrical potentials at the endocardial surface generated by these traditional processes suffer many defects. Traditional systems have been limited in resolution by the number of electrodes used. The number of electrodes dictated the number of points for which the electrical activity of the endocardial surface could be mapped. Therefore, progress in endocardial mapping has involved either the introduction of progressively more electrodes on the mapping catheter or improved flexibility for moving a small mapping probe with electrodes from place to place on the endocardial surface. Direct contact with electrically active tissue is required by most systems in the prior art in order to obtain well conditioned electrical signals. An exception is a non-contact approach with spot electrodes. These spot electrodes spatially average the electrical signal through their conical view of the blood media. This approach therefore also produces one signal for each electrode. The small number of signals from the endocardial wall will result in the inability to accurately resolve the location of ectopic tissue masses. In the prior art, iso-potentials are interpolated and plotted on a rectilinear map which can only crudely represent the unfolded interior surface of the heart. Such two-dimensional maps are generated by interpolation processes which “fill in” contours based upon a limited set of measurements. Such interpolated two-dimensional maps have significant deficiencies. First, if a localized ectopic focus is between two electrode views such a map will at best show the ectopic focus overlaying both electrodes and all points in between and at worst will not see it at all. Second, the two dimensional map, since it contains no chamber geometry information, cannot indicate precisely where in the three dimensional volume of the heart chamber an electrical signal is located. The inability to accurately characterize the size and location of ectopic tissue frustrates the delivery of certain therapies such as “ablation”.  
       BRIEF SUMMARY OF THE INVENTION  
       [0007]     In general the present invention provides a method for producing a high-resolution, three-dimensional map of electrical activity of the inside surface of a heart chamber.  
         [0008]     The invention uses a specialized catheter system to obtain the information necessary to generate such a map.  
         [0009]     In general the invention provides a system and method which permits the location of catheter electrodes to be visualized in the three-dimensional map.  
         [0010]     The invention may also be used to provide a two-dimensional map of electrical potential at or below the myocardial tissue surface. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS/FIGURES  
       [0011]     Additional features of the invention will appear from the following description in which the illustrative embodiment is set forth in detail in conjunction with the accompanying drawings. It should be understood that many modifications to the invention, and in particular to the preferred embodiment illustrated in these drawings, may be made without departing from the scope of the invention.  
         [0012]      FIG. 1  is a schematic view of the system.  
         [0013]      FIG. 2  is a view of the catheter assembly placed in an endocardial cavity.  
         [0014]      FIG. 3  is a schematic view of the catheter assembly.  
         [0015]      FIG. 4  is a view of the mapping catheter with the deformable lead body in the collapsed position.  
         [0016]      FIG. 5  is a view of the mapping catheter with the deformable lead body in the expanded position.  
         [0017]      FIG. 6  is a view of the reference catheter.  
         [0018]      FIG. 7  is a schematic view representing the display of the three-dimensional map.  
         [0019]      FIG. 8  is a side view of an alternate reference catheter.  
         [0020]      FIG. 9  is a side view of an alternate reference catheter.  
         [0021]      FIG. 10  is a perspective view of an alternate distal tip.  
         [0022]      FIG. 11  is a schematic view representing the display of the subsurface two-dimensional map.  
         [0023]      FIG. 12  is a schematic flow chart of the steps in the method.  
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0024]     In general, the system of the present invention is used for mapping the electrical activity of the interior surface of a heart chamber  80 . The mapping catheter assembly  14  includes a flexible lead body  72  connected to a deformable distal lead body  74 . The deformable distal lead body  74  can be formed into a stable space filling geometric shape after introduction into the heart cavity  80 . This deformable distal lead body  74  includes an electrode array  19  defining a number of electrode sites. The mapping catheter assembly  14  also includes a reference electrode preferably placed on a reference catheter  16  which passes through a central lumen  82  formed in the flexible lead body  72  and the distal lead body  74 . The reference catheter assembly  16  has a distal tip electrode assembly  24  which may be used to probe the heart wall. This distal contact electrode assembly  24  provides a surface electrical reference for calibration. The physical length of the reference catheter  16  taken with the position of the electrode array  19  together provide a reference which may be used to calibrate the electrode array  19 . The reference catheter  16  also stabilizes the position of the electrode array  19  which is desirable.  
         [0025]     These structural elements provide a mapping catheter assembly which can be readily positioned within the heart and used to acquire highly accurate information concerning the electrical activity of the heart from a first set of preferably non-contact electrode sites and a second set of in-contact electrode sites.  
         [0026]     The mapping catheter assembly  14  is coupled to interface apparatus  22  which contains a signal generator  32 , and voltage acquisition apparatus  30 . Preferably, in use, the signal generator  32  is used to measure the volumetric shape of the heart chamber through impedance plethysmography. This signal generator is also used to determine the position of the reference electrode within the heart chamber. Other techniques for characterizing the shape of the heart chamber may be substituted.  
         [0027]     Next, the signals from all the electrode sites on the electrode array  19  are presented to the voltage acquisition apparatus  30  to derive a three-dimensional, instantaneous high resolution map of the electrical activity of the entire heart chamber volume. This map is calibrated by the use of a surface electrode  24 . The calibration is both electrical and dimensional. Lastly this three-dimensional map, along with the signal from an intramural electrode  26  preferably at the tip of the reference catheter  16 , is used to compute a two-dimensional map of the intramural electrical activity within the heart wall. The two-dimensional map is a slice of the heart wall and represents the subsurface electrical activity in the heart wall itself.  
         [0028]     Both of these “maps” can be followed over time which is desirable. The true three-dimensional map also avoids the problem of spatial averaging and generates an instantaneous, high resolution map of the electrical activity of the entire volume of the heart chamber and the endocardial surface. This three-dimensional map is an order of magnitude more accurate and precise than previously obtained interpolation maps. The two-dimensional map of the intramural slice is unavailable using prior techniques.  
         [0000]     Hardware Description  
         [0029]      FIG. 1  shows the mapping system  10  coupled to a patient&#39;s heart  12 . The mapping catheter assembly  14  is inserted into a heart chamber and the reference electrode  24  touches the endocardial surface  18 .  
         [0030]     The preferred array catheter  20  carries at least twenty-four individual electrode sites which are coupled to the interface apparatus  22 . The preferred reference catheter  16  is a coaxial extension of the array catheter  20 .  
         [0031]     This reference catheter  16  includes a surface electrode site  24  and a subsurface electrode site  26  both of which are coupled to the interface apparatus  22 .  
         [0032]     It should be understood that the electrode site  24  can be located directly on the array catheter. The array catheter  20  may be expanded into a known geometric shape, preferably spherical. Resolution is enhanced by the use of larger sized spherical shapes. A balloon  77  or the like should be incorporated under the electrode array  19  to exclude blood from the interior of the electrode array  19 . The spherical shape and exclusion of blood are not required for operability but they materially reduce the complexity of the calculations required to generate the map displays.  
         [0033]     The reference electrode  24  and/or the reference catheter  16  serves several purposes. First they stabilize and maintain the array  19  at a known distance from a reference point on the endocardial surface  18  for calibration of the shape and volume calculations. Secondly, the surface electrode  24  is used to calibrate the electrical activity measurements of the endocardial surface  18  provided by the electrode array  19 .  
         [0034]     The interface apparatus  22  includes a switching assembly  28  which is a multiplexor to sequentially couple the various electrode sites to the voltage acquisition apparatus  30 , and the signal generator apparatus  32 . These devices are under the control of a computer  34 . The voltage acquisition apparatus  30  is preferably a 12 bit A to D convertor. A signal generator  32  is also supplied to generate low current pulses for determining the volume and shape of the endocardial chamber using impedance plethysmography, and for determining the location of the reference catheter.  
         [0035]     The computer  34  is preferably of the “workstation” class to provide sufficient processing power to operate in essentially real time. This computer operates under the control of software set forth in the flow charts of  FIGS. 12A and 12B .  
         [0000]     Catheter Description  
         [0036]      FIG. 2  shows a portion of the mapping catheter assembly  14  placed into a heart chamber  80 . The mapping catheter assembly  14  includes a reference catheter  16  and an array catheter  20 . In  FIG. 2  the array catheter  20  has been expanded through the use of a stylet  92  to place the electrode array  19  into a stable and reproducible geometric shape. The reference catheter  16  has been passed through the lumen  82  of the array catheter  20  to place a distal tip electrode assembly  24  into position against an endocardial surface. In use, the reference catheter  16  provides a mechanical location reference for the position of the electrode array  19 , and the tip electrode assembly  24  provides an electrical potential reference at or in the heart wall for the mapping process.  
         [0037]     Although the structures of  FIG. 1  are preferred there are several alternatives within the scope of the invention. The principle objective of the preferred form of the catheter system is to reliably place a known collection of electrode sites away from the endocardial surface, and one or more electrode sites into contact with the endocardium. The array catheter is an illustrative structure for placing at least some of the electrode sites away from the endocardial surface. The array catheter itself can be designed to mechanically position one or more electrode sites on the endocardial surface. The reference catheter is a preferred structure for carrying one or more electrode sites and may be used to place these electrode sites into direct contact with the endocardial surface.  
         [0038]     It should be understood that the reference catheter could be replaced with a fixed extension of the array catheter and used to push a segment of the array onto the endocardial surface. In this alternate embodiment the geometric shape of the spherical array maintains the other electrodes out of contact with the endocardial surface.  
         [0039]      FIG. 3  shows the preferred construction of the mapping catheter assembly  14  in exaggerated scale to clarify details of construction. In general, the array catheter  20  includes a flexible lead body  72  coupled to a deformable lead body  74 . The deformable lead body  74  is preferably a braid  75  of insulated wires, several of which are shown as wire  93 , wire  94 , wire  95  and wire  96 . An individual wire such as  93  may be traced in the figure from the electrical connection  79  at the proximal end  81  of the flexible lead body  72  through the flexible lead body  72  to the distal braid ring  83  located on the deformable lead body  74 . At a predetermined location in the deformable lead body  74  the insulation has been selectively removed from this wire  93  to form a representative electrode site  84 . Each of the several wires in the braid  75  may potentially be used to form an electrode site. Preferably all of the typically twenty-four to one-hundred-twenty-eight wires in the braid  75  are used to form electrode sites. Wires not used as electrode sites provide mechanical support for the electrode array  19 . In general, the electrode sites will be located equidistant from a center defined at the center of the spherical array. Other geometrical shapes are usable including ellipsoidal and the like.  
         [0040]     The proximal end  81  of the mapping catheter assembly  14  has suitable electrical connection  79  for the individual wires connected to the various electrode sites. Similarly the proximal connector  79  can have a suitable electrical connection for the distal tip electrode assembly  24  of the reference catheter  16  or the reference catheter  16  can use a separate connector. The distance  90  between the electrode array  19  and the distal tip assembly  24  electrode can preferentially be varied by sliding the reference catheter through the lumen  82 , as shown by motion arrow  85 . This distance  90  may be “read” at the proximal end  81  by noting the relative position of the end of the lead body  72  and the proximal end of the reference catheter  16 .  
         [0041]      FIG. 4  is a view of the mapping catheter with the deformable lead body  74  in the collapsed position.  
         [0042]      FIG. 5  shows that the wire stylet  92  is attached to the distal braid ring  83  and positioned in the lumen  82 . Traction applied to the distal braid ring  83  by relative motion of the stylet  92  with respect to the lead body  72  causes the braid  75  to change shape. In general, traction causes the braid  75  to move from a generally cylindrical form seen in  FIG. 4  to a generally spherical form seen best in  FIG. 2  and  FIG. 5 .  
         [0043]     The preferred technique is to provide a stylet  92  which can be used to pull the braid  75  which will deploy the electrode array  19 . However, other techniques may be used as well including an optional balloon  77  shown as in  FIG. 3 ; which could be inflated under the electrode array  19  thereby causing the spherical deployment of the array  19 . Modification of the braid  75  can be used to control the final shape of the array  19 . For example an asymmetrical braid pattern using differing diameter wires within the braid can preferentially alter the shape of the array. The most important property of the geometric shape is that it spaces the electrode sites relatively far apart and that the shape be predictable with a high degree of accuracy.  
         [0044]      FIG. 6  shows a first embodiment of the reference catheter  16  where the distal electrode assembly  24  is blunt and may be used to make a surface measurement against the endocardial surface. In this version of the catheter assembly the wire  97  ( FIG. 2 ) communicates to the distal tip electrode and this wire may be terminated in the connector  79 .  
         [0045]      FIG. 8  shows an alternate reference catheter  98  which is preferred if both surface and/or subsurface measurements of the potential proximate the endocardial surface are desired. This catheter  98  includes both a reference electrode  24  and an extendable intramural electrode body  100 .  
         [0046]      FIG. 9  illustrates the preferred use of an intramural electrode stylet  101  to retract the sharp intramural electrode body  100  into the reference catheter lead body  102 . Motion of the intramural electrode body  100  into the lead body  102  is shown by arrow  103 .  
         [0047]      FIG. 10  shows the location of the intramural electrode site  26  on the electrode body  100 . It is desirable to use a relatively small electrode site to permit localization of the intramural electrical activity.  
         [0048]     The array catheter  20  may be made by any of a variety of techniques. In one method of manufacture, the braid  75  of insulated wires  93 ,  94 ,  95 ,  96  can be encapsulated into a plastic material to form the flexible lead body  72 . This plastic material can be any of various biocompatible compounds with polyurethane being preferred. The encapsulation material for the flexible lead body  72  is selected in part for its ability to be selectively removed to expose the insulated braid  75  to form the deformable lead body  74 . The use of a braid  75  rather than a spiral wrap, axial wrap, or other configuration inherently strengthens and supports the electrodes due to the interlocking nature of the braid. This interlocking braid  75  also insures that, as the electrode array  19  deploys, it does so with predictable dimensional control. This braid  75  structure also supports the array catheter  20  and provides for the structural integrity of the array catheter  20  where the encapsulating material has been removed.  
         [0049]     To form the deformable lead body  74  at the distal end of the array catheter  20 , the encapsulating material can be removed by known techniques. In a preferred embodiment this removal is accomplished by mechanical removal of the encapsulating material by grinding or the like. It is also possible to remove the material with a solvent. If the encapsulating material is polyurethane, tetrahydrofuran or cyclohexanone can be used as a solvent. In some embodiments the encapsulating material is not removed from the extreme distal tip to provide enhanced mechanical integrity forming a distal braid ring  83 .  
         [0050]     With the insulated braid  75  exposed, to form the deformable lead body  74  the electrodes sites can be formed by removing the insulation over the conductor in selected areas. Known techniques would involve mechanical, thermal or chemical removal of the insulation followed by identification of the appropriate conducting wire at the proximal connector  79 . This method makes it difficult to have the orientation of the proximal conductors in a predictable repeatable manner. Color coding of the insulation to enable selection of the conductor/electrode is possible but is also difficult when large numbers of electrodes are required. Therefore it is preferred to select and form the electrode array through the use of high voltage electricity. By applying high voltage electricity (typically 1-3 KV) to the proximal end of the conductor and detecting this energy through the insulation it is possible to facilitate the creation of the electrode on a known conductor at a desired location. After localization, the electrode site can be created by removing insulation using standard means or by applying a higher voltage (e.g. 5 KV) to break through the insulation.  
         [0051]     Modifications can be made to this mapping catheter assembly without departing from the teachings of the present invention. Accordingly the scope of the invention is only to be limited only by the accompanying claims.  
         [0000]     Software Description  
         [0052]     The illustrative method may be partitioned into nine steps as shown in  FIG. 12 . The partitioning of the step-wise sequence is done as an aid to explaining the invention and other equivalent partitioning can be readily substituted without departing from the scope of the invention.  
         [0053]     At step  41  the process begins. The illustrative process assumes that the electrode array assumes a known spherical shape within the heart chamber, and that there are at least twenty-four electrodes on the electrode array  19 . This preferred method can be readily modified to accommodate unknown and non-reproducible, non-spherical shaped arrays. The location of each of these electrode sites on the array surface is known from the mechanical configuration of the displayed array. A method of determining the location of the electrode array  19  and the location of the heart chamber walls (cardiac geometry) must be available. This geometry measurement (options include ultrasound or impedance plethysmography) is performed in step  41 . If the reference catheter  16  is extended to the chamber wall  18  then its length can be used to calibrate the geometry measurements since the calculated distance can be compared to the reference catheter length. The geometry calculations are forced to converge on the known spacing represented by the physical dimensions of the catheters. In an alternative embodiment reference electrode  24  is positioned on array catheter  20  and therefore its position would be known.  
         [0054]     In step  42  the signals from all the electrode sites in the electrode array  19  are sampled by the A to D converter in the voltage acquisition apparatus  30 . These measurements are stored in a digital file for later use in following steps. At this point (step  43 ) the known locations of all the electrodes on the electrode array  19  and the measured potentials at each electrode are used to create the intermediate parameters of the three-dimensional electrical activity map. This step uses field theory calculations presented in greater detail below. The components which are created in this step (Φ lm ) are stored in a digital file for later use in following steps.  
         [0055]     At the next stage the question is asked whether the reference catheter  16  is in a calibrating position. In the calibrating position, the reference catheter  16  projects directly out of the array catheter  20  establishing a length from the electrode array  19  which is a known distance from the wall  18  of the heart chamber. This calibration position may be confirmed using fluoroscopy. If the catheter is not in position then the process moves to step  45 ,  46  or  47 .  
         [0056]     If the reference catheter  16  is in the calibrating position then in step  44  the exact position of the reference catheter  16  is determined using the distance and orientation data from step  41 . The available information includes position in space of the reference catheter  16  on the chamber wall  18  and the intermediate electrical activity map parameters of the three-dimensional map. Using these two sets of information the expected electrical activity at the reference catheter surface electrode site  24  is determined. The actual potential at this site  24  is measured from the reference catheter by the A to D converter in the voltage acquisition apparatus  30 . Finally, a scale factor is adjusted which modifies the map calculations to achieve calibrated results. This adjustment factor is used in all subsequent calculations of electrical activity.  
         [0057]     At step  47  the system polls the user to display a three-dimensional map. If such a map is desired then a method of displaying the electrical activity is first determined. Second an area, or volume is defined for which the electrical activity is to be viewed. Third a level of resolution is defined for this view of the electrical activity. Finally the electrical activity at all of the points defined by the display option, volume and resolution are computed using the field theory calculations and the adjustment factor mentioned above. These calculated values are then used to display the data on computer  34 .  
         [0058]      FIG. 7  is a representative display  71  of the output of process  47 . In the preferred presentation the heart is displayed as a wire grid  36 . The iso-potential map for example is overlaid on the wire grid  36  and several iso-potential lines such as iso-potential or isochrone line  38  are shown on the drawing. Typically the color of the wire grid  36  and the iso-potential or isochrone lines will be different to aid interpretation. The potentials may preferably be presented by a continuously filled color-scale rather than iso-potential or isochrone lines. The tightly closed iso-potential or isochrone line  39  may arise from an ectopic focus present this location in the heart. In the representative display  71  of process  47  the mapping catheter assembly will not be shown.  
         [0059]     In step  45  a subthreshold pulse is supplied to the surface electrode  24  of the reference catheter  16  by the signal generator  32 . In step  54  the voltages are measured at all of the electrode sites on the electrode array  19  by the voltage acquisition apparatus  30 . One problem in locating the position of the subthreshold pulse is that other electrical activity may render it difficult to detect. To counteract this problem step  55  starts by subtracting the electrical activity which was just measured in step  44  from the measurements in step  54 . The location of the tip of the reference catheter  16  (i.e. surface electrode  24 ), is found by first performing the same field theory calculations of step  45  on this derived electrode data. Next, four positions in space are defined which are positioned near the heart chamber walls. The potentials at these sites are calculated using the three-dimensional electrical activity map. These potentials are then used to triangulate, and thus determine, the position of the subthreshold pulse at the surface electrode  24  of the reference catheter  16 . If more accurate localization is desired then four more points which are much closer to the surface electrode  24  can be defined and the triangulation can be performed again. This procedure for locating the tip of the reference catheter  16  can be performed whether the surface electrode  24  is touching the surface or is located in the blood volume and is not in contact with the endocardial surface.  
         [0060]     At step  48  the reference catheter&#39;s position in space can be displayed by superimposing it on the map of electrical activity created in step  47 . An example of such a display  71  is presented in  FIG. 7 .  
         [0061]     When step  46  is reached the surface electrode  24  is in a known position on the endocardial surface  18  of the heart chamber which is proper for determining the electrical activity of the tissue at that site. If the intramural or subsurface extension  100  which preferentially extends from the tip of the reference catheter  102  is not inserted into the tissue then the user of the system extends the subsurface electrode  26  into the wall  18 . The potentials from the surface electrode  24  and from the intramural subsurface  26  electrode are measured by voltage acquisition apparatus  30 . Next a line  21  along the heart chamber wall which has the surface electrode  24  at its center is defined by the user of the system. The three-dimensional map parameters from step  43  are then used to compute a number of points along this line including the site of the reference catheter surface electrode  24 . These calculations are adjusted to conform to the measured value at the reference catheter surface electrode  24 . Next a slice of tissue is defined and bounded by this line  21  ( FIG. 7 ) and the location of the intramural subsurface electrode  26  ( FIG. 11 ) and computed positions such as  23  and  25 . Subsequently a two-dimensional map  27  of the electrical activity of this slice of tissue is computed using the center of gravity calculations detailed below in the section on algorithm descriptions. Points outside of the boundary of the slice cannot be computed accurately. In step  49  this map  27  of electrical activity within the two-dimensional slice is displayed as illustrated in  FIG. 11 . In this instance the iso-potential line  17  indicates the location within the wall  18  of the ectopic focus.  
         [0000]     Description of the Preferred Computing Algorithms  
         [0062]     Two different algorithms are suitable for implementing different stages of the present invention.  
         [0063]     The algorithm used to derive the map of the electrical activity of the heart chamber employs electrostatic volume-conductor field theory to derive a high resolution map of the chamber volume. The second algorithm is able to estimate intramural electrical activity by interpolating between points on the endocardial surface and an intramural measurement using center of gravity calculations.  
         [0064]     In use, the preliminary process steps identify the position of the electrode array  19  consequently the field theory algorithm can be initialized with both contact and non-contact type data. This is one difference from the traditional prior art techniques which require either contact or non-contact for accurate results, but cannot accommodate both. This also permits the system to discern the difference between small regions of electrical activity close to the electrode array  19  from large regions of electrical activity further away from the electrode array  19 .  
         [0065]     In the first algorithm, from electrostatic volume-conductor field theory it follows that all the electrodes within the solid angle view of every locus of electrical activity on the endocardial surface are integrated together to reconstruct the electrical activity at any given locus throughout the entire volume and upon the endocardium. Thus as best shown in  FIG. 7  the signals from the electrode array  19  on the catheter  20  produce a continuous map of the whole endocardium. This is another difference between the present method and the traditional prior art approach which use the electrode with the lowest potential as the indicator of cardiac abnormality. By using the complete information in the algorithm, the resolution of the map shown in  FIG. 7  is improved by at least a factor of ten over prior methods. Other improvements include: the ability to find the optimal global minimum instead of sub-optimal local minima; the elimination of blind spots between electrodes; the ability to detect abnormalities caused by multiple ectopic foci; the ability to distinguish between a localized focus of electrical activity at the endocardial surface and a distributed path of electrical activity in the more distant myocardium; and the ability to detect other types of electrical abnormalities including detection of ischemic or infarcted tissue.  
         [0066]     The algorithm for creating the 3D map of the cardiac volume takes advantage of the fact that myocardial electrical activity instantaneously creates potential fields by electrotonic conduction. Since action potentials propagate several orders of magnitude slower than the speed of electrotonic conduction, the potential field is quasi-static. Since there are no significant charge sources in the blood volume, Laplace&#39;s Equation for potential completely describes the potential field in the blood volume: 
 
 v   2 φ=0 
 
         [0067]     LaPlace&#39;s equation can be solved numerically or analytically. Such numerical techniques include boundary element analysis and other interactive approaches comprised of estimating sums of nonlinear coefficients.  
         [0068]     Specific analytical approaches can be developed based on the shape of the probe (i.e. spherical, prolate spherical or cylindrical). From electrostatic field theory, the general spherical harmonic series solution for potential is:  
         ϕ   ⁡     (     x   ,   θ   ,   φ     )       =       ∑             ⁢   ∞       l   =   0       ⁢           ⁢       ∑     m   =     -   l       l     ⁢           ⁢       {         A   l     ⁢     r   l       +       B   l     ⁢     r     -     (     l   -   1               }     ⁢     ϕ   lm     ⁢       Y   lm     ⁡     (     θ   ,   φ     )                 
 
         [0069]     In spherical harmonics, Y lm  (θ, φ) is the spherical harmonic series made up of Legendre Polynomials. Φ lm  is the lm th  component of potential and is defined as: 
 
φ lm   =∫V (θ,φ) Y   lm (θ,φ) dΩ 
 
 where V(θ, φ) is the measured potential over the probe radius R and dΩ is the differential solid angle and, in spherical coordinates, is defined as: 
 
 d Ω=sin θ dθdφ 
 
         [0070]     During the first step in the algorithmic determination of the 3D map of the electrical activity each Φ lm  component is determined by integrating the potential at a given point with the spherical harmonic at that point with respect to the solid angle element subtended from the origin to that point. This is an important aspect of the 3D map; its accuracy in creating the 3D map is increased with increased numbers of electrodes in the array and with increased size of the spherical array. In practice it is necessary to compute the Φ lm  components with the subscript l set to 4 or greater. These Φ lm  components are stored in an l by m array for later determination of potentials anywhere in the volume within the endocardial walls.  
         [0071]     The bracketed expression of equation 1 (in terms of A l , B l , and r) simply contains the extrapolation coefficients that weight the measured probe components to obtain the potential components anywhere in the cavity. Once again, the weighted components are summed to obtain the actual potentials. Given that the potential is known on the probe boundary, and given that the probe boundary is non-conductive, we can determine the coefficients A l  and B l , yielding the following final solution for potential at any point within the boundaries of the cavity, using a spherical probe of radius R:  
         ϕ   ⁡     (     r   ,   θ   ,   φ     )       =       ∑     l   =   0     ∞     ⁢       ∑     m   =     -   l       l     ⁢       [         (       l   +   1         2   ⁢   l     +   1       )     ⁢       (     r   R     )     l       +       (     l       2   ⁢   l     +   1       )     ⁢       (     r   R     )         -   l     -   1           ]     ⁢     ϕ   lm     ⁢       Y   lm     ⁡     (     θ   ,   φ     )                 
 
         [0072]     One exemplary method for evaluating the integral for Φ lm  is the technique of Filon integration with an estimating sum, discretized by p latitudinal rows and q longitudinal columns of electrodes on the spherical probe.  
         ϕ   lm     ≥         4   ⁢   π     pq     ⁢       ∑     i   =   1     p     ⁢       ∑     j   =   1     q     ⁢       V   ⁡     (       θ   i     ,     φ   j       )       ⁢       Y   lm     ⁡     (       θ   i     ,     φ   j       )                   
 
 Note that p times q equals the total number of electrodes on the spherical probe array. The angle θ ranges from zero to π radians and φ ranges from zero to 2π radians. 
 
         [0073]     At this point the determination of the geometry of the endocardial walls enters into the algorithm. The potential of each point on the endocardial wall can now be computed by defining them as r, θ, and φ. During the activation sequence the graphical representation of the electrical activity on the endocardial surface can be slowed down by 30 to 40 times to present a picture of the ventricular cavity within a time frame useful for human viewing.  
         [0074]     A geometric description of the heart structure is required in order for the algorithm to account for the inherent effect of spatial averaging within the medium (blood). Spatial averaging is a function of both the conductive nature of the medium as well as the physical dimensions of the medium.  
         [0075]     Given the above computed three-dimensional endocardial potential map, the intramural activation map of  FIG. 11  is estimated by interpolating between the accurately computed endocardial potentials at locations  23  and  25  ( FIG. 7 ), and actual recorded endocardial value at the surface electrode  24  and an actual recorded intramural value at the subsurface electrode  26  site. This first-order estimation of the myocardial activation map assumes that the medium is homogeneous and that the medium contains no charge sources. This myocardial activation estimation is limited by the fact that the myocardial medium is not homogeneous and that there are charge sources contained within the myocardial medium. If more than one intramural point was sampled the underlying map of intramural electrical activity could be improved by interpolating between the endocardial surface values and all the sample intramural values. The center-of-gravity calculations can be summarized by the equation:  
         V   ⁡     (       I   x     _     )       =         ∑     i   =   1     n     ⁢       V   i     ⁡     (                I   nx     _     -       I   i     _              -   k       )             ∑     i   =   1     n     ⁢                I   x     _     -       I   i     _              -   k               
 
 where, V( x ) represents the potential at any desired point defined by the three-dimensional vector  x  and, V i  represents each of n known potentials at a point defined by the three-dimensional vector  i  and, k is an exponent that matches the physical behavior of the tissue medium. 
 
         [0076]     From the foregoing description, it will be apparent that the method for determining a continuous map of the electrical activity of the endocardial surface of the present invention has a number of advantages, some of which have been described above and others of which are inherent in the invention. Also modifications can be made to the mapping probe without departing from the teachings of the present invention. Accordingly the scope of the invention is only to be limited as necessitated by the accompanying claims.