Abstract:
Methods and systems method for sensing a position of an object in a body include positioning a probe in the body, making measurements of mapping electrical currents passing between at least a first electrode on the probe and a plurality of second electrodes on a surface of the body, calibrating the measurements so as to compensate for one or more non-ideal features of the measurements including effects of system-dependent electrical coupling to one or more devices other than the first electrode and the second electrodes, and computing the position of the probe in the body using the calibrated measurements.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    This Application claims the benefit of U.S. Provisional Application No. 61/113,722, filed Nov. 12, 2008, which is herein incorporated by reference. 
     
    
     BACKGROUND OF THE INVENTION 
       [0002]    1. Field of the Invention 
         [0003]    This invention relates to sensing of electrical signals within a living body. More particularly, this invention relates to sensing of electrical signals, while tracking an object in the body using impedance measurements. 
         [0004]    2. Description of the Related Art 
         [0005]    A wide range of medical procedures involve placing objects, such as sensors, tubes, catheters, dispensing devices, and implants, within the body. Position sensing systems have been developed for tracking such objects. For example, U.S. Pat. No. 5,983,126, to Wittkampf, whose disclosure is incorporated herein by reference, describes a system in which catheter position is detected using electrical impedance methods. U.S. Patent Application Publications 2006/0173251, to Govari et al., and 2007/0038078, to Osadchy, which are herein incorporated by reference, describe impedance-based methods for sensing the position of a probe by passing electrical currents through the body between an electrode on the probe and a plurality of locations on a surface of the body. 
       SUMMARY OF THE INVENTION 
       [0006]    Impedance-based position measurements typically assume a certain ideal model of current flow and impedance among the elements of the position sensing system. In practice, however, the measurements are affected by non-ideal conditions, such as varying impedance and current leakage through other conductive components that are connected to the patient&#39;s body. Embodiments of the present invention, as described hereinbelow, provide methods and systems for calibrating and compensating for the real, non-ideal measurement conditions in which the position sensing system must actually operate. 
         [0007]    An embodiment of the invention provides a method for sensing a position of an object in a body, which is carried out by positioning the object in the body, making measurements of mapping electrical currents passing between at least a first electrode on the object and a plurality of second electrodes on a surface of the body, calibrating the measurements so as to compensate for one or more non-ideal features of the measurements including effects of system-dependent electrical coupling to one or more medical devices other than the first electrode and the second electrodes, and computing the position of the object in the body using the calibrated measurements. 
         [0008]    According an aspect of the method, calibrating the measurements includes calculating the effects of system-dependent electrical coupling, and calculating mapping generator-induced crosstalk. 
         [0009]    In one aspect of the method, calculating the effects of system-dependent electrical coupling is performed prior to positioning the object in the body, and includes providing respective patch measurement circuits to determine respective portions of the mapping electrical currents passing through the second electrodes, electrically bypassing the patch measurement circuits, and thereafter determining respective crosstalk signals experienced by the second electrodes using the patch measurement circuits. 
         [0010]    According to another aspect of the method, determining respective crosstalk signals includes determining for each of the second electrodes phases between currents and voltages experienced therein, wherein the currents and voltages are coupled from transmitters connected to the at least one first electrode, respectively. 
         [0011]    According to an additional aspect of the method, the one or more medical devices comprise an ablator linked to the object, and a third electrode on the surface of the body, wherein calibrating the measurements includes measuring leakage current flowing in a path extending from the at least one first electrode through the ablator and the third electrode to the second electrodes on the body surface, rather than directly from the at least one first electrode to the second electrodes as desired, and wherein computing the position is performed while the ablator is connected to the body. 
         [0012]    According to one aspect of the method, calibrating the measurements also includes linking the second electrodes to respective body surface receivers and body surface generators, and using the body surface receivers and the body surface generators to determine a patch-to-patch conductance matrix among the second electrodes. 
         [0013]    A further aspect of the invention includes disconnecting the ablator from the probe, determining an ablator leakage current passing from a generator of one of the mapping electrical currents through the ablator and the third electrode, and determining respective components of the ablator leakage current at the second electrodes and calculating ratios between the components and the ablator leakage current, respectively. 
         [0014]    A further aspect of the method includes applying the patch-to-patch conductance matrix to perform frequency compensation of currents measured by the body surface receivers. 
         [0015]    Other embodiments of the invention provide apparatus for carrying out the above-described method. 
         [0016]    BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS 
         [0017]    For a better understanding of the present invention, reference is made to the detailed description of the invention, by way of example, which is to be read in conjunction with the following drawings, wherein like elements are given like reference numerals, and wherein: 
         [0018]      FIG. 1  is a pictorial illustration of a system for detecting areas of abnormal electrical activity and performing ablative procedures on a heart of a living subject, which is constructed and operative in accordance with a disclosed embodiment of the invention; 
         [0019]      FIG. 2  is a schematic illustration of an impedance-based positioning sub-system of the system shown in  FIG. 1 , which is constructed and operative in accordance with a disclosed embodiment of the invention; 
         [0020]      FIG. 3  is an electrical schematic of a body electrode receiver of the sub-system shown in  FIG. 2 , which is constructed and operative in accordance with a disclosed embodiment of the invention; 
         [0021]      FIG. 4  is an electrical schematic of an ablator filter of the sub-system shown in  FIG. 2 , which is constructed and operative in accordance with a disclosed embodiment of the invention; and 
         [0022]      FIG. 5  is a schematic diagram of the positioning sub system shown in  FIG. 2 , which is configured for crosstalk calibration, in accordance with a disclosed embodiment of the invention. 
     
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0023]    In the following description, numerous specific details are set forth in order to provide a thorough understanding of the various principles of the present invention. It will be apparent to one skilled in the art, however, that not all these details are necessarily always needed for practicing the present invention. In this instance, well-known circuits, control logic, and the details of computer program instructions for conventional algorithms and processes have not been shown in detail in order not to obscure the general concepts unnecessarily. 
       System Architecture  
       [0024]    Turning now to the drawings, reference is initially made to  FIG. 1 , which is a pictorial illustration of a system  10  for detecting areas of abnormal electrical activity and performing ablative procedures on a heart  12  of a living subject  40  in accordance with a disclosed embodiment of the invention. A probe or catheter  14  having a tip  18  is a component of the system  10 , and is percutaneously inserted by an operator  16  through the patient&#39;s vascular system into a chamber or vascular structure of the heart. The operator  16  brings a distal portion of the catheter  14  into contact with the heart wall at a target site that is to be evaluated. Electrical activation maps are then prepared, according to the methods disclosed in the above-noted U.S. Pat. Nos. 6,226,542, and 6,301,496, and in commonly assigned U.S. Pat. No. 6,892,091, whose disclosures are herein incorporated by reference. 
         [0025]    Electrical signals can be conveyed from the heart  12  through one or more electrodes  32  located at or near the distal tip  18  of the catheter  14  and through wires  34  to a console  24 . Pacing signals and other control signals may be conveyed from the console  24  through the wires  34  and the electrodes  32  to the heart  12 . The electrodes  32  also function as components of an impedance-based positioning system for locating the catheter, which is described below. Wire connections  28  link the console  24  with body surface electrodes  30 . 
         [0026]    Additionally, areas determined to be abnormal by evaluation of the electrical activation maps can be ablated by application of thermal energy, e.g., by passage of radiofrequency electrical current through wires  34  in the catheter to the electrodes  32 , which apply the radiofrequency energy to the myocardium. The energy is absorbed in the tissue, heating it to a point (typically about 50° C.) at which it permanently loses its electrical excitability. When successful, this procedure creates non-conducting lesions in the cardiac tissue, which disrupt the abnormal electrical pathway causing the arrhythmia. The principles of the invention can be applied to different heart chambers, to mapping in sinus rhythm, and when many different cardiac arrhythmias are present. 
         [0027]    The catheter  14  typically comprises a handle  20 , having suitable controls to enable the operator  16  to steer, position and orient the distal end of the catheter as desired for the ablation. A positioning processor  22  calculates location and orientation coordinates of the catheter  14 . 
         [0028]    The console  24  contains a generator  25 , the output of which is connected to one or more electrodes  32  on the outer surface of the catheter  14  by wires  34 . The electrodes  32  are at least dual-purpose, being employed to transmit first electrical signals to the heart  12  through the body of the subject  40  to body surface electrodes  30 , to be ultimately evaluated by the positioning processor  22 . In some embodiments, the operator  16  may cause second electrical signals, containing ablative radiofrequency energy to be conducted to the electrodes  32  from an ablation power generator  36 , which can be incorporated in the console  24 . Such techniques are disclosed in commonly assigned U.S. Pat. No. 6,814,733, which is herein incorporated by reference. 
         [0029]    As noted above, the catheter  14  is coupled to the console  24 , which enables the operator  16  to observe and regulate the functions of the catheter  14 . The positioning processor  22  is preferably a computer with appropriate signal processing circuitry. The processor is coupled to drive a display monitor  29 . The signal processing circuits, typically including an electrocardiographic device  38 , receive, amplify, filter and digitize signals from the catheter  14 , including signals conveyed via the electrodes  32 . The digitized signals are received and analyzed in the console  24  to derive electrical information of medical interest. The information derived from this analysis is used to generate an electrophysiological map of at least a portion of the heart  12  or related structures such as the pulmonary venous ostia. The map may be employed for diagnostic purposes, such as locating an arrhythmogenic area in the heart, or to facilitate therapeutic ablation. 
         [0030]    Other signals used by the positioning processor  22  are transmitted from the console  24  through the wires  34  and the electrodes  32  in order to compute the position and orientation of the catheter  14 . 
         [0031]    The electrocardiographic device  38  may provide an ECG synchronization signal to the console  24 , which may be displayed on the display monitor  29  or on a separate display (not shown). The system  10  typically also includes a reference position sensor, either on an externally-applied reference electrode attached to the exterior of the subject&#39;s body, or on another internally-placed reference catheter (not shown), which is inserted into the heart  12  and maintained in a fixed position relative to the heart  12 . By comparing the position of the catheter  14  to that of the reference catheter, the coordinates of catheter  14  are accurately determined relative to the heart  12 , irrespective of heart motion. Alternatively, any other suitable method may be used to compensate for heart motion. 
         [0032]    Reference is now made to  FIG. 2 , which is a schematic illustration of an impedance-based positioning system  26 , which is a component of the system  10  ( FIG. 1 ), shown connected to a patient body  42 , in accordance with a disclosed embodiment of the invention. This arrangement is similar to that described in the above-mentioned publications by Osadchy and Govari, modified to operate in accordance with the principles of the present invention. A brief description follows for convenience of presentation: 
         [0033]    A plurality of body surface electrodes  30 , which can be adhesive skin patches, are coupled to a body surface  44  (e.g., the skin) of the subject. The body surface electrodes  30  are sometimes referred to herein as “patches”. In cardiac applications the body surface electrodes  30  are usually distributed so as to surround the heart, three on the chest of the subject and three on the back. However, the number of the body surface electrodes  30  is not critical, and they may be placed at convenient locations on the body surface  44  in the general vicinity of the site of the medical procedure. 
         [0034]    A control unit  46 , normally disposed in the console  24  ( FIG. 1 , includes current measurement circuitry  48  and one or more catheter electrode transmitters  50  for driving a current through one or more of the electrodes  32  to one or more of the body surface electrodes  30  at respective working frequencies. The control unit  46  is linked to the positioning processor  22  ( FIG. 1 ). The control unit  46  is linked to an ablator  54 , which comprises at least one ablation generator  52 . Currents through the body surface electrodes  30  and an ablator body surface electrode  56  flow in a circuit with the ablation generator  52  and are measured by respective current measurement circuits that are disposed within body electrode receivers  58 , sometimes referred to herein as “patch measurement circuits”. The body electrode receivers  58  are typically incorporated in the control unit  46 . Alternatively, they may be affixed to the body surface electrodes  30 . Catheter electrodes are represented in  FIG. 2  as measurement electrodes  60  (circles) and a dual-purpose electrode  62  (ellipse). The dual-purpose electrode  62  functions as an ablation electrode and also serves as one of the measurement electrodes. 
         [0035]    The body surface electrodes  30  are connected to the body electrode receivers  58  via a patch box  64 , which protects the system from ablation and defibrillation currents. Typically the system is configured with six body electrode receivers  58 . The patch box parasitic impedances  66  (Z), are measured during production and thus known a priori. These impedances are discussed below. 
         [0036]    Typically, although only two measurement electrodes  60  are shown for convenience, about 80 measurement electrodes are used for impedance measurements. Typically there are one or two ablation electrodes. The coordinates of a catheter inside the body are determined in the positioning system  26  by passing currents between electrodes on the catheter and the body surface electrodes  30 . 
         [0037]    The control unit  46  may also control an ablation circuit, comprising ablator  54 , and the dual-purpose electrode  62 . The ablator  54  is typically disposed externally to the control unit  46  and incorporates the ablation generator  52 . It connects with the ablator body surface electrode  56  and to an ablator filter  68 , which in this example is shown within the control unit  46 . However this location is not essential. A switch  70  configures the ablator circuit for different modes of operation as described below. Voltage measurement circuitry  72  is provided for determining the output of the catheter electrode transmitters  50 . It will be noted from inspection of  FIG. 2  that the ablation circuit is connected to one of the catheter electrode transmitters  50 . The significance of this connection is described below in the section entitled “Ablation Leakage Training Phase”. 
         [0038]    Reference is now made to  FIG. 3 , which is a schematic of an exemplary body electrode receiver  58  ( FIG. 2 ), which is constructed and operative in accordance with a disclosed embodiment of the invention. Ideally, the impedance between the body surface electrodes  30  and ground should be zero. In practice it is not zero and thus it affects the current distribution among the body surface electrodes  30 . The effect is frequency dependent and as such, it affects each electrode differently. As will be apparent from the discussion below, during calibration currents of respective frequencies flow through the body surface electrodes  30 . This makes it impossible to predict one electrode location based on a mapping performed by another electrode. Another effect that preferably requires compensation is the leakage of positioning current generated by the catheter electrode transmitters  50  ( FIG. 2 ) through the ablation generator  52  and the ablator body surface electrode  56  to the body surface electrodes  30 . The objective of the calibration and compensation procedures is to estimate the current that would have flowed if the input impedance of the body surface electrodes  30  were zero and there were no ablator  54  ( FIG. 2 ). 
         [0039]    It will be noted that the body electrode receiver  58  includes a body surface electrode generator  74 , a current measurement device  76 , and a voltage measurement device  78 . The body surface electrode generator  74  in different instances of the body electrode receiver  58  may be assigned respective frequencies. Alternatively, the body surface electrode generator  74  may be assigned the same frequency in all instances of the body electrode receiver  58  and they may be time-division multiplexed. 
         [0040]    The quantities described with reference to  FIG. 3  are as follows:
       i—body surface electrode index.   j—Frequency index. This denotes the frequency f j , which is transmitted through body surface electrode j.   Z ij —The a priori known impedance of the patch box  64  ( FIG. 2 ). This quantity may be fixed during manufacture, or determined in a post-production procedure. In any case it is treated as a known stable quantity.   q ij —The a priori known impedance of a component of the transmission path through the body surface electrode that is not included in voltage measurement.   r ij —The a priori known impedance of a component of the transmission path through the body surface electrode that is included in voltage measurement.   E i —Voltage source (unknown) that drives the body surface electrode i with frequency f i .   I ij —Current measured at body surface electrode i at frequency f j .   V ij —Voltage measured at body surface electrode i at frequency f j .       
 
         [0049]    Additional quantities not shown in  FIG. 3  are:
       Cv ij —The a priori known voltage calibration constants; and   Ci ij —The a priori known current calibration constants.       
 
         [0052]    The quantities q ij  and r ij  are also referred to as “body surface receiver parasitic impedances”. 
         [0053]    Reference is now made to  FIG. 4 , which is an electrical schematic of the ablator filter  68  ( FIG. 2 ), showing a notch filter  80  and a current measurement element  82 . In normal operation, the notch filter  80  stops most of the current transmitted through the measurement electrodes  60  ( FIG. 2 ), from leaking through the ablator  54  and the ablator body surface electrode  56 . The current measurement element  82  measures the residual leakage current through the ablator  54 . This measurement is used for ablator leakage compensation during normal operation. 
       Crosstalk Calibration  
       [0054]    Reference is now made to  FIG. 5 , which is a schematic circuit diagram of the positioning system  26  ( FIG. 2 ), which is configured for crosstalk calibration, in accordance with a disclosed embodiment of the invention. The body electrode receivers  58  are connected to a network of resistors  84  that approximately simulate body impedance. Each of the resistors  84  has a value of about 10 Ohms. The resistive network replaces the connections to the body surface electrodes  30  of normal operation as shown in  FIG. 2 . 
         [0055]    Crosstalk calibration is normally done once, either after completion of manufacture, or during initial field installation. During the crosstalk calibration process, the ablator  54  ( FIG. 2 ) is omitted The switch  70  is closed. The catheter electrode transmitters  50  are all turned on with their outputs grounded. The voltages of the catheter electrode transmitters  50  are measured simultaneously. The ratios between measured crosstalk current and the transmitter voltages are computed: 
         [0000]    
       
         
           
             
               
                 K 
                 ij 
               
               = 
               
                 
                   I 
                   ij 
                 
                 
                   V 
                   j 
                 
               
             
             , 
           
         
       
     
         [0000]    where:
       I ij —Current measurement at patch i, from electrode j (frequency f j ).   V j —Electrode j transmitter measured voltage (frequency f j ).       
 
         [0058]    The following calibration data is saved in order to perform crosstalk compensation:
       X ij ≡Abs(I ij )—Absolute crosstalk value at patch i, from electrode j (frequency f j ).   φ X/V   ij ≡ARG(K ij )—Phase between current at patch i, from electrode j, and voltage at electrode j.       
 
       Training Phase  
       [0061]    Reference is again made to  FIG. 2 . The calculations which follow may be performed by software programs incorporated in the positioning processor  22  ( FIG. 1 ). Additionally or alternatively the calculations may be performed using hardware implementations in the positioning processor  22 . 
         [0062]    During normal operation, the transmitter voltages and the phase relations between the voltages and total current output are stable. Thus it is possible to perform training infrequently. Alternatively, by training the system as a preliminary to patient procedures, the operator may achieve a higher degree of confidence in the accuracy of the crosstalk compensation. 
         [0063]    Referring again to  FIG. 1 , during the training phase of calibration, at least one of the electrodes  32  should be in the mapping volume, i.e., within a chamber of the heart  12 . The positioning system  26  transmits current through this electrode, and the system operates in a first mode, wherein transmitter voltage is measured along with the resulting patch currents. A second (normal) mode of operation, which involves measurements of ablator leakage currents, is described below. 
         [0064]    During the training phase the switch  70  ( FIG. 2 ) is closed. The training phase is nearly frequency-independent. Thus it is necessary to perform training with respect to only one of the measurement electrodes  60 . 
         [0065]    The ratio between the transmitter voltage and the sum of the patch currents is averaged over 5 seconds. We then calculate the phase between the transmitter voltage and total current (sum of patch currents): 
         [0000]    
       
         
           
             
               
                 φ 
                 
                   V 
                   / 
                   I 
                 
               
               = 
               
                 Arg 
                 ( 
                 
                   
                     V 
                     e 
                   
                   
                     
                       ∑ 
                       i 
                     
                      
                     
                       I 
                       i 
                       e 
                     
                   
                 
                 ) 
               
             
             , 
           
         
       
     
         [0000]    where:
       e—Is the transmitting electrode.   V e —Is the measured transmitter voltage.   I i   e —Current measurement at patch i, from the transmitting electrode.       
 
         [0069]    The use of these measurements is described below. 
       Online Operation  
       [0070]    During normal system operation, the crosstalk current is calculated for every transmitting electrode as follows: 
         [0000]    
       
         
           
             
               I 
               ij 
               X 
             
             = 
             
               
                 
                   X 
                   ij 
                 
                 · 
                 Exp 
               
                
               
                 { 
                 
                    
                   ( 
                   
                     
                       φ 
                       ij 
                       
                         X 
                         / 
                         V 
                       
                     
                     + 
                     
                       φ 
                       
                         V 
                         / 
                         I 
                       
                     
                     + 
                     
                       Arg 
                       ( 
                       
                         
                           ∑ 
                           i 
                         
                          
                         
                           I 
                           ij 
                         
                       
                       ) 
                     
                   
                   ) 
                 
                  
                 
                     
                 
                 } 
               
             
           
         
       
     
         [0000]    where:
       X ij , φ X/V   ij —crosstalk calibration constants (as defined above).   φ V/I —Phase between electrode transmitters and currents (see below).   I ij —Current measured at patch i at frequency f j .       
 
         [0074]    The compensation is done by subtracting the estimated crosstalk current: 
         [0000]    
       
      
       Q 
       ij 
       =I 
       ij 
       −I 
       ij 
       X  
      
     
         [0075]    The values Q ij  are used in the discussion below. 
       Body Impedance Estimation  
       [0076]    Estimation of the body impedance matrix is essential for ablator leakage compensation and frequency compensation, as described below. 
         [0077]    The measurements are represented as DFT (Discrete Fourier Transform) results: Q ij  (after crosstalk compensation) for I ij  measurement and P j  for {tilde over (V)} j  measurement. 
       Patch-To-Patch Conductance Matrix Estimation  
       [0078]    Denote voltages on the patch as X ij  (for patch i and frequency f j ). Also represent s respective body surface electrode generator  74 , which is incorporated in the body electrode receiver  58  ( FIG. 2 ) as multi-frequency E ij ≡δ ij E j  (which actually means that patch i transmits only frequency f j ). Then: 
         [0000]    
       
         
           
             
               V 
               ij 
             
             = 
             
               
                 E 
                 ij 
               
               + 
               
                 
                   r 
                   ij 
                 
                  
                 
                   I 
                   ij 
                 
               
             
           
         
       
       
         
           
             
               
                 P 
                 j 
               
               ≡ 
               
                 
                   ∑ 
                   i 
                 
                  
                 
                   
                     V 
                     ij 
                   
                   
                     Cv 
                     ij 
                   
                 
               
             
             = 
             
               
                 
                   ∑ 
                   i 
                 
                  
                 
                   
                     
                       
                         δ 
                         ij 
                       
                        
                       
                         E 
                         j 
                       
                     
                     + 
                     
                       
                         r 
                         ij 
                       
                        
                       
                         I 
                         ij 
                       
                     
                   
                   
                     Cv 
                     ij 
                   
                 
               
               = 
               
                 
                   
                     E 
                     j 
                   
                   
                     Cv 
                     
                       jj 
                        
                       
                           
                       
                     
                   
                 
                 + 
                 
                   
                     ∑ 
                     i 
                   
                    
                   
                     
                       
                         r 
                         ij 
                       
                        
                       
                         I 
                         ij 
                       
                     
                     
                       Cv 
                       ij 
                     
                   
                 
               
             
           
         
       
     
         [0079]    It follows that: 
         [0000]    
       
         
           
             
               E 
               j 
             
             = 
             
               
                 ( 
                 
                   
                     P 
                     j 
                   
                   - 
                   
                     
                       ∑ 
                       i 
                     
                      
                     
                       
                         
                           r 
                           ij 
                         
                          
                         
                           I 
                           ij 
                         
                       
                       
                         Cv 
                         ij 
                       
                     
                   
                 
                 ) 
               
                
               
                 Cv 
                 jj 
               
             
           
         
       
     
         [0080]    The voltages on the patches can now be estimated as: 
         [0000]    
       
         
           
             
               
                 
                   
                     X 
                     ij 
                   
                   = 
                     
                    
                   
                     
                       E 
                       ij 
                     
                     + 
                     
                       
                         ( 
                         
                           
                             r 
                             ij 
                           
                           + 
                           
                             q 
                             ij 
                           
                           + 
                           
                             z 
                             ij 
                           
                         
                         ) 
                       
                        
                       
                         I 
                         ij 
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     
                       
                         δ 
                         ij 
                       
                        
                       
                         E 
                         j 
                       
                     
                     + 
                     
                       ( 
                       
                         
                           r 
                           ij 
                         
                         + 
                         
                           q 
                           ij 
                         
                         + 
                         
                           z 
                           ij 
                         
                       
                       ) 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     
                       
                         
                           δ 
                           ij 
                         
                         ( 
                         
                           
                             P 
                             j 
                           
                           - 
                           
                             
                               ∑ 
                               k 
                             
                              
                             
                               
                                 
                                   r 
                                   kj 
                                 
                                  
                                 
                                   I 
                                   kj 
                                 
                               
                               
                                 Cv 
                                 kj 
                               
                             
                           
                         
                         ) 
                       
                        
                       
                         Cv 
                         jj 
                       
                     
                     + 
                     
                       
                         ( 
                         
                           
                             r 
                             ij 
                           
                           + 
                           
                             q 
                             ij 
                           
                           + 
                           
                             z 
                             ij 
                           
                         
                         ) 
                       
                        
                       
                         I 
                         ij 
                       
                     
                   
                 
               
             
           
         
       
     
         [0081]    The value of I ij  can be calculated from the measuremenet Q ij  by: 
         [0000]    
       
      
       I 
       ij 
       =Ci 
       ij 
       ·Q 
       ij  
      
     
         [0082]    The patch voltages can be calculated now: 
         [0000]    
       
         
           
             
               X 
               ij 
             
             = 
             
               
                 
                   
                     δ 
                     ij 
                   
                   ( 
                   
                     
                       P 
                       j 
                     
                     - 
                     
                       
                         ∑ 
                         k 
                       
                        
                       
                         
                           
                             r 
                             kj 
                           
                            
                           
                             Ci 
                             kj 
                           
                            
                           
                             Q 
                             kj 
                           
                         
                         
                           Cv 
                           kj 
                         
                       
                     
                   
                   ) 
                 
                  
                 
                   Cv 
                   jj 
                 
               
               + 
               
                 
                   ( 
                   
                     
                       r 
                       ij 
                     
                     + 
                     
                       q 
                       ij 
                     
                     + 
                     
                       z 
                       ij 
                     
                   
                   ) 
                 
                  
                 
                   Ci 
                   ij 
                 
                  
                 
                   Q 
                   ij 
                 
               
             
           
         
       
     
         [0083]    The patch currents and voltages are related via the patient body impedance matrix (which does not depend on frequency): 
         [0000]    
       
         
           
             
               - 
               
                 I 
                 ij 
               
             
             = 
             
               
                 ∑ 
                 k 
               
                
               
                 
                   σ 
                   ik 
                 
                  
                 
                   
                     X 
                     kj 
                   
                   . 
                 
               
             
           
         
       
     
         [0000]    The minus sign is due to a convention that positive current flow into the body—but measured as current flowing out of the body. In matrix notation: −I=σ·X. The patient body impedance matrix is estimated by σ=−I·X −1 , Here, I represents the current matrix, and not the identity matrix: 
         [0000]        σ=−[Ci   ij   ·Q   ij   ]             [X   ij ] −1    
         [0084]    Some additional corrections to σ follow, in which there is a transposition of σ at the end: 
         [0000]    
       
         
           
             
               S 
               j 
             
             ≡ 
             
               
                 ∑ 
                 i 
               
                
               
                 σ 
                 ij 
               
             
           
         
       
       
         
           
             T 
             ≡ 
             
               
                 ∑ 
                 j 
               
                
               
                 S 
                 j 
               
             
           
         
       
       
         
           
             
               σ 
               ij 
             
             ← 
             
               
                 σ 
                 ji 
               
               - 
               
                 
                   
                     S 
                     i 
                   
                    
                   
                     S 
                     j 
                   
                 
                 T 
               
             
           
         
       
     
       Ablator Patch Compensation  
       [0085]    In this section all the currents are “true measured currents”, which means that the patch current DFT values are multiplied by the corresponding calibration constant Ci p,f     j   , and the ablator leakage current DFT values are multiplied by the corresponding calibration constant Ci abl   f     j   . 
         [0086]    Referring again to  FIG. 2 , the ablator  54  connects to the patient and the positioning system  26 . The switch  70  is closed. An ablator electrode is typically located at the tip  18  ( FIG. 1 ) of the catheter  14  and corresponds to dual-purpose electrode  62 . Not all of the current that is driven into the dual-purpose electrode  62  flows through the patient body  42  into body surface electrodes  30 . Part of the current produced by the catheter electrode transmitters  50  also goes into the ablator  54 , entering the patient body  42  through the ablator body surface electrode  56 , and finally flows into the body surface electrodes  30 . The measurement electrodes  60  are affected, too. Components of their currents follow a path leading through the dual-purpose electrode  62 , through the ablator input resistance into the ablator  54 , the ablator body surface electrode  56  and finally through the body surface electrodes  30 . 
       Ablation Leakage Training Phase  
       [0087]    Continuing to refer to  FIG. 2 , The ablation leakage training phase of the positioning system  26  begins once the body surface electrodes  30  and the ablator body surface electrode  56  are in place. 
         [0088]    During ablation leakage training, the switch  70  is open, so that all the current that would otherwise be driven through the dual-purpose electrode  62  by the corresponding catheter electrode transmitter  50  is forced to flow through the ablator  54  via the ablator body surface electrode  56  to the body surface electrodes  30 . The currents through the body surface electrodes  30  I abl   p,f     M1   ≡{right arrow over (I)} abl   f     M1    (p is patch index; f M1  is M1 (ablation electrode) frequency) are measured together with the total current through the ablator body surface electrode  56 , I 8   f     M1   . The sum of these currents should be equal to the output of the ablation generator  52  within 20%: 
         [0000]    
       
         
           
             
               
                 ∑ 
                 p 
               
                
               
                 I 
                 
                   p 
                   , 
                   
                     f 
                     
                       M 
                        
                       
                           
                       
                        
                       1 
                     
                   
                 
                 abl 
               
             
             ≈ 
             
               I 
               
                 f 
                 
                   M 
                    
                   
                       
                   
                    
                   1 
                 
               
               8 
             
           
         
       
     
         [0089]    The frequency-compensated current is calculated: 
         [0000]        {right arrow over (I)}   cal   f     M1   =( I+σ·R   f     M1   ) {right arrow over (I)}   abl   f     M1      
         [0090]    Now we can calculate the currents {right arrow over (I)} abl   f     k    for every working frequency by using the estimation of the patch-to-patch conductance matrix σ as described above: 
         [0000]        {right arrow over (I)}   abl   f     k   =( I+σ·R   f     k   ) −1   ·{right arrow over (I)}   cal   f     M1      
         [0091]    I—Identity matrix. 
         [0092]    σ—Patch to patch conductance matrix estimated as explained above. 
         [0093]    R f     k   —Diagonal matrix with (r ik +q ik +z ik ) as the i th  diagonal element (the catheter transmits frequency f k ). 
         [0094]    The ablation current ratios at every frequency are then calculated as: 
         [0000]    
       
         
           
             
               
                 α 
                 
                   p 
                   , 
                   
                     f 
                     k 
                   
                 
               
               = 
               
                 
                   I 
                   
                     p 
                     , 
                     
                       f 
                       k 
                     
                   
                   abl 
                 
                 
                   
                     ∑ 
                     k 
                   
                    
                   
                     I 
                     
                       k 
                       , 
                       
                         f 
                         
                           k 
                            
                           
                               
                           
                         
                       
                     
                     abl 
                   
                 
               
             
             , 
           
         
       
     
         [0000]    where I abl   p,f     k    is the p component of the vector {right arrow over (I)} abl   f     k   . The parameters α p,f     k    should be averaged over a predefined time (30 seconds). 
       Normal Operation  
       [0095]    Continuing to refer to  FIG. 2 , during normal system operation, the switch  70  is closed, and it is assumed that the ablator  54  may be operating at any time thereafter. The currents through the body surface electrodes  30  I p,f     k    are measured together with the current through the ablator body surface electrode  56  I 8   f     k   . Using the parameters α p,f     k   , estimated at the initialization phase, the compensation is performed as follows: 
         [0000]        I   a   p,f     k     =I   p,f     k   −α p,f     k     ·I   8   f     k      
         [0096]    The resulting compensated currents I a   p,f     k   ≡{right arrow over (I)} a   f     k    are transferred forward to a frequency compensation module, which may be implemented as a software routine or a hardware module in the positioning processor  22  ( FIG. 1 ). 
       Frequency Compensation  
       [0097]    We write the body conductance matrix as: 
         [0000]    
       
         
           
             
               
                 σ 
                 body 
               
               = 
               
                 ( 
                 
                   
                     
                       e 
                     
                     
                       
                         s 
                         T 
                       
                     
                   
                   
                     
                       s 
                     
                     
                       σ 
                     
                   
                 
                 ) 
               
             
             , 
           
         
       
     
         [0000]    where we separate σ body  into a catheter component and patch component as follows: 
         [0098]    e—Total current emitted from the catheter electrode (if excited by a 1V source) 
         [0099]    S—Vector of currents received at the patches from the electrode 
         [0100]    σ—The patch to patch conductance matrix, as estimated above. 
         [0101]    Let the matrix {tilde over (R)} f     k    represent the electrode and patch resistances at frequency f k  ({tilde over (R)} f     k    is a diagonal matrix with the electrode and patch resistances at the diagonal). We will separate {tilde over (R)} f     k    into catheter (no resistance) and patch parts, 
         [0000]    
       
         
           
             
               
                 
                   R 
                   ~ 
                 
                 
                   f 
                   k 
                 
               
               = 
               
                 ( 
                 
                   
                     
                       0 
                     
                     
                       0 
                     
                   
                   
                     
                       0 
                     
                     
                       
                         R 
                         
                           
                             f 
                             k 
                           
                            
                           
                               
                           
                         
                       
                     
                   
                 
                 ) 
               
             
             , 
           
         
       
     
         [0000]    where R f     k    is a diagonal matrix, with (z ik +q ik +r ik ) as the diagonal element number i. 
         [0102]    The complete conductance matrix (body+patch resistances) is given by 
         [0000]      {tilde over (σ)} body =( I+σ   body   {tilde over (R)}   f     k   ) −1 σ body    
         [0103]    Making the electrode and patches separation again we get: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       σ 
                       _ 
                     
                     body 
                   
                   = 
                     
                    
                   
                     
                       ( 
                       
                         
                           
                             ~ 
                           
                           
                             ~ 
                           
                         
                         
                           
                             
                               s 
                               ~ 
                             
                           
                           
                             ~ 
                           
                         
                       
                       ) 
                     
                     = 
                     
                       
                         
                           
                             ( 
                             
                               
                                 ( 
                                 
                                   
                                     
                                       1 
                                     
                                     
                                       0 
                                     
                                   
                                   
                                     
                                       0 
                                     
                                     
                                       I 
                                     
                                   
                                 
                                 ) 
                               
                               + 
                               
                                 
                                   ( 
                                   
                                     
                                       
                                         e 
                                       
                                       
                                         
                                           s 
                                           T 
                                         
                                       
                                     
                                     
                                       
                                         s 
                                       
                                       
                                         
                                           σ 
                                            
                                           
                                               
                                           
                                         
                                       
                                     
                                   
                                   ) 
                                 
                                  
                                 
                                   ( 
                                   
                                     
                                       
                                         0 
                                       
                                       
                                         0 
                                       
                                     
                                     
                                       
                                         0 
                                       
                                       
                                         
                                           R 
                                           
                                             f 
                                             k 
                                           
                                         
                                       
                                     
                                   
                                   ) 
                                 
                               
                             
                             ) 
                           
                           
                             - 
                             1 
                           
                         
                          
                         
                           ( 
                           
                             
                               
                                 e 
                               
                               
                                 
                                   s 
                                   T 
                                 
                               
                             
                             
                               
                                 s 
                               
                               
                                 σ 
                               
                             
                           
                           ) 
                         
                       
                       = 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     
                       
                         ( 
                         
                           
                             
                               1 
                             
                             
                               
                                 
                                   s 
                                   T 
                                 
                                  
                                 
                                   R 
                                   
                                     f 
                                     k 
                                   
                                 
                               
                             
                           
                           
                             
                               0 
                             
                             
                               
                                 I 
                                 + 
                                 
                                   σ 
                                    
                                   
                                       
                                   
                                    
                                   
                                     R 
                                     
                                       f 
                                       k 
                                     
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                       
                         - 
                         1 
                       
                     
                      
                     
                       ( 
                       
                         
                           
                             e 
                           
                           
                             
                               s 
                               T 
                             
                           
                         
                         
                           
                             s 
                           
                           
                             σ 
                           
                         
                       
                       ) 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     ( 
                     
                       
                         
                           ~ 
                         
                         
                           ~ 
                         
                       
                       
                         
                           
                             
                               
                                 ( 
                                 
                                   I 
                                   + 
                                   
                                     σ 
                                      
                                     
                                         
                                     
                                      
                                     
                                       R 
                                       
                                         f 
                                         k 
                                       
                                     
                                   
                                 
                                 ) 
                               
                               
                                 - 
                                 1 
                               
                             
                              
                             s 
                           
                         
                         
                           ~ 
                         
                       
                     
                     ) 
                   
                 
               
             
           
         
       
     
         [0104]    In the final step only relevant quantities were computed. This means that the ideal measurement (where patch resistances are zero) S can be estimated from the real measurement {tilde over (S)} by: 
         [0000]        s =( I+σR   f     k   ) {tilde over (s)}   
       Compensation Computation  
       [0105]    Writing the ablation compensated current in place of {tilde over (s)} we get the frequency-compensated currents as: 
         [0000]        {right arrow over (I)}   c   k   =Abs (( I+σR   f     k   )           Ĩ   a   f     k   ). 
         [0106]    Here we convert complex values to real by taking their absolute values. 
         [0107]    I—Identity matrix. 
         [0108]    σ—Patch to patch conductance matrix estimated above. 
         [0109]    R f     k   —Diagonal matrix with (r ik +q ik +z ik ) as the i th  diagonal element (the catheter transmits frequency f k ). 
         [0110]    {right arrow over (I)} a   f     k   —Current after ablation leakage compensation. 
         [0111]    The resulting vector {right arrow over (I)} c   k  is a compensated, frequency-independent measure that depends only on the electrode position. 
         [0112]    It will be appreciated by persons skilled in the art that the present invention is not limited to what has been particularly shown and described hereinabove. Rather, the scope of the present invention includes both combinations and subcombinations of the various features described hereinabove, as well as variations and modifications thereof that are not in the prior art, which would occur to persons skilled in the art upon reading the foregoing description.