Patent Description:
There is a growing competitive drive in the electrophysiology market to develop basket or balloon type, multi-electrode catheters to provide more detailed electrograms, which result in more accurate maps. The usefulness of the information from such a catheter is greatly improved if location information is also available.

<CIT>, describes a basket catheter that is stated to be useful for mapping the heart. The catheter comprises an elongated catheter body having proximal and distal ends and at least one lumen therethrough, and a basket-shaped electrode assembly is mounted at the distal end of the catheter body.

<CIT>, describes a catheter that is stated to be useful for simultaneously mapping multiple points within the heart. The catheter includes a mapping assembly including a plurality of flexible spines, each having a free distal end, and the spines are supported by a support structure that permits the spines to be arranged relative to one another.

<CIT>, describes a probe that may be used to create circumferential lesions in body tissue and that may also be used to perform mapping functions. The probe includes a collapsible/expandable structure that supports electrodes or other operative elements against the body tissue.

<CIT>, and <CIT>, describe an electrode support structure comprising a guide body having at its distal end a flexible spline leg. The spline leg is flexed to define an arcuate shape to facilitate intimate contact against tissue, and an electrode element is carried by the spline leg for movement along its axis.

<CIT>, describes a basket style cardiac mapping catheter having a flexible electrode assembly for detection of cardiac rhythm disorders. The catheter includes a plurality of flexible splines having proximal portions, distal portions and medial portions therein between, and there is an anchor for securably affixing the proximal portions of the splines.

<CIT>, describes a family of catheter electrode assemblies that includes a flexible circuit having a plurality of electrical traces and a substrate, a ring electrode surrounding the flexible circuit and electrically coupled with at least one of the plurality of electrical traces, and an outer covering extending over at least a portion of the electrode.

<CIT>, describes a method for detection of cardiac rhythm disorders using a basket style cardiac mapping catheter. The method includes providing a basket assembly including a plurality of flexible splines for guiding a plurality of exposed electrodes, and the electrodes are substantially flat electrodes that are substantially unidirectionally oriented towards a direction outside of the basket.

<CIT>, describes how catheterization of the heart may be carried out by inserting a probe having electrodes into a heart of a living subject. The probe may be a basket catheter having multiple ribs, each rib having multiple electrodes.

<CIT>, describes an expandable catheter assembly with flexible printed circuit board electrical pathways. The expandable assembly can comprise a plurality of splines forming a basket array or basket catheter.

In <CIT>, there is described a medical probe which includes an insertion tube for insertion into a patient's body, and multiple arms that are attached to a distal end of the insertion tube. Each arm includes a braid of wires that traverse the arm. Multiple electrodes are coupled to the arms and electrically connected to respective selected wires of the braid. The electrodes are configured to exchange signals over the wires with a system external to the patient body.

The invention is defined by appended claim <NUM>.

It is important, for a basket or balloon catheter probe, that the location of the catheter is known as accurately as possible. Typically, this knowledge is acquired from one or more sensors that are incorporated into the catheter. In contrast, embodiments of the present invention use the splines of the basket or balloon catheter as individual single turn single axis magnetic sensors, the signals from which, when in an alternating magnetic field, providing a location for the sensors. A large area single turn sensor is as accurate as a multi-turn small area sensor because the overall areas of the two types of sensors are similar. The signals from the splines may be used on their own, or together with other location sensors incorporated in the catheter, to provide the location of a volume encompassed by the splines of the catheter.

Thus, an embodiment of the present invention comprises a probe that can be inserted into an organ, typically the heart, of a human patient. The probe, typically cylindrical, defines an axis of symmetry. At least two conductors are positioned on the probe at a distal end thereof, and the probe comprises at least two flexible conductive splines. Each conductive spline has a first termination and a second termination, and the first terminations are electrically connected together at a region on the probe axis beyond the probe distal end. Each second termination is electrically connected to a respective one of the conductors, and the splines are configured to bend in respective arcuate forms that encompass a volume.

A processor receives voltages induced on the splines via the conductors, the voltages being induced on the splines by an alternating magnetic field traversing the volume encompassed by the splines. The processor calculates a position and an orientation of the volume in response to the received voltages.

<FIG> is a schematic illustration of a medical system <NUM>, comprising a medical probe <NUM> having a proximal end <NUM> and a distal end <NUM>, according to an embodiment of the present invention. <FIG>, <FIG>, and <FIG> are schematic illustrations of distal end <NUM> of probe <NUM>, according to an embodiment of the present invention. System <NUM> may be based, for example, on the CARTO system produced by Biosense Webster Inc. , of <NUM> Technology Drive, Irvine, CA <NUM> USA,
In embodiments described hereinbelow, medical probe <NUM> is used for diagnostic or therapeutic treatment, such as for mapping electrical potentials and/or for performing ablation procedures in a heart <NUM> of a patient <NUM>. Alternatively, probe <NUM> may be used, mutatis mutandis, for other therapeutic and/or diagnostic purposes in the heart or in other body organs.

During a medical procedure using system <NUM>, a medical professional <NUM> inserts medical probe <NUM> into a biocompatible sheath (not shown) that has been prepositioned in a lumen of the patient so that a balloon <NUM>, described in more detail with reference to <FIG>, <FIG>, and <FIG>, affixed to distal end <NUM> of the medical probe enters a chamber of heart <NUM>.

System <NUM> is controlled by a system processor <NUM> which may be embodied as a single processor, or as a cooperatively networked or clustered set of processors. Processor <NUM> is typically a programmed digital computing device comprising a central processing unit (CPU), random access memory (RAM), non-volatile secondary storage, such as a hard drive or CD ROM drive, network interfaces, and/or peripheral devices. Program code, including software programs, and/or data are loaded into the RAM for execution and processing by the CPU and results are generated for display, output, transmittal, or storage, as is known in the art. Using its CPU and memories, processor <NUM> can be programmed to perform algorithms disclosed herein, using one or more modules, described hereinbelow, contained in a module bank <NUM> with which the processor communicates.

While for simplicity in the description herein processor <NUM> is assumed to be as described above, it will be understood that the scope of the invention includes a processor formed from any suitable integrated circuits, including, but not limited to, an ASIC (application specific integrated circuit), an FPGA (field-programmable gate array), an MCU (microcontroller unit), and a CPU.

In some embodiments processor <NUM> comprises real-time noise reduction circuitry <NUM>, typically configured as an FPGA, followed by an analog-to-digital (A/D) signal conversion integrated circuit <NUM>. The processor can pass the signals from A/D circuit <NUM> to modules described herein. The processor uses circuitry <NUM> and circuit <NUM>, as well as features of the modules referred to above, in order to perform the algorithms.

Processor <NUM> is typically located in an operating console <NUM> of the system. Console <NUM> comprises controls <NUM> which are used by professional <NUM> to communicate with processor <NUM>. Console <NUM> typically comprises a screen <NUM> upon which visual information generated by the processor, such as a map <NUM> of heart <NUM>, may be presented to professional <NUM>.

Console <NUM> is connected by a cable <NUM> to a location pad <NUM>, typically situated beneath patient <NUM>, comprising a plurality of fixed alternating magnetic field radiators. In one embodiment there are three sets of generally similar radiators 27A, 27B, and 27C, each radiator comprising three orthogonal coils which radiate respective magnetic fields at different frequencies, so that in this case there are nine separate fields that are radiated. Radiators 27A, 27B, and 27C, collectively herein termed radiators <NUM>, are powered by a magnetic tracking module <NUM> in module bank <NUM>, and radiate their magnetic fields into a volume including heart <NUM> and its surroundings.

In addition to powering radiators <NUM>, module <NUM> is configured to record voltages developed by conductive elements on balloon <NUM>, the voltages being created in response to the alternating magnetic fields, generated by radiators <NUM>, that traverse the conductive elements. The voltage generation is described in more detail below, and, as is also described below, from the recorded voltages, processor <NUM> is able to derive the position and orientation of balloon <NUM>.

<FIG> and <FIG> are respectively schematic perspective illustrations of balloon <NUM> in a generally spherical form and in a generally ellipsoidal form, and <FIG> is a schematic illustration of balloon <NUM> as viewed from a point distal to the balloon. Balloon <NUM> is assumed to enclose a volume <NUM>. <FIG> illustrates the balloon when fully inflated, and <FIG> illustrates the balloon in an at least partially inflated configuration. Typically, when partially or completed inflated, balloon <NUM> has a diameter of the order of about <NUM> to about <NUM>.

As stated above, balloon <NUM> is fixed to distal end <NUM>, and the distal end defines a probe axis of symmetry <NUM> of the balloon when it is at least partially inflated. In order to convey the balloon through the prepositioned sheath referred to above, the balloon is initially in a deflated form, and in this form distal end <NUM> is inserted into heart <NUM>. Once in place in heart <NUM>, the balloon may be inflated, typically by injecting a fluid, such as saline solution, into the balloon. Once the procedure for which the balloon has been positioned in heart <NUM> has been completed, the balloon may be deflated and probe <NUM> (with the deflated balloon) may be withdrawn from patient <NUM>.

So that the balloon may be deflated and inflated, balloon <NUM> is formed from a biocompatible flexible plastic material <NUM>, and the material is fixed to a plurality of generally similar flexible splines 64A, 64B,. Splines 64A, 64B,. are generically referred to herein as splines <NUM> and the splines are typically distributed symmetrically about axis <NUM>. In the disclosure and in the claims, a spline is assumed to be a long, narrow, thin strip or slat. Furthermore, because of its shape, a spline may be bent into a generally arcuate form.

While the number of splines <NUM> may be any convenient odd or even number of splines that is two or more, in the following description, by way of example, there are assumed to be eight splines 64A, 64B,. In some embodiments splines <NUM> are internal to material <NUM>, so that the splines act as ribs or spines covered by material <NUM>. Alternatively, splines <NUM> are external to material <NUM>, and the splines are attached by cement to the external surface of material <NUM> so as to support the material in place. Typically splines <NUM> are formed from flexible printed circuit (PC), a flexible wire such as nitinol, or a composition of such materials.

As is illustrated in <FIG> and <FIG>, splines <NUM> surround, i.e., encompass, volume <NUM> enclosed by balloon <NUM>.

For simplicity and clarity, in the following description, splines <NUM> are assumed to be external to material <NUM> and to be formed from flexible PC, and those having ordinary skill in the art will be able to adapt the description, mutatis mutandis, for the case of splines <NUM> being internal to the balloon material, and/or being formed from other materials referred to above.

Splines <NUM> typically comprise other elements, such as sensors, typically thermocouples or thermistors, to measure the temperature of heart tissue contacted by the splines, and electrodes. The electrodes may be used, inter alia, for radiofrequency (RF) ablation of the heart tissue, and/or for measuring and recording electrocardiogram (ECG) signals generated by the heart tissue. In some embodiments the other elements also comprise location sensors, typically coils, which provide signals in response to magnetic fields from radiators <NUM> traversing the sensors. Processor <NUM> may be configured to use such signals to find the location, i.e. the position and orientation, of the sensors. However, in some embodiments there are no such location sensors, since, as is described below, processor <NUM> uses signals from conductors in splines <NUM> to determine the position and the orientation of balloon <NUM>.

Signals to and from such other elements are typically analyzed by, and/or generated by, processor <NUM> together with respective modules in module bank <NUM>. For simplicity, such other elements and their respective modules are not shown in the figures.

Each spline 64A, 64B,. <NUM> comprises a respective conductor 66A, 66B,. <NUM>, the conductors being generically referred to herein as conductors <NUM>. Conductors <NUM> may be formed on splines <NUM> by any convenient method, such as, but not limited to, by plating onto the splines. Thus splines <NUM> are also referred to herein as conductive splines <NUM>. Conductors <NUM> have a common first termination <NUM> at a distal region <NUM> of the balloon, region <NUM> being beyond distal end <NUM> and being on axis <NUM>, where the axis cuts material <NUM>. In addition, conductors 66A, 66B,. <NUM> have respective second, separated, terminations 74A, 74B,. <NUM>, collectively referred to as <NUM>. Signals from terminations 74A, 74B,. <NUM>, produced as described below, are conveyed by respective conductors 76A, 76B,. <NUM> to proximal end <NUM> of probe <NUM> and then to module <NUM>, and processor <NUM> uses the module to analyze the signals, as is also described below.

In some embodiments one or more of conductors <NUM> may be configured to perform multiple functions, such as being able to act as the electrodes, and/or as at least one terminal of the temperature sensors, and/or as at least one terminal of the location sensors, all of which are referred to above.

When balloon <NUM> is at least partially inflated, each pair of conductors <NUM> is connected at common termination <NUM>, terminates at respective different second terminations <NUM>, and encloses a region defined by the specific pair of conductors <NUM> (i.e., defined by 66A, 66B, 66C. It will be understood that the specific pair of conductors <NUM> acts as a coil having a single turn. Thus, when the region enclosed by the single turn coil is traversed by alternating magnetic fields from radiators <NUM>, Faraday's law of induction provides that an induced voltage is developed across the different second terminations <NUM> of the pair <NUM>, and that the voltage depends on the area of the region enclosed, the intensity of the magnetic fields at the region, and the orientation of the region with respect to the magnetic fields.

<FIG> illustrates the voltages developed between different terminations 74A, 74B,. <NUM> and common termination <NUM>, according to an embodiment of the present invention. As is illustrated in the figure, voltages VA, VB,. VH may be considered to be generated between second terminations 74A, 74B,. <NUM> and common first termination <NUM> of conductors <NUM>, and the measured voltage between any two second terminations is the sum of the two voltages assumed to be generated on the two conductors. For example, a measured voltage VAC between terminations 74A and 74C is assumed to be given by equation (<NUM>): <MAT>.

Single axis sensors (SASs) having a coil with multiple turns are known in the art, and providing they are positioned in alternating magnetic fields that have been spatially mapped, it will be understood that the voltage developed across the coil can be used to find the position and orientation of the coil in the magnetic field. The Appendix below describes an algorithm for finding the position and orientation of an SAS in a mapped magnetic field, and those persons skilled in the art will be able to use the description of the algorithm, mutatis mutandis, to find the position and orientation of a single turn coil, such as a specific single turn coil defined by a pair of conductors <NUM>. The algorithm is applicable since, inter alia, the overall area of a multiple turn SAS, typically having a diameter of the order of <NUM>, is of the same order as a single turn coil formed by a pair of conductors <NUM> on a balloon having a diameter of the order of <NUM>, so that the voltages formed by the multiple turn coil and the single turn coil (in the same magnetic field) are also of the same order.

For n conductors <NUM> (in splines <NUM>), where n is an integer equal to or greater than <NUM>, there are ( <MAT>) different possible pairs of conductors forming single turn coils generating ( <MAT>) respective voltages. Thus, for the <NUM> conductors (in their respective splines) considered here, there are <NUM> possible different single turn coils. This relationship would govern different single turn coils regardless of the number of n conductors. For example, where n=<NUM>, there are <NUM> possible different single turn coils; where n=<NUM>, there are <NUM> possible different single turn coils; where n= <NUM>, there are <NUM> possible different single turn coils and so on.

The voltage across each single turn coil gives the position and orientation of the coil, and the geometric relationships between the conductors, as well as the geometric relationships of the conductors to the balloon, are known or can be estimated. From the geometric relationships, and from the voltages developed by the <NUM> different single turn coils, processor <NUM> is able to estimate the position and orientation of volume <NUM> of balloon <NUM>.

It will thus be understood that for n splines forming ( <MAT>) pairs of single turn coils, from the geometric relationships, and from the voltages developed by the ( <MAT>) coils, processor <NUM> is able to estimate the position and orientation of volume <NUM> of balloon <NUM>.

Furthermore, rather than using all the ( <MAT>) pairs of single turn coils, processor <NUM> may be configured to estimate the position and orientation of volume <NUM> of balloon <NUM> using a selected subset of the coils.

Thus, in a disclosed embodiment, rather than analyzing the <NUM> different voltages generated by the set of eight conductors <NUM>, processor <NUM> is configured to analyze the four sets of voltages generated by the subset of the eight conductors comprising four opposing pairs of conductors <NUM>, (66A, 66E), (66B, 66F), (66C, <NUM>), (66D, <NUM>). , the processor records and analyzes the voltages given by equations (<NUM>): <MAT>.

Each opposing pair of conductors <NUM> (e.g., 66A and 66E forming one pair) in general forms a planar ellipse. (In the case of full inflation of balloon <NUM> the ellipse is approximately circular with an approximately unity ellipticity. ) Furthermore, the centers of each of the four ellipses are approximately the same, corresponding to the center of volume <NUM>. Because of the symmetry of splines <NUM> each of the four ellipses typically has substantially the same ellipticity, so that balloon <NUM> is effectively an ellipsoid of revolution around axis <NUM>. Because, by virtue of the known construction of splines <NUM> on balloon <NUM>, the orientation of the four ellipses with respect to each other is known, these orientations may be used to calculate an orientation of the balloon and a magnitude of its enclosed volume. By estimating the location of the balloon, i.e. its position and orientation, as well as its volume, the processor is able to provide a virtual representation of the actual size of the physical balloon and its actual location relative to the structures of the heart in a medical procedure.

<FIG> is a flowchart of steps of a balloon catheter algorithm implemented by processor <NUM> for balloon <NUM>, according to an embodiment of the present invention. The algorithm assumes that voltages of the four pairs of opposing conductors <NUM> of the disclosed embodiment described above, describing the four ellipses of the balloon, are measured. From the measured voltages, processor <NUM> finds the position and orientation of volume <NUM>.

In a generation step <NUM>, a magnetic field model Bmodel(x, y, z) is generated from magnetic field measurements made in a region (that will surround heart <NUM> in a subsequent step of the algorithm) by a magnetic sampling detector scanned within the region at predefined points. The magnetic fields in the region are provided by the nine radiators <NUM>, which are typically configured to transmit simultaneously at nine different frequencies. The magnetic field model, which provides a correspondence between a position (x,y,z) and the nine measured magnetic fields at the position, is fitted to the magnetic field measurements at the predefined points.

In a calibration step <NUM>, balloon <NUM> is inflated, typically so that the balloon is approximately spherical, and the area of each of the four ellipses is measured. If the balloon is approximately spherical, then the ellipses are approximately circles, and the area of each ellipse is the same and is known from the balloon diameter. The area of each ellipse is herein assumed to be Areacal.

The inflated balloon is inserted into a known magnetic field Φ, typically produced by a Helmholtz coil, and voltages Meascal of each of the four ellipses are measured and recorded by processor <NUM>. It will be understood that there are nine voltages for each ellipse (from the nine radiators <NUM>). From Faraday's law of induction the voltage is directly proportional to the product of Areacal and a projection Φp of the magnetic field Φ onto the ellipse, so that <MAT> where k is a constant of proportionality.

The processor stores the value of k for use in an ellipticity calculation step <NUM>.

In a catheter insertion step <NUM>, patient <NUM> is moved so that their heart is in the magnetic field region, and probe <NUM> is inserted into the patient so that balloon <NUM> enters the heart of the patient. The balloon is then inflated, and voltages Meas generated at second terminations 74A, 74B,. <NUM>, of spline conductors <NUM>, are measured and recorded by processor <NUM> using module <NUM>. For each ellipse formed by opposing conductors <NUM>, there are nine different voltages generated by the nine magnetic fields from radiators <NUM>.

In a location calculation step <NUM>, processor <NUM> calculates the position and orientation of a specific ellipse, using the nine voltages measured and the magnetic field model Bmodel(x, y, z) derived in step <NUM>. Methods for calculating the position and orientation of a coil in a plurality of alternating magnetic fields are known in the art, and are used, for example, in the CARTO system referred to above. A method for calculating the position and orientation of a coil in a plurality of alternating magnetic fields is described in <CIT> to Montag. In addition, a method for calculating the position and orientation of a coil in a plurality of alternating magnetic fields is described in the Appendix below. The two latter methods are based on minimization. In step <NUM> the processor may also calculate the area of the specific ellipse, typically using a method as described in the Appendix below. Alternatively or additionally, the area may be calculated as described below in step <NUM>.

In ellipticity calculation step <NUM>, processor <NUM> calculates the ellipticity of the specific ellipse, i.e., the ratio between the semi-major axis length a and the semi-minor axis length b using magnitudes of the nine voltages Meas measured in step <NUM>. Values of the magnitudes enable the processor to estimate an area A of the specific ellipse, as is explained below.

The ellipses of calibration step <NUM> are typically deformed in step <NUM>, having an unknown area A. However, as stated above, the voltages produced by any given ellipse are directly proportional to the area of the ellipse and to the projection of the magnetic field onto the ellipse, so that using equation (<NUM>) the following equation holds: <MAT> where (vx,vy,vz) is a direction vector subject to the constraint that ∥(vx, vy, vz)∥ = <NUM>.

In step <NUM> processor <NUM> uses equation (<NUM>), and the value of constant k derived in step <NUM>, to estimate the area A of each ellipse. In equation (<NUM>) there are six unknowns; however, since there are nine independent radiators <NUM>, there is more than sufficient information for processor <NUM> to use equation (<NUM>) to estimate a given ellipse area.

Equations (<NUM>) and (<NUM>) below are equations respectively relating the area A of an ellipse to a and b, and a perimeter p of the ellipse to a and b. The value of perimeter p is the total length of the conductors <NUM> forming the ellipse, and this value is known. <MAT> <MAT>.

Using the values of A and p, processor <NUM> solves equations (<NUM>) and (<NUM>) for a and b, and thus the ellipticity of the specific ellipse.

As indicated by an arrow <NUM>, the processor repeats the calculations of steps <NUM> and <NUM> for all the four ellipses generated by opposing conductors <NUM>.

In a concluding step <NUM> of the algorithm, the processor averages the four positions of the ellipses to find the position of volume <NUM>. The processor also finds an orientation of volume <NUM> from the four ellipse orientations. An average of the ellipticities of the ellipses gives a value for the ellipticity of the ellipsoid of revolution of volume <NUM>.

Since volume <NUM> is an ellipsoid of revolution, a magnitude V of this volume, i.e. the volume enclosed by balloon <NUM>, is given by equation (<NUM>): <MAT>.

In a disclosed embodiment, using the position, orientation, and magnitude of volume <NUM> as determined above, the processor may present in step <NUM>, on map <NUM> of the heart (<FIG>), a virtual representation of the actual size of balloon <NUM> and the balloon's actual location relative to the structures of the heart. The presentation may be implemented during a medical procedure.

Alternatively or additionally, the processor may present on screen <NUM> a numerical value of magnitude V. Professional <NUM> may estimate from the numerical value, and/or from the virtual representation, if balloon <NUM> has been underinflated or overinflated.

While the description above for the flowchart of <FIG> considers splines forming four pairs of coils, those persons skilled in the art will be able to adapt the description, mutatis mutandis, for other possible numbers of pairs of coils, and all such possible numbers are considered to be within the scope of the present invention.

<FIG> illustrates experimental results obtained by the inventors, using a system similar to system <NUM>, according to an embodiment of the present invention. The results are for the four ellipse systems described above with reference to <FIG> and <FIG>. The figure shows, for seven selected positions of volume <NUM> enclosed by balloon <NUM>, three of the four ellipses that processor <NUM> calculates at each of the seven positions.

<FIG> is a flowchart describing steps of a position and orientation (P&O) algorithm for tracking a single axis sensor (SAS) of a catheter, according to an embodiment of the present invention. The flowchart assumes that the SAS comprises one or more turns of a coil, and that the SAS is in a region of interest (ROI) irradiated by i alternating magnetic fields generated by i respective magnetic field generators, where i is a positive integer. In the following description i = <NUM>, corresponding to radiators <NUM> described above, and the ROI may be assumed to comprise a region containing heart <NUM>. The P&O algorithm is assumed to be implemented by processor <NUM> using magnetic tracking module <NUM>.

In a generation step <NUM>, a magnetic field model Bmodel(x, y, z), substantially the same as step <NUM> of the balloon catheter algorithm, is generated from magnetic field measurements made in the ROI by a magnetic sampling detector scanned within the ROI at predefined points. The magnetic field model is fitted to the magnetic field measurements at the predefined points.

At a definition step <NUM>, an initial position vector is defined by arbitrarily assigning an initial SAS position vector r= (x, y, z) of the distal tip of the catheter, at a point such as a center of the ROI.

In a first measurement step <NUM>, i initial magnetic field measurements, measi, are measured at the single axis sensor. The field measurements are received by module <NUM> and relayed to processor <NUM>.

In a choosing step <NUM>, an initial orientation vector is chosen from one of six unit vectors, e.g., ((<NUM>,<NUM>,<NUM>), (-<NUM>,<NUM>,<NUM>), (<NUM>,<NUM>,<NUM>), (<NUM>,-<NUM>,<NUM>), (<NUM>,<NUM>,<NUM>), (<NUM>,<NUM>,<NUM>)). Processor <NUM> computes six cost functions cost using equations (A)-(C) below. <MAT> <MAT> where ΔMeas<NUM> is a penalty function given by <MAT> vx, vy, vz, are components of an SAS orientation vector v= (vx, vy, vz), <MAT>.

In step <NUM> processor <NUM> uses the initial field measurement from step <NUM>, the six unit vectors, and the initial position vector defined in step <NUM>. The initial orientation vector chosen is the one that gives the lowest value of cost in six cost function computations of equation (B).

In a first decision step <NUM>, if this is the initial position and orientation measurement, processor <NUM> bypasses a second measurement step <NUM>, since the fields were already measured in step <NUM>. If this is not the initial measurement, fields measi are measured at the single axis sensor in second measurement step <NUM>.

In a varying step <NUM> and a second decision step <NUM>, processor <NUM> initiates an iteration loop after step <NUM> to minimize the cost function value cost. In step <NUM> SAS position vector r= (x, y, z) and SAS orientation vector v= (vx, vy, vz) are varied to reduce the cost function.

While in the iteration loop, not only is the cost function reduced, typically monotonically, but processor <NUM> also computes the seven differential variables (∂x, ∂y, ∂z, ∂vx, ∂vy, ∂vz, ∂Area) using a Levenberg-Marquardt (L-M) variation of the Gauss-Newton (G-N) optimization method, according to equation (D): <MAT> where J is the Jacobian matrix, JT is the transpose of J, diag(J) is a diagonal matrix whose elements are the diagonal elements of J, and λ is a non-negative scalar parameter, which is typically approximately <NUM>, and which shrinks by a factor of <NUM> in every iteration. ΔMeas in equation (D) is a <NUM> x <NUM> matrix, which comprises nine terms from the nine radiators <NUM> and one penalty function term from equation (C).

The seven differentials (∂x, ∂y, ∂z, ∂vx, ∂vy, ∂vz, ∂Area) computed iteratively from equation (D) represent the differential changes of the components of position vector r= (x, y, z), the differential changes of the components of orientation vector v= (vx, vy, vz), and the change in area between successive iteration loop cycles.

Using the seven differentials, processor <NUM> calculates a change in the position vector <MAT>, a change in the orientation vector <MAT>, and a change in the area ∂Area between iteration loop cycles.

In a second decision step <NUM>, when |∂ r|, |∂ v|, and |∂Area|/Area are not below a predefined threshold, typically <NUM>, the iteration loop continues with varying step <NUM>. If |∂ r|, |∂ v|, and |∂Area|/Area are below the predefined threshold, processor <NUM> assigns the computed position, orientation, and area as the found position, orientation, and area in an assignment step <NUM>, i.e. the measured position and orientation vector, and the area, of the SAS.

While the description above has assumed splines forming a balloon catheter positioned in a heart, it will be understood that embodiments of the present invention may be implemented for splines forming a basket catheter. It will also be understood that embodiments of the present invention may be used for procedures on organs other than the heart, such as sinuplasty procedures.

Claim 1:
Apparatus, comprising:
a probe (<NUM>) having a proximal end (<NUM>) and a distal end (<NUM>), the probe being configured to be inserted into an organ of a human patient and defining a probe axis;
at least two conductors (<NUM>) positioned on the probe at the distal end;
at least two flexible conductive splines (<NUM>), each conductive spline having a first termination (<NUM>) and a second termination (<NUM>), each of the first terminations being electrically connected together at a region (<NUM>) on the probe axis beyond the distal end of the probe and forming one or more pairs, each pair of the one or more pairs comprising two flexible conductive splines of the at least two flexible conductive splines such that each pair of the one or more pairs forms a respective single turn coil comprising the two flexible conductive splines, each second termination being electrically connected to a respective one of the at least two conductors, the at least two flexible conductive splines being configured to bend into respective arcuate forms that encompass a volume (<NUM>); and
a processor (<NUM>) configured to receive one or more voltages induced on each respective single turn coil via the at least two conductors and to calculate a position and orientation of the volume in response to the one or more received voltages.