Method for navigating a catheter probe

Abstract

A system for navigating a catheter probe through a body cavity includes a sensing coil affixed to a distal end of the probe. Magnetic fields are projected into the body cavity to induce voltage signals in the sensing coil that are sufficient to describe the orientation and position of the probe. A set of magnetic coils each generates a substantially uniform field in a single respective dimension. The orientation angles of the sensing coil may be determined from known values of the unidirectional fields and the measured induced voltage signals. Gradient magnetic fields with components in two dimensions are projected into the body cavity to induce another group of voltage signals. The geometrical intersection of constant voltage surfaces developed by certain gradient fields that produce the measured induced voltage signals is a set of lines on which the catheter is located. The point of intersection of such lines yields the positional coordinates.

Description

This relationship for a single coil may be used to determine the induced voltage within a coil of N turns. Assuming that each turn of the coil is separately and equally linked by the magnetic flux (e.g., in tightly wound coils), the induced voltage within the entire coil assembly may be approximated as the summation of the induced voltages developed in each turn. Accordingly, the total voltage across the entire coil assembly is N times the induced voltage for a single turn; hence, the induced voltage V_ind is equivalent to
V_ind=−Nωπd²B_o cosθcosωt
Clearly, the induced voltage in the sensing coil will vary with changes in the angular orientation between the coil axis and the direction of the magnetic field lines.

A useful reference frame for spatially conceptualizing the interaction between the sensing coil and the magnetic fields is the Cartesian coordinate system defined by mutually perpendicular axes x-y-z. For purposes of illustration, a nonzero vector â is selected to coincide with the axis through the sensing coil of the present invention (hereinafter “coil axis”).

The angles α, β, and γ that the vector â makes with the unit coordinate vectors î, ĵ, and {circumflex over (k)}, respectively, are called the direction angles of â; the trigonometric terms cosα, cosβ, and cosγ represent direction cosine values. Employing vector product notation, the following expressions are developed: â·î=∥â∥cosα; â·ĵ=∥â∥cosβ; and â·k=∥â∥cosγ. Referencing the induced voltage equations set forth above, these angles α, β and γ correspond to the angular displacement of the coil axis with respect to uniform fields generated along the x-axis, y-axis, and z-axis directions, respectively. Thus, the correspondence between direction cosine expressions is as follows:

• • cosα corresponds to sinφcosθ;
  • cosβ corresponds to sinθsinφ; and
  • cosγ corresponds to cosφ.
    Accordingly, the following relationships illustrate the dependence of induced voltage on the orientation parameters φ and θ:
• V_x≈sinφcosθ;
  • V_y≈sinθsinφ; and
  • V_z≈cosφ,
    where the subscript indicates the direction of the magnetic field that produced the measured induced voltage.

FIG. 4 is a flowchart detailing the location algorithm according to the present invention and should be referenced in connection with the discussion below.

As noted above, the last navigation point (LNP) refers to the x-y-z positional coordinates of the sensing coil as determined by the immediately previous computation cycle of the algorithm. For the first cycle, the LNP is the center of the viewing field.

In accordance with a preferred embodiment of the present invention for implementing the location algorithm, a magnetic assembly of nine individual coil sets are used to generate the magnetic fields sufficient to develop a corresponding set of nine induced voltage signals that are fully representative of the location of the sensing coil. The nine coil sets correspond to a group of three unidirectional coil sets for generating uniform fields in the x, y, and z-directions; a first delta coil group including a short coil set at 0° and a long coil set at 0°; a second delta coil group including a short coil set at 120° and a long coil set at 120°; and a third delta coil group including a short coil set at 240° and a long coil set at 240°. The angular designations associated with the delta coil groups indicate the angle with respect to the z-axis of the coil dimension that is perpendicular to the direction of elongation of the delta coils. Accordingly, the three delta coil groups are arranged pair-wise in a circular orientation about the y-axis at angles of 0°, 120°, and 240°.

The look-up-table (LUT) consists of a database containing the magnetic field values (H_x H_y H_z) at every x-y-z coordinate location within the navigational domain for five coil sets: the unidirectional coil sets for generating the uniform fields in the x, y, and z-directions; the short coil (SC) set at 0°; and the long coil (LC) set at 0°. The magnetic field value data for the short and long coil sets at 120° and 240° may be obtained from the LUT by rotating the field vectors for the long and short coil sets at 0° by the angle (i.e., ±120°) appropriate for the given coil set. The input data for the LUT consists of the x-y-z coordinates and a designation of which coil set is being used to generate the magnetic fields. In response to this input data, the LUT supplies the magnetic field values H_x H_y H_z at the selected x-y-z coordinates for the designated coil set.

The LUT is present to speed up the operational sequence of the location algorithm. Otherwise, an undesirable computational delay exists if the required magnetic fields from the nine coil sets must be individually calculated during each iteration of the algorithm. By predetermining the magnetic field values and storing them in LUT, the location algorithm need only access the LUT to retrieve the appropriate field value without endeavoring into any complex field analysis. At x-y-z coordinates other than those for which magnetic field values are determined in the LUT, an interpolation procedure is employed to calculate the field value.

Determining Angular Orientation of the Sensing Coil

The location algorithm of the present invention initially undertakes a procedure to determine the angular orientation of the sensing coil. An assumption is first made that the coil orientation does not appreciably change during the period between cycle computations. Accordingly, the magnetic field values corresponding to the uniform field pattern at the LNP are used as an approximation for the magnetic field values at the current but as yet undetermined location.

The unidirectional coils are activated in succession, each generating a substantially uniform field that projects into the navigational domain and induces a corresponding voltage signal in the sensing coil. The induced voltage signals are measured by an appropriate detection unit coupled to a proximal end of the catheter device where an electrical connection to the sensing coil is established via suitable connection means extending along the body of the catheter device.

The LUT is then accessed three times to acquire the magnetic field values at the LNP for each of the three unidirectional coils. These values and the measured voltage signals are then substituted into the appropriate equations set forth below to solve for the unknown variables φ and θ that define the coil orientation.

As a general principle, the voltage induced within the sensing coil may be resolved into components along each of the axial dimensions as determined by the extent to which the magnetic flux density is developed along these axial dimensions. For example, a general formula for the induced voltage produced by the unidirectional coil which generates a substantially uniform field in the x-direction is as follows:
V_x=H_xxK sinφcosθ+H_yxK sinφsinθ+H_zxK cosφ
where magnetic field intensity H is related to magnetic flux density by B=μH and K=μ_o ωNπd². The first subscript in the field intensity term indicates the axial dimension along which the magnetic field value was determined by accessing the LUT for the given coil set at the LNP, while the second subscript indicates the field-generating coil set. For an x-directed substantially uniform field, the terms H_yz and H_zx are small compared to H_xx. Similar equations are developed below for the induced voltages produced by the unidirectional coils successively generating a y-directed and z-directed substantially uniform field:
V_y=H_xyK sinφcosθ+H_yyK sinφsinθ+H_zyK cosφ,
and
V_z=H_xzK sinφcosθ+H_yzK sinφsinθ+H_zzK cosφ.
The terms H_xy and H_zy in the equation for V_y and the terms H_xz and H_yz in the equation for V_z are small compared to H_yy and H_zz, respectively. After substituting the measured values for the induced voltage signals, the equations are simultaneously solved to determine the unknown variables φ and θ defining the orientation of the sensing coil.

Determining Positional Coordinates of the Sensing Coil

By way of summary, the procedure for determining the positional coordinates of the sensing coil in accordance with the present invention first involves activating each delta coil in succession and measuring the induced voltage thereby developed in the sensing coil. Next, the LUT is accessed to obtain the magnetic field values at the LNP for each specified delta coil. These magnetic field values and the as-computed values for the orientation angles φ and θ are then substituted into the appropriate induced voltage equations to calculate for each delta coil the expected value of the voltage signal induced in the sensing coil. This expected value of the induced signal corresponds to a specific and unique member of the family of constant signal surfaces of the delta coils.

Based on the difference between the measured and expected values for the induced voltage signals, a gradient is calculated (representative of the rate of change of the induced signal) that permits identification of the specific constant signal surface that is responsible for generating the measured value of the induced signal. This procedure is repeated for each delta coil.

For the activation of each delta coil group (comprised of one long coil set and one short coil set), there is an intersection line defined by the intersection of the two constant signal surfaces (which were identified as developing the measured induced signal) on which the sensing coil is located. The intersection of the three such lines from the three delta coil groups uniquely provides the x-y-z coordinates of the sensing coil. Although two such lines are sufficient to describe the position of the sensing coil, greater accuracy and more reliable performance in determining the catheter position is achieved with three lines.

The following is a more detailed discussion of the procedure summarized above for determining the positional coordinates.

The magnetic field pattern generated by the entire assembly of short coil and long coil sets is characterized by a family of surfaces of constant signal or constant voltage developed by the sensing coil, each having non-zero components in two of the axis directions and a small component in the remaining axis direction. For example, the magnetic field surfaces generated by the short and long coil sets oriented at 0° relative to the x-axis have a small value in the x-direction. The short coil positioned at 0° (i.e., SC(0°)) and long coil positioned at 0° (i.e., LC(0°)) are each independently activated. The induced voltage in the sensing coil is measured for each coil set. The LUT is then accessed to determine the magnetic field values for the SC(0°) and LC(0°) coil set at the LNP.

These magnetic field values (i.e., H_x=small and non-zero H_y H_z components) are used in conjunction with the as-computed orientation angles φ and θ to calculate the values of the induced catheter signals that would be expected from such magnetic field values. The expected and measured induced voltage values are compared, and the difference is used to identify the constant signal surface from each of the SC(0°) and LC(0°) coil sets that would have produced the measured induced signals. The intersection of these identified magnetic constant signal surfaces is a line parallel to the x-axis (thereby resolving the y-z coordinates).

The aforementioned procedure involving the long and short coils oriented at 0° is iteratively repeated for a long and short coil set oriented at 120° (i.e., SC(120°) and LC(120°)) and 240° (i.e., SC(240°) and LC(240°)).

More specifically, the coil sets SC(120°) and LC(120°) are sequentially activated to induce corresponding catheter signals in the sensing coil. In order to utilize the LUT data on the coil sets oriented at 0° for determining the magnetic field components at the LNP generated by the coil sets SC(120°) and LC(120°), a modified LNP is calculated that is equivalent to the original LNP rotationally displaced by 120°. The LUT is then accessed with the modified LNP to determine the magnetic field values generated by the SC(120°) and LC(120°) coil sets at the modified LNP. The field vectors produced by the LUT for both the long coil and short coil are then rotated (−120°) to go from the modified LNP to the actual LNP. Based upon these field values, a pair of induced catheter signals are calculated that correspond to the expected signal values arising from the magnetic field values for the SC(120°) and LC(120°) coil sets. The difference between the measured and expected induced catheter signals is used to identify the magnetic constant signal surface for each of the SC(120°) and LC(120°) coil sets that could produce the measured catheter signal. The intersection of these identified magnetic constant signal surfaces is a line oriented at 120° to the x-axis.

A similar procedure is used involving a modified LNP that is rotationally displaced 240° to simulate the magnetic field patterns for the SC(240°) and LC(240°) coil sets using the SC(0°) and LC(0°) field data. A line oriented at 240° to the x-axis is then identified along which the catheter is located.

Each of the field lines oriented at 0°, 120° and 240° to the x-axis is weighted according to the strength of the measured catheter signals. For example, a weak measurement indicates a relatively imprecise identification of the intersection line, resulting in a weaker weighting. This weighting reflects the accuracy of the estimation used to determine the location of the catheter with the specified coil set. An averaging technique is used to compute a weighted estimate of the intersection of the lines L(0°), L(120°) and L(240°). The intersection is the new value for x-y-z and will replace the x-y-z of the old LNP to become the next LNP. The algorithm iteratively repeats the aforementioned operations using the updated LNP to arrive at the location of the sensing coil after each computation cycle (e.g., every 0.1 s).

Magnetic Assembly for Determining Angular Orientation of Sensing Coil

FIG. 1 schematically illustrates a perspective view of an examination deck that facilitates implementation of the location algorithm in accordance with a preferred embodiment of the present invention, and which employs a magnetic coil assembly arranged in a flat configuration. The examination deck includes a planar top platform 10 suitable for accommodating a recumbent patient disposed lengthwise on the planar top. The navigational domain is illustratively depicted as the spherical volume 12 enclosing a sensing coil 14 attached via suitable connection means 16 to an external signal detection apparatus (not shown). The coil sets embedded in platform 10 (and described in connection with FIGS. 2A-C and 3) are activated by a signal drive unit (not shown) connected via line 18. The examination deck is preferably constructed from a suitable magnetically-permeable material to facilitate magnetic coupling between the embedded coil sets and the overlying sensing coil.

Coil Set for Generating X-Directed Field

FIG. 2A schematically illustrates the unidirectional coil set for generating a substantially uniform x-directed field throughout the navigational domain 12. The coil set includes a first coil pair with elements 20 and 24 and a second coil pair with elements 22 and 26, where the current flow as supplied by drive unit 28 is indicated by the arrow symbol. Coil elements 20 and 22 are disposed in the major surface of platform 10, while elements 24 and 26 are disposed in the lateral walls of platform 10. Elements 24 and 26 are preferably used as compensation coils to substantially cancel undesirable field components generated by elements 20 and 22 in the y- and z-directions. The coils cumulatively generate a substantially uniform x-directed field as indicated by representative field line 27.

Coil Set for Generating Y-Directed Field

FIG. 2B schematically illustrates the unidirectional coil set for generating a substantially uniform y-directed field throughout the navigational domain 12. The coil set includes a coil pair with elements 30 and 32 disposed in spaced-apart and parallel relationship within platform 10, with the indicated current flow as supplied by drive unit 34. The coils generate a substantially uniform y-directed field as indicated by representative field line 33.

Coil Set for Generating Z-Directed Field

FIG. 2C schematically illustrates the unidirectional coil set for generating a substantially uniform z-directed field throughout the navigational domain 12. The coil set includes a first coil pair with elements 36 and 40 and a second coil pair with elements 38 and 42, with the indicated current flow as supplied by drive unit 44. Coil elements 36 and 38 are disposed in the major surface of platform 10, while elements 40 and 42 are disposed in the lateral walls of platform 10. Elements 40 and 42 are preferably used as compensation coils (e.g., Cunard coils) to substantially cancel undesirable field components generated by elements 36 and 38 in the x- and y-directions. The coils cumulatively generate a substantially uniform z-directed field as indicated by representative field line 43.

The coil configurations shown in the Figures are only illustrative and should not be construed as a limitation of the present invention, as it should be apparent to those skilled in the art that other coil configurations are possible within the scope of the present invention provided such other configurations produce the desired magnetic field patterns. A suitable connection means (not shown) couples the sensing coil 14 to a signal measuring device.

Magnetic Assembly for Determining Positional Coordinates of Sensing Coil

FIGS. 3 and 5 show the coil configuration used to determine the positional coordinates of the sensing coil in accordance with a preferred embodiment of the present invention. The configuration includes six coils grouped into three pairs of long and short delta coils (50-52, 54-56, 58-60). The delta coils are mutually coplanar and are disposed in the planar top of the examination deck immediately beneath the recumbent patient. Interconnection means between a signal drive unit (not shown) and the delta coil groups is shown representatively for only coils 50-52.

The coils are preferably arranged in a circular orientation about the y-axis such that there is an axis perpendicular to the direction of elongation of the coils at 0°, 120° and 240° relative to the z-axis. The magnetic field generated by the first group of long (50) and short delta coils (52) is shown representatively by the field lines extending from the upper region of the coils. The field lines from this delta coil group form the family of constant signal surfaces shown within the navigational domain 12. Superposition of the constant signal surfaces generated by the long and short coils of a delta coil group produces a fishnet pattern as shown in FIG. 6. The intersection of two such constant signal surfaces generated by a short and long coil pair is a single line represented by the dotted line 70.

A constant signal surface (72 and 74) is identified for each short coil and long coil activation of a delta coil pair by determining the surface that matches the induced signals developed in the sensing coil. This procedure is repeated for the other two delta coil pairs to produce two other lines comparable to line 70. The intersection of these three lines determines the position of the catheter.

FIG. 7 shows an upper plan schematic view of the entire delta coil arrangement relative to an inner circular space representing the projection of the navigational domain into the plane of the delta coils. It is an object of the present invention to design coils having high spatial gradience in two of the axis dimensions and a substantially zero field value in the remaining axial dimension. This particular design is accomplished by modifying the termination points of the coils with compensation coils such that the modified coil is effectively operative as an infinitely long coil. The long coil sets are further compensated by a central “sucker” coil 88. Accordingly, each of the long coils and short coils is modified by representative compensation coils 80-82, 84-86, 88 and 90-94, 92-96 respectively, disposed at the indicated endpoints and center of the corresponding delta coil. The long coil and short coil configurations are shown schematically for only sets 50-52, but similar configurations likewise exist for the coil sets 54-56 and 58-60 shown representatively as the indicated lines.

The quality of the coils, as measured by the degree of uniformity of the uniform field coils or how close to zero is the field in the non-gradient direction for the delta coils, determines the size of the navigational domain over which the variable separation technique for navigating the catheter will converge and therefore be capable of initially finding the catheter, and hence be of functional utility.

FIG. 8 schematically depicts an examination deck in accordance with another embodiment of the present invention. The deck includes a first rail member 100 and a second rail member 102 in opposed spaced-apart relationship and attached to the platform along respective supporting edges. The navigational domain is illustratively depicted as the spherical volume 12. The deck includes an apertured opening 104. Each rail member has an inner wall and an outer wall. The railed configuration is characterized by the embedding of coil sets in both the planar top and in the rail members. The examination deck is preferably constructed from a magnetically permeable material.

FIGS. 9A-C schematically illustrate the unidirectional coils for implementing the railed configuration used in conjunction with the examination deck of FIG. 8. The magnet assembly for the x-directed unidirectional coil set is shown in FIG. 9A and includes two coil elements 110 and 112 each embedded in a respective rail member. Each coil pair is designed to project a substantially uniform field in the x-direction throughout the navigational domain. FIG. 9B schematically depicts the y-directed unidirected coils including coil elements 114 and 116 each embedded in respective rail members, and further including coil elements 118 and 120 embedded in the planar top of the examination deck. FIG. 9C schematically depicts the z-directed unidirected coils including coil elements 122-124 in one rail member and elements 126-128 in the other rail member. The current flow through each coil configuration is indicated by the arrows. FIG. 9D shows the delta coil arrangement used in the railed configuration. This arrangement is the same as used in the flat configuration described above.

In accordance with another embodiment of the present invention, a second sensing coil is used for stabilization purposes. Inaccurate readings of the catheter probe location may occur from motion artifacts due to breathing action, heart motion, or patient movement. The stabilized location coordinates may be determined by placing a second sensing coil on the sternum of the patient at a known location within the navigational domain. The incremental movement experienced by the second sensing coil due to motion artifacts is detected and subtracted from the measured location value of the probe to arrive at the actual location coordinates of the probe. Further extensions of the present invention are possible to facilitate multi-catheter applications by attaching an additional sensing coil to the distal end of each additional catheter.

Since certain changes may be made in the above apparatus and method without departing from the scope of the invention herein described, it is intended that all matter contained in the above description or shown in the accompanying drawings shall be interpreted in an illustrative and not in a limiting sense.

Claims

1. A method of determining the location of a magnetically-sensitive, electrically conductive sensing coil affixed to a distal end of a catheter probe partially inserted into a body cavity within a navigational domain, comprising the steps of:

inducing within said sensing coil a set of orientation signal values each representative of an orientation of said sensing coil and independent of a position of said sensing coil;

determining the orientation of said sensing coil using said induced orientation signal values;

inducing within said sensing coil a set of positional signal values each representative of the position of said sensing coil; and

determining the position of said sensing coil using said positional signal values and said determined orientation.

2. The method as recited in claim 1, wherein the step of inducing said set of orientation signal values comprises the steps of:

generating from outside said body a series of magnetic fields each penetrating at least said navigational domain and characterized substantially by a principal magnetic component in one axial dimension and relatively smaller magnetic components in two other axial dimensions.

3. The method as recited in claim 1, wherein the step of inducing said set of positional signal values comprises the steps of:

generating from outside said body a series of magnetic fields each penetrating at least said navigational domain and characterized substantially by two principal gradient magnetic components in respective axial dimensions and a relatively smaller magnetic components in a third axial dimension.

4. The method as recited in claim 3, wherein said generating step further includes the steps of:

generating said fields to provide a plurality of constant signal surfaces for the sensing coil such that an intersection between two such surfaces with components in the same axial dimensions produces a line along which said sensing coil is located;

wherein said two such surfaces are identified from among said plurality of constant signal surfaces by their ability to induce one of said positional signal values.

5. The method as recited in claim 4, further comprises the steps of:

weighting each line in accordance with a signal strength of said corresponding constant signal surface; and

determining an intersection of said weighted lines.

6. The method as recited in claim 5, wherein six constant signal surfaces are generated to produce three intersection lines.

7. A system for determining the location of a magnetically-sensitive, electrically conductive sensing coil affixed to a distal end of a catheter probe partially inserted into a body cavity within a navigational domain, comprising:

first transmit means for projecting into said navigational domain magnetic energy that is sufficient to induce signal values within said sensing coil representative of an orientation of said sensing coil and independent of the position of said sensing coil;

second transmit means for projecting into said navigational domain magnetic energy that is sufficient to induce signal values within said sensing coil representative of the position of said sensing coil; and

analysis means, coupled to said first transmit means and said second transmit means, for determining the position and orientation of said sensing coil from said induced signal values.

8. A system for determining the location of a magnetically-sensitive, electrically conductive sensing coil affixed to a distal end of a catheter probe partially inserted into a body cavity within a navigational domain, comprising:

first signal-inducing means for inducing within said sensing coil orientation signals that are representative of the orientation of said sensing coil;

analysis means, coupled to said first signal-inducing means, for determining the orientation of said sensing coil using said induced orientation signals and independent from a position of said sensing coil;

second signal-inducing means for inducing within said sensing coil position signals that are representative of the position of said sensing coil; and

analysis means, coupled to said second signal-inducing means, for determining the position of said sensing coil using said determined orientation and said induced position signals.

9. The system as recited in claim 8, wherein the first signal-inducing means comprises:

field generation means for successively generating magnetic field patterns projected into said navigational domain, each characterized substantially by a principal magnetic field component in one direction and relatively smaller magnetic components in two other directions.

10. The system as recited in claim 9, wherein said field generation means comprises a set of magnetic coils.

11. The system as recited in claim 10, wherein said magnetic coils are disposed in a planar top of an examination deck upon which a patient is disposed during a surgical procedure.

12. The system as recited in claim 10, wherein said magnetic coils are disposed in a planar top and in rail members edge supported by said planar top for an examination deck upon which a patient is disposed during a surgical procedure.

13. The system as recited in claim 8, wherein the second signal-inducing means comprises:

field generation means for successively generating magnetic field patterns each characterized by a first and second gradient field component in respective directions and a relatively smaller third component in another direction.

14. The system as recited in claim 13, wherein the field generation means comprises a magnetic coil assembly.

15. A method of determining the location of a magnetically-sensitive, electrically conductive sensing coil affixed to a distal end of a catheter probe partially inserted into a body cavity within a navigational domain, comprising the steps of:

defining the location of said sensing coil with a set of independent location parameters; and

sequentially generating within said navigational domain a sequence of magnetic fields for inducing within said sensing coil a corresponding sequence of induced signals each defined by an induced signal expression that functionally relates said induced signal to certain ones of said location parameters, such that said set of location parameters is determinable by sequentially solving individual signal expression groups each including certain ones of said induced signal expressions and sufficient to represent a subset of said location parameters.

16. The method as recited in claim 15, wherein said sequence of magnetic fields comprises:

a series of unidirectional magnetic fields each characterized substantially by a principal magnetic field component in one direction and relatively smaller magnetic components in two other directions; and

a series of gradient magnetic fields each characterized by a first and second gradient field component in respective directions and a relatively smaller third component in another direction.

17. The method as recited in claim 16, wherein said signal expression groups include:

an orientation group including induced signal expressions each functionally related to a respective one of said unidirectional magnetic fields and an orientation of said sensing coil, and independent of a position of said sensing coil; and

a position group including induced signal expressions each functionally related to a respective one of said gradient magnetic fields, the orientation of said sensing coil, and the position of said sensing coil.

18. The method as recited in claim 17, wherein the step of sequentially solving said individual signal expression groups includes the steps of:

initially solving the induced signal expressions of said orientation group; and

next solving the induced signal expressions of said position group.

19. A system for determining the location of a magnetically-sensitive, electrically conductive sensing coil affixed to a distal end of a catheter probe partially inserted into a body cavity within a navigational domain, comprising:

means for defining the location of said sensing coil with a set of independent location parameters; and

field generation means for sequentially generating within said navigational domain a sequence of magnetic fields for inducing within said sensing coil a corresponding sequence of induced signals each defined by an induced signal expression that functionally relates said induced signal to certain ones of said location parameters, such that said set of location parameters is determinable by sequentially solving individual signal expression groups each including certain ones of said induced signal expressions and sufficient to represent a subset of said location parameters.

20. The system as recited in claim 19, wherein said sequence of magnetic fields comprises:

a series of unidirectional magnetic fields each characterized substantially by a principal magnetic field component in one direction and relatively smaller magnetic components in two other directions; and

a series of gradient magnetic fields each characterized by a first and second gradient field component in respective directions and a relatively smaller third component in another direction.

21. The system as recited in claim 20, wherein said signal expression groups include:

an orientation group including induced signal expressions each functionally related to a respective one of said unidirectional magnetic fields and an orientation of said sensing coil, and independent of a position of said sensing coil; and

a position group including induced signal expressions each functionally related to a respective one of said gradient magnetic fields, the orientation of said sensing coil, and the position of said sensing coil.

22. The system as recited in claim 21, wherein said field generation means comprises:

analysis means for solving the induced signal expressions of said orientation group; and

analysis means for solving the induced signal expressions of said position group.

23. A method of determining a location of a magnetically-sensitive, electrically conductive sensing coil affixed to a distal end of a catheter probe inserted into a body cavity within a navigational domain, comprising the steps of:

inducing within said sensing coil a set of orientation signal values each representative of an orientation of said sensing coil and independent of a position of said sensing coil;

determining the orientation of said sensing coil using said induced orientation signal values;

inducing within said sensing coil a set of positional signal values each representative of the position of said sensing coil; and

determining the position of said sensing coil using said positional signal values and said determined orientation.

24. The method as recited in claim 23, wherein the step of inducing said set of orientation signal values comprises the steps of:

generating from outside said body a series of magnetic fields each penetrating at least said navigational domain and characterized substantially by a principal magnetic component in one axial dimension and relatively smaller magnetic components in two other axial dimensions;

wherein the step of inducing said set of positional signal values comprises the steps of:

generating from outside said body a series of magnetic fields each penetrating at least said navigational domain and characterized substantially by two principal gradient magnetic components in respective axial dimensions and a relatively smaller magnetic components in a third axial dimension.

25. The method of claim 23, further comprising:

generating a field within the navigational domain within the body cavity with a delta coil.

26. The method of claim 25 further comprising:

providing the delta coil as a set of delta coils including a long coil and a short coil;

modifying a termination point of the long coil with a compensation coil so that the long coil effectively operates as an infinitely long coil; and

modifying the termination point of the short coil with a compensation coil so that the short coil effectively operates as an infinitely long coil.

27. The method of claim 26, further comprising:

modifying two terminal ends of the long coil and the short coil with the compensation coils.

28. The method of claim 26, further comprising:

compensating the long coil with a central sucker coil positioned near a center of the long coil.

29. The method of claim 28, wherein providing the set of delta coils includes providing a plurality of delta coil sets positioned angularly offset from each other around a central axis.

30. The method of claim 28, wherein providing the set of delta coils includes positioning three delta coil sets offset 120 degrees from one another around a central axis.

31. The method of claim 30 further comprising:

generating a look-up table that includes a database containing magnetic field values for a selected X coordinate, Y coordinate, and Z coordinate in the navigational domain and one of the delta coil sets.

32. The method of claim 31, further comprising:

obtaining a magnetic field value for the other of the two delta coil sets by rotating field vectors of the long and short coil sets by the angle of offset from the delta coil set saved in the look-up table database.