Method for real time tracking of catheter spline

Abstract

To monitor a shape of a deflectable spline shape of a distal end assembly of a catheter.SOLUTION: A method for real-time tracking of spline shape in a distal end assembly of a catheter comprises: (a) receiving first endpoint location data and second endpoint location data based on a first position sensor assembly and a second position sensor assembly respectively mounted near a first end and a second end of a flexible spline at a distal tip of a catheter; (b) performing coarse determination of a location of an external control point of a quadratic Bezier curve for approximating a shape of the flexible spline; (c) refining the location of the control point; and (d) rendering a shape of the flexible spline based on the quadratic Bezier curve defined by the first endpoint location, the refined external control point location, and the second endpoint location.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The subject matter of this disclosure relates generally to the field of real-time monitoring of the shape of deflectable splines in a distal tip assembly of a catheter. [Background technology]

[0002] Techniques for estimating the curvature of splines in catheter tip assemblies using Bezier curves are described in US Provisional Patent Application No. 17 / 874,224.

[0003] The technique includes receiving end point position data and spline tangent data from a pair of position sensors attached to opposite ends of a distal tip of a catheter, the distal tip including a plurality of flexible splines and a plurality of electrodes disposed on each of the flexible splines, the end point position data and spline tangent data being received while the distal tip is positioned within a heart chamber; calculating Bezier curve control points based on the end point position data and spline tangent data; determining estimated positions of the plurality of electrodes based on the Bezier curve control points; and updating an electroanatomical map of the heart chamber, which is rendered on a display, based on the determined estimated positions.

[0004] A method for estimating the length of a Bézier curve is described in a paper by Raph Levien entitled "How long is that Bézier", which can be found on the World Wide Web at https: / / raphlinus.github.io / curves / 2018 / 12 / 28 / bezier-arclength.html. Summary of the Invention [Means for solving the problem]

[0005] Calculating the length of a Bezier curve over several iterations using the techniques described in U.S. Patent Application No. 17 / 874,224 can be relatively computationally intensive. Such computational burden may make it difficult and / or expensive to render and display the spline curves of a catheter tip device in real time, and may also make it difficult and / or expensive to display several, e.g., eight or ten, spline curves of a catheter tip device in real time.

[0006] Several less computationally intensive methods for calculating the shape of the quadratic Bezier curve and determining the estimated locations of the electrodes on the splines of the catheter tip device are described below.

[0007] The length of the splines in the catheter tip device is known, which is a physical attribute of the catheter tip device. The positions of the distal and proximal ends of the splines may also be known, which may be measured in a variety of ways.

[0008] In one non-limiting exemplary method, to draw a quadratic Bezier curve corresponding to the spline shape of the catheter tip device, the outer control points P of the quadratic Bezier curve are c can be estimated. Knowing these estimated locations of the quadratic Bézier curve control points that are not on the Bézier curve, as well as the measured locations of the distal and proximal ends of the spline, a quadratic Bézier curve that approximates the shape of the spline can be drawn, for example, on a display.

[0009] In this application and claims, when referring to a quadratic Bézier curve, the three control points of the quadratic Bézier curve will be referred to as the two end points of the quadratic Bézier curve and one outer control point of the quadratic Bézier curve that is not on the Bézier curve.

[0010] A non-limiting example method disclosed herein uses the known length of the spline to determine estimated locations of the external control points based on the locations of the proximal and distal ends of the spline where the length of the quadratic Bézier curve equals the known length of the spline (or achieves a predetermined degree of match with the known length of the spline).

[0011] A non-limiting example of estimating the initial positions of the external control points of the quadratic Bézier curve may include constraining the positions of the quadratic Bézier curve to a first predetermined region based on known mechanisms of the distal end assembly. For example, estimating the positions of the external control points of the quadratic Bézier curve may include determining that the initial positions should be located (i.e., constrained) somewhere on a particular line that is perpendicular to a line connecting two end positions of the quadratic Bézier curve and intersects the line at a midpoint of the line.

[0012] Another non-limiting example of estimating the initial positions of the outer control points of a quadratic Bézier curve includes determining that the initial positions should be (i.e., constrained to be) somewhere on a particular line that is perpendicular to the line connecting the two end points of the quadratic Bézier curve.

[0013] Another non-limiting example of estimating the initial positions of the outer control points of the quadratic Bézier curve may include determining that the initial positions should be somewhere on a particular (predetermined) path with respect to the two end points of the quadratic Bézier curve. The predetermined path may be determined by analyzing the mechanical attributes (e.g., shape, flexibility, structural integrity, etc.) of the catheter's distal end assembly in a calibration facility and / or the type of medical application for the catheter.

[0014] Another non-limiting example of estimating the initial positions of the outer control points of the quadratic Bézier curve includes determining that the initial positions should be somewhere within a specific region with respect to the two end point positions of the quadratic Bézier curve. The specific region (i.e., zone) may be determined based on known attributes of the distal end assembly of the catheter in a calibration facility, such as, for example, the mechanical properties of the deflectable spline (e.g., shape, flexibility, structural integrity, etc.) and / or the type of medical application of the catheter.

[0015] In some embodiments, an iterative process is used, whereby the length of a quadratic Bézier curve defined based on the initial and end positions of the external control points of the quadratic Bézier curve is determined based on an integral over the defined quadratic Bézier curve, the length of the quadratic Bézier curve is compared to the known length of the spline, and new estimated positions of the external control points of the quadratic Bézier curve are shifted until the estimated length of the quadratic Bézier curve is sufficiently close to the known length of the spline. The shift of the external control points of the quadratic Bézier curve may be constrained to a first predetermined region (i.e., the specific region described above). In some embodiments, a threshold is set to determine how much difference between the estimated length of the quadratic Bézier curve and the known length of the spline is acceptable.

[0016] For example, refinement may include accurately calculating the length of the Bézier curve based on the initial positions of the external control points, and when the exact (i.e., more accurate / precise) length of the quadratic Bézier curve is compared to the known length of the spline, a refined position of the quadratic Bézier curve can be identified.

[0017] As a non-limiting example, a more accurate method for calculating the length of a quadratic Bézier curve may optionally be a method such as that described in the aforementioned U.S. patent application Ser. No. 17 / 874,224. In this disclosure, methods used to accurately calculate the refined length of a quadratic Bézier curve may generally be referred to hereinafter as numerical methods (or numerical integration). For example, methods such as the trapezoidal rule, Simpson's rule, quadrature method, composite method, etc. may be included.

[0018] In some embodiments, an iterative process is used whereby the length of the quadratic Bézier curve is calculated based on an integral over the defined Bézier curve. The calculated length of the quadratic Bézier curve based on the integral is compared to the known length of the spline, and the positions of the external control points of the quadratic Bézier curve are shifted until the calculated length of the quadratic Bézier curve is sufficiently close to the known length of the spline. The shift of the external control points of the quadratic Bézier curve may be constrained to a second predetermined region. The first and second predetermined regions may be different shapes. In some embodiments, a threshold is set to determine how much difference between the calculated length of the quadratic Bézier curve and the known length of the spline is acceptable.

[0019] In some embodiments, the shapes of multiple splines may be calculated using the above method, and the more splines for which such shapes are calculated using the simplified method for an initial guess, the greater the savings in computational load. [Brief explanation of the drawings]

[0020] In order to better understand the subject matter disclosed herein and to illustrate how it may be carried out in practice, embodiments will now be described, by way of non-limiting example only, with reference to the accompanying drawings, in which: [Figure 1] 1 illustrates an example system in which one or more features of the presently disclosed subject matter may be implemented, according to one or more embodiments. [Figure 2] 1 illustrates a catheter tip assembly, according to one embodiment. [Figure 3] FIG. 1 illustrates a simplified method for estimating the length of a quadratic Bezier curve based on the length of a chord connecting a first end point location and a second end point location, and the length of a control line formed by the first end point location, the location of an outer control point, and the second end point location, in accordance with some embodiments. [Figure 4A] FIG. 1 is a simplified diagram of the external control points of a quadratic Bezier curve located on a line, according to one embodiment; [Figure 4B]1 is a simplified diagram of the external control points of a quadratic Bezier curve located on a particular straight line path, according to one embodiment. [Figure 5A] 1 is a simplified flowchart illustrating a method for real-time tracking of a spline profile in a distal tip assembly of a catheter, according to one embodiment. [Figure 5B] 1 is a simplified flowchart illustrating a method for real-time tracking of a spline profile in a distal tip assembly of a catheter, according to one embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0021] The subject matter of this disclosure relates generally to the field of calculating the shape of quadratic Bezier curves, more particularly to a rapid method for locating external control points for calculating the shape of quadratic Bezier curves that represent the shape of splines within catheter tip assemblies, and even more particularly, but not exclusively, to visualization of catheter tip assemblies using rapid calculation of Bezier curve shapes.

[0022] Referring to FIG. 1, an exemplary system in which one or more features of the presently disclosed subject matter may be implemented is shown, according to one or more embodiments.

[0023] 1 is a diagram of an exemplary system (e.g., a medical device apparatus) that may implement one or more features of the subject matter herein, according to one or more embodiments, shown as system 100. All or a portion of system 100 may be used to detect, diagnose, and / or treat cardiac disease.

[0024] The system 100 includes a catheter 110 including a manipulator 114, a shaft 112 disposed through a sheath 113, and a distal tip in the shape of a basket (referred to herein as a "catheter basket" 116), as shown. The catheter basket 116 includes a plurality of electrodes 111 disposed on a plurality of bendable splines 109. A puller element 118 pulls or pushes the distal end 304 of the catheter basket 116 to expand or collapse the catheter basket 116. In some embodiments, the catheter basket 116 includes one or more position sensors that enable sensing the positions of the proximal and distal ends of the catheter basket 116.

[0025] Also shown in FIG. 1 are a physician 115 (or medical professional, technician, clinician, etc.), a heart 120, a patient 125, and a bed 130 (or table). Note that insets 140 and 150 show the heart 120 and catheter 110 in more detail. System 100 also includes a console 160 (including one or more processors 222 and memory 162 that provide control and processing capabilities) and a display 165, as shown. Note further that each element and / or item of system 100 represents one or more of that element and / or item. The example system 100 shown in FIG. 1 can be modified to implement embodiments disclosed herein. The embodiments of the present disclosure may be similarly applied using other system components and configurations. Furthermore, system 100 may include additional components, such as elements for sensing electrical activity, wired or wireless connectors, processing devices, and display devices.

[0026] Treatment of cardiac disorders, such as cardiac arrhythmias, often requires obtaining detailed mapping of cardiac tissue, chambers, veins, arteries, and / or electrical pathways. For example, a prerequisite for successfully performing catheter ablation (as described herein) is that the source of the cardiac arrhythmia be accurately localized in a chamber of heart 120. Such localization may be performed by an electrophysiological study, during which electrical potentials are detected and spatially resolved by a mapping catheter (e.g., catheter 110) introduced into a chamber of heart 120. This electrophysiological study, also known as electroanatomical mapping, therefore provides 3D mapping data that may be displayed on a monitor. Often, mapping and therapy functions (e.g., ablation) are provided by a single catheter or a group of catheters, with the mapping catheter also simultaneously acting as a therapy (e.g., ablation) catheter. Mapping software 101 interfaces with catheter 110 to perform mapping operations, as described in further detail herein.

[0027] Catheter 110 includes a plurality of flexible splines 109 and a plurality of electrodes 111 disposed on each of flexible splines 109. Catheter 110 is configured to acquire biometric data, such as electrical signals, of an internal organ (e.g., heart 120) and / or ablate tissue in that region (e.g., a chamber of heart 120).

[0028] In some embodiments, the catheter 110 is a basket catheter. The basket catheter can be designed to hold its electrodes in intimate contact with the endocardial surface when deployed within a patient's body. As an example, the basket catheter can be inserted into a lumen such as a pulmonary vein ("PV"). The basket catheter can be inserted into the PV with its proximal end at a maximum distance from its distal end, so that the basket catheter does not occupy its maximum volume while inserted into the PV. The basket catheter can be expanded while inside the PV by moving its proximal end toward its distal end, so that the electrodes on the basket catheter contact the entire circular portion of the PV. Such contact with the entire circular portion of the PV or any other lumen can enable efficient imaging and / or ablation.

[0029] Catheter 110 and other items of system 100 may be connected to console 160. Console 160 may include any computing device that uses mapping software 101. According to an exemplary embodiment, console 160 includes one or more processors 222 (any computing hardware) and memory 162 (any non-transitory tangible medium), where one or more processors 222 execute computer instructions for mapping software 101 and memory 162 stores these instructions for execution by one or more processors 222. For example, console 160 may be configured to receive and / or store biometric data on a database in memory 162, process the biometric data, and determine whether a given tissue region conducts electricity.

[0030] A display 165, which may be any electronic device for visually presenting biometric data, is connected to the console 160. According to an exemplary embodiment, during a procedure, the console 160 may facilitate the presentation of a rendering of the body part to the physician 115 on the display 165 and store data representing the rendering of the body part in the memory 162. For example, a map indicative of motion characteristics may be rendered / constructed based on trajectory information sampled at a sufficient number of points within the heart 120.

[0031] Among other things, the mapping software 101 maps the positions of the electrodes 111 of the catheter 110. The catheter 110 has position tracking elements at the proximal and distal ends of the catheter basket 116, but the electrodes 111 themselves may not have associated position sensors. The electrodes 111 may be disposed on a flexible spline 109 that bends based on both the relative positions of the proximal and distal ends of the catheter basket 116 and the deflection of the entire catheter 110 relative to the shaft 112. Thus, the mapping software 101 performs operations that determine the shape and position of the spline 109 based on the detected positions and orientations of the proximal and distal ends of the catheter basket 116 and the deflection angle of the catheter basket 116.

[0032] In some embodiments, the mapping software 101 generates Bezier curves that represent the shape, position, and / or deflection of the spline 109 and obtains the position of the electrode 111 based on the shape, position, and / or deflection.

[0033] Reference is now made to Figure 2, which illustrates a catheter tip assembly according to one embodiment.

[0034] 2 shows a catheter tip assembly in the form of a basket 116, which includes a shaft 112 coupled to a proximal end 302 of the catheter basket 116 and a distal end 304 of the catheter basket 116. Splines 109 are coupled to the proximal and distal ends 302, 304 of the catheter basket 116. Electrodes 111 are disposed on the splines 109. The proximal and distal ends 302, 304 are movable relative to one another. A puller element 118 coupled to the distal end 304 of the catheter basket 116 can be pulled toward the proximal end 302 of the catheter basket, moving the distal end 304 closer to the proximal end 302, or pushed away from the proximal end 302, moving the distal end 304 farther from the proximal end 302.

[0035] Moving the distal end 304 relative to the proximal end 302 deforms the splines 109. Note that the catheter basket 116 can be deflected at an angle relative to the shaft 112 at the proximal end 302. In other words, the basket assembly can bend at the proximal end 302 relative to the "angle of incidence" of the shaft 112.

[0036] For example, when a portion of the catheter basket 116, such as one or more of the splines 109, contacts an anatomical structure, the catheter basket 116 is deflected at an angle relative to the shaft 112 at the proximal end 302. Thus, the shape of the splines 109, and therefore the position of the electrodes 111, depends on the relative positions of the proximal and distal ends 302, 304, and the angle of deflection of the catheter 110 relative to the shaft 112 at the proximal end 302.

[0037] The proximal end 302 and distal end 304 each include one or more position sensors (proximal end position sensor 307 and distal end position sensor 305), which allows the mapping software 101 (e.g., in conjunction with the position system 223) to directly determine their three-dimensional ("3D") positions. However, some or all of the splines 109 may not have position sensors, and further, the shape may vary. Thus, the mapping software 101 estimates the position and shape of the splines 109 in order to calculate the shape of the splines and, optionally, use that information to display the splines 109.

[0038] In some embodiments, three single-axis sensors may be located at the distal end 304 .

[0039] In some embodiments, not all splines have sensors.

[0040] In some embodiments, the distal end of the end assembly may be rigid and define a plane based on which the endpoints of each spline can be determined.

[0041] Introduction One approach to calculating curve arc lengths, including quadratic Bézier curve lengths, is to sample the curve at a series of points and then sum the lengths of all segments between consecutive points. Such a method is equivalent to flattening the curve into lines and summing the lengths of all the lines. While this method is simple and robust, it can be relatively slow or computationally expensive when high accuracy is desired. For every doubling of the number of samples, accuracy quadruples. In other words, the number of samples

[0042]

number

[0043] A rapid method for estimating the length of a quadratic Bezier curve may optionally allow for rapid determination of the shape of a spline within the catheter tip assembly and, based thereon, rapid determination of the estimated location of an electrode on the spline based on knowing the location of the electrode along the spline. Such a method may also allow for updating the shape of the spline and real-time visualization of the device at the distal end of the catheter. Such a method may optionally allow for updating the electroanatomical map of the catheter tip assembly and heart chambers rendered on a display.

[0044] As a non-limiting example, a simple and fast method for estimating the initial positions of the external control points of a quadratic Bézier curve may involve using an analytical formula to estimate the length of the quadratic Bézier curve based on the length of a chord connecting a first end point location and a second end point location and the length of a control line formed by the first end point location, the positions of the external control points, and the second end point location. The initial positions of the external control points may be determined as the position (or one of the positions) where the estimated length of the quadratic Bézier curve equals the known spline length. Determining the initial positions of the control points may also involve constraining the positions of the control points to a particular path.

[0045] The term "control polyline" may be used herein and in the claims to refer to a line formed by connecting a first line connecting a first Bézier curve endpoint to an external control point and a second line connecting the external control point to a second Bézier curve endpoint. A control polyline may also be called a Bézier polygon or a control polygon. However, to avoid confusing the connected line with a closed polygon, the term "polyline" is used herein.

[0046] The quadratic Bézier curve length estimate proposed in Raph Levien's paper can approximate the actual length of a quadratic Bézier curve to within ±2% error.

[0047] In some embodiments, estimating the initial positions of the external control points of the quadratic Bézier curve may provide the external control points of the quadratic Bézier curve, which may serve as a starting point for more accurately identifying the external control points whose corresponding quadratic Bézier curves match the known length of the catheter spline. Accurately identifying the external control points (i.e., refining the positions of the control points) may include calculating the length of the quadratic Bézier curve relative to the initial positions, comparing the calculated length to the actual length of the spline, and determining whether the lengths are close enough to use the shape of the quadratic Bézier curve to render the shape of the spline, or whether the positions of the control points require adjustment. In some embodiments, refining the positions involves shifting or adjusting the positions of the external control points to minimize the difference between the calculated length of the quadratic Bézier curve and the actual length of the catheter spline to below a certain threshold.

[0048] In some examples, estimating the initial positions of the outer control points of the quadratic Bézier curve may provide outer control points of the quadratic Bézier curve that can serve as starting points for iteratively determining more precise positions of the outer control points by comparing the calculated lengths with the actual lengths of the spline and determining whether the lengths are close enough to use the shape of the quadratic Bézier curve to render the shape of the spline. If not, the estimated positions of the outer control points are shifted and the calculations are repeated.

[0049] In some examples, estimating the location of the initial position of the quadratic Bézier curve may provide initial positions of control points for the quadratic Bézier curve that may already be useful for rendering the shape of a spline based on the quadratic Bézier curve.

[0050] Reference is now made to FIG. 3, which is a diagram of a simplified method, according to some embodiments, for estimating the length of a quadratic Bézier curve based on the length of a chord connecting a first end point location and a second end point location, and the length of a control line formed by the first end point location, the location of an outer control point, and the second end point location.

[0051] FIG. 3 shows a quadratic Bezier curve 405 extending from a first endpoint P1 401 to a second endpoint P2 402, and a quadratic Bezier curve control point Pc 403.

[0052] The quadratic Bezier curve 405 is the path traced by the function B(t) given point P1 401, quadratic Bezier curve control points Pc 403, and P2 402. B(t)=P c +(1-t) 2 (P1-P c )+t 2 (P2-P c ), where 0≦t≦1 Equation 1

[0053] By taking the end points P1 401 and P2 402 as the known locations of the end points of the spline of the catheter tip assembly and selecting the initial external control points of the quadratic Bezier curve Pc 403 for curve 405, the length of the quadratic Bezier curve 405 can be estimated.

[0054] L p is the control line of a quadratic Bezier curve (L 1c +L 2c ) and the length L of the quadratic Bezier curve 405 s Overestimate.

[0055] The line or chord L between P1401 and P2402 c The length of 410 underestimates the length of curve 405 .

[0056] In some embodiments, the length L of the curve 405 s The estimated value of L est The analytical expression for can be given by: L est =(2L c +L p ) / 3=1.002L s formula 2

[0057] Calculated estimated length L est is the actual length L of the quadratic Bézier curve 405 sNote that this is within about 0.2 percent of

[0058] When the shape of the quadratic Bezier curve 405 is taken to represent the shape of the catheter end assembly spline 109, the calculated estimated length L est Note that can be considered to be within about 0.2 percent of the actual length of the catheter end assembly spline 109.

[0059] Here, the length L est to calculate the external control points P rather than knowing the length of the spline c A method for estimating the location of 403 using an exemplary calculation such as the exemplary calculation of Equation 2 will now be described.

[0060] End point location In some embodiments, the locations of the end points P1401 and P2402 are selected based on the known location of the end of the catheter tip assembly and the geometric relationship between the known location of the end of the catheter tip assembly and the end points of the spline 109.

[0061] In some embodiments, the locations of endpoints P1 401 and / or P2 402 are selected based on the known locations of the ends of the splines, for example, obtained by imaging the catheter tip assembly within the patient's body.

[0062] In some embodiments, the location of the end points P1 401 and / or P2 402 is determined based on position sensors located at each end of the spline 109.

[0063] Example of rough determination of external control point positions by direct calculation A non-limiting example of estimating the initial positions of the outer control points of a quadratic Bézier curve includes determining that the initial positions should be somewhere on a particular line that is perpendicular to a line connecting the two end positions (i.e., chords) of the quadratic Bézier curve and intersects the line at its midpoint.

[0064] Other non-limiting examples of estimating the initial positions of the outer control points of a quadratic Bézier curve may include determining that the initial positions should be somewhere on a particular path, possibly a straight path, or region relative to the two end points of the quadratic Bézier curve.

[0065] Another non-limiting example of estimating the initial positions of the external control points of a quadratic Bezier curve is described with reference again to FIG. c The initial position of the external control point 403 may be determined based on data indicating the orientation of the catheter spline near the first and second endpoints. Sensors located at or near the ends of the spline may allow the orientation of the catheter spline near the first and second endpoints to be estimated. Thus, determining the initial position is achieved when the positions of two points P1 401 and P2 402 are known and therefore the position of the line L is known. c 410 is defined as P1401, P2402, and P c The triangle defined by P1 403 can be derived from the polygon, e.g., the line L in P1 401. 1c and the line L in P2402 2c The angle may be determined based on data collected by the sensor.

[0066] line L c If the angles at P410 and P1401 and P2402 are all known, the triangle is fully defined and the outer control point P c The position of 403 can be calculated.

[0067] Reference is now made to FIG. 4A, which is a simplified illustration of the external control points of a quadratic Bezier curve lying on a line, according to one embodiment.

[0068] FIG. 4A illustrates a quadratic Bezier curve 405 extending from a first endpoint P1 401 to a second endpoint P2 402 and an outer control point P c 403A and indicates.

[0069] FIG. 4A also shows a line L connecting a first end point P1 401 to a second end point P2 402.c 410 (see angle 422A) and at the midpoint between the two end points P1 401 and P2 402, the line L c A line 420A intersecting with 410 is shown.

[0070] In some embodiments, the external control point P c The position of 403A is constrained to be on a particular path, such as line 420A. c A coarse determination of the location of 403 can be calculated analytically as follows: L 1c 411A and L 2c Since the lengths of 412A are equal, the estimated length L est spline L s By setting the lengths of the , and , to be equal to the lengths of the , and , Equation 2 allows us to calculate their lengths as follows: L s =(2L c +L p ) / 3=(2L c +L 1c +L 2c ) / 3=(2L c +2L 1c ) / 3 formula 3

[0071] Since the positions of P1401 and P2402 are known, the line L c 410 is defined. Line L 1c 411 and L 2c The (equal) length of 412 is calculated by Equation 3, and therefore the outer control point P c The position of 403 can be calculated.

[0072] X424A is P c 403A and line L c X represents the distance between the midpoint of line L and the midpoint of line L. c 410, as measured from the midpoint between known positions P1 401 and P2 402 in a vertical direction. c 403. Equation 4 below defines an exemplary location of the outer control point P c This allows for direct estimation of the location of the 403.

[0073]

number

[0074] Reference is now made to FIG. 4B, which is a simplified illustration of the external control points of a quadratic Bezier curve located on a particular straight line path, according to one embodiment.

[0075] FIG. 4B illustrates a quadratic Bezier curve 405 extending from a first endpoint P1 401 to a second endpoint P2 402 and an outer control point P c 403B and indicates.

[0076] FIG. 4B also shows a line L connecting a first endpoint P1 401 to a second endpoint P2 402. c 410 (see angle 422B) and some known point P between the two end points P1 401 and P2 402 Y At 414, line L c The line 420B intersecting with 410 is shown.

[0077] In some embodiments, the external control point P c The location of 403B is chosen to be on line 420B. c The location of 403 is P1401, P Y 414, and P c The first triangle defined by P2 402, P Y 414, and the second triangle defined by Pc403B, it can also be calculated as follows:

[0078] P1401 and P Y The distance between P2402 and P414 is known and defined here as Y426B. Y The distance between 414 is also known and is equal to (Lc-Y).

[0079] P Y The distance of Pc403B from 414 is defined as X424B.

[0080] L s , Lc Since (the distance between P1 401 and P2 402) and Y 426B are known and angle 422B is a right angle, X 424B can be calculated.

[0081] Determining the location of external control points by calibration In some embodiments, the catheter tip assembly may be measured in a calibration laboratory, and the shape of the spline may be measured under various conditions and various distortions of the catheter tip assembly. Under these conditions, the positions of the external control points Pc for drawing the correct shape of the spline may be determined and recorded. Based on the recorded data, the positions of the spline end points and the direction of a directional sensor, such as a single-axis sensor, may be used to determine the positions of the external control points Pc. c A suitable location for the .times. ...

[0082] Example of external control point location In some embodiments, the outer control point Pc 403 is a line L connecting the end points of the quadratic Bézier curve 405 at a 90 degree angle. c It may be selected (i.e., constrained) to be on a particular straight line path (see line 420B in FIG. 4B) passing through 410. See, for example, the description of FIGS. 4A and 4B.

[0083] In some embodiments, the outer control point Pc 403 is a first line L connecting the end points of the quadratic Bézier curve 405. c 410 and may be selected (i.e., constrained) to lie on a particular straight line path (see line 420A in FIG. 4A) that is perpendicular to and passes through its midpoint. See, e.g., the description of FIG. 4A.

[0084] In some embodiments, the external control point Pc 403 may be selected (i.e., constrained) to lie along a particular straight line path at a certain angle relative to the line 410 between P1401 and P2402 that intersects the line 410 at a location between P1401 and P2402.

[0085] In some embodiments, the location of the external control point Pc403 relative to the end points P1401 and P2402 may be constrained within a particular path or region depending on the known geometric and / or mechanical properties of the catheter spline and / or its medical application.

[0086] In some embodiments, determining the position of the external control point Pc403 relative to the end points P1401 and P2402 may involve measuring and / or analyzing the shape of the spline as part of a catheter tip assembly that is measured / analyzed outside the patient's body.

[0087] Optionally, a second method for calculating the length is used to improve accuracy. In some embodiments, after candidate control point locations have been identified in the coarse determination stage (e.g., after one or more iterations using the estimation formula to bring the level of accuracy below a desired first threshold), more accurate and more computationally intensive methods are optionally used to further refine the accuracy.

[0088] In some embodiments, the length of the quadratic Bézier curve may optionally be calculated by a numerical method along the Bézier curve from one end point of the Bézier curve to the other end of the Bézier curve. If the quadratic Bézier curve length calculated by the numerical method is not close enough to the actual spline length, the control points may be shifted (optionally within a second specific path / region) and the quadratic Bézier curve length may be calculated again and compared to the actual spline length until it is close enough.

[0089] In some embodiments, the length of the quadratic Bezier curve may optionally be calculated by methods such as those described in, by way of non-limiting example, U.S. Provisional Patent Application No. 17 / 874,224. If the quadratic Bezier curve length calculated by the numerical method is not close enough to the actual spline length, the control points may be shifted (optionally within a second specific path / region) and the quadratic Bezier curve length may be recalculated and compared to the actual spline length until it is close enough.

[0090] Reference is now made to FIG. 5A, which is a simplified flowchart illustrating a method for real-time tracking of a spline profile of a catheter distal end assembly, according to one embodiment.

[0091] In a first step 502, the method includes receiving first endpoint position data P1 based on a first position sensor assembly mounted near a first end of a flexible spline at the distal tip of the catheter, and receiving second endpoint position data P2 based on a second position sensor assembly mounted near a second end of the flexible spline.

[0092] In a second step 504, the method includes forming a flexible spline L s In a third step 506, the method includes defining a normal to a line (i.e., a chord) connecting the spline end positions P1 and P2. In a fourth step 508, the method includes receiving a known length of the external control point P c The method includes calculating an estimated (coarse) position of the quadratic Bézier curve. The coarse determination may be based on a relationship between the known length of the flexible spline and the estimated length of the quadratic Bézier curve. The estimated length of the quadratic Bézier curve may be calculated based on the length of a chord connecting the first and second end points and the length of a control line formed by the first end point, the positions of the control points, and the second end point. The coarse position of the control point may be a position normal to the chord (i.e., the first predetermined path / region) where the estimated length of the quadratic Bézier curve is equal to (or sufficiently close to) the known length of the spline.

[0093] In a fifth step 510, the method uses more accurate methods, such as numerical integration, to find the control points P c Quadratic Bezier curve L for the coarse position of B This involves calculating the length of

[0094] In a sixth step 512, the method includes: B This involves comparing Ls with Ls.

[0095] In the seventh step 514, when the absolute value |L s -L B |<T, where T is a threshold value, the quadratic Bézier curve L c defined by the end point positions P1 and P2 and the external control point P B is close enough to the desired spline shape, and the method includes rendering the spline shape as a Bézier curve based on P1, P2, and P c (514).

[0096] In the eighth step 516, when the absolute value |L s -L B |>T, the method includes comparing the real values of L s and L B .

[0097] In the ninth step 518, when L s >L B (516), the quadratic Bézier curve L c defined by the end point positions P1 and P2 and the external control point P B is not yet close enough to the desired spline shape, and the method shifts the control point P c along the normal away from the straight line connecting the spline ends (518), and returns to calculating the length of the quadratic Bézier curve L<{ B according to the fifth step (510).

[0098] In the tenth step, when L s <L B , the method includes shifting the control point P c along the normal towards the straight line connecting the spline ends (520), and returning to calculating the length of the quadratic Bézier curve L B according to the fifth step (510).

[0099] In some cases, the end point position data P1 and P2 may be determined based on magnetic position sensing.

[0100] In some cases, the endpoint position data P1 and P2 may be determined based on imaging the catheter tip assembly.

[0101] In some cases, flexible spline L s The length of may optionally be stored in and / or retrieved from memory.

[0102] Optionally, the method of FIG. 5A may further include, in step 508, determining an external control point P c 4 to calculate the estimated position of L s is the known length of the flexible spline, and L c is the calculated distance between the first end point location data P1 and the second end point location data P2.

[0103] In some embodiments, the normal may intersect the line between the two endpoints at the midpoint between the two endpoints.

[0104] In some embodiments, the normal line may optionally intersect the line between the two endpoints at other locations based on known mechanics of the catheter tip assembly.

[0105] In some embodiments, the location where the normal intersects the line between the two end points may be predefined and / or stored in memory.

[0106] Reference is now made to FIG. 5B, which is a simplified flowchart illustrating a method for real-time tracking of a spline profile of a catheter distal end assembly, according to one embodiment.

[0107] In a first step 532, the method includes receiving first and second endpoint position data based on a first and second position sensor assembly mounted near a first end and a second end, respectively, of a flexible spline at the distal tip of the catheter.

[0108] In a second step 534, the method includes performing a coarse determination of the positions of the external control points of a quadratic Bézier curve to approximate the shape of the flexible spline, the quadratic Bézier curve being defined by a first point and a second point corresponding to a first end point position and a second end point position, and by the external control points, the coarse determination being based on a relationship between the known length of the flexible spline and an estimated length of the quadratic Bézier curve.

[0109] In a third step 536, the method includes refining the positions of the control points by: (i) calculating a refined length of the quadratic Bézier curve associated with the positions of the external control points determined in the second step (534) by numerical integration of said quadratic Bézier curve; (ii) Adjusting the positions of the external control points to minimize the difference between the known catheter spline length and the refined length of the Bezier curve.

[0110] In a fourth step 538, the method includes rendering the shape of the flexible spline based on a quadratic Bezier curve defined by the first endpoint location, the refined control point locations determined in step 536, and the second endpoint location.

[0111] In some embodiments, the estimated length of the quadratic Bézier curve in the coarse determination is calculated based on the length of the chord connecting the first end point position and the second end point position, and the length of the control line formed by the first end point position, the position of the control point, and the second end point position. [Example]

[0112] The following is a non-exhaustive list of some exemplary embodiments of the present disclosure. The present disclosure also includes embodiments that include fewer than all of the features of an embodiment, and embodiments that use features from multiple embodiments, even if not listed below.

[0113] Example 1: 1. A method for real-time tracking of a spline profile in a distal tip assembly of a catheter, comprising: a) receiving (532) first and second endpoint position data based on a first and second position sensor assembly mounted near a first end and a second end of a flexible spline at a distal tip of the catheter, respectively; b) performing a coarse determination (534) of positions of external control points of a quadratic Bézier curve to approximate the shape of the Flexibility Spline, the quadratic Bézier curve being defined by a first point and a second point corresponding to the first end position and the second end position, and by the external control points, the coarse determination being based on a relationship between a known length of the Flexibility Spline and an estimated length of the quadratic Bézier curve, the estimated length of the quadratic Bézier curve in the coarse determination being calculated based on the length of a chord connecting the first end position and the second end position, and the length of a control line formed by the first end position, the position of the control point, and the second end position; c) the position of the control point, (i) calculating, by numerical integration of the quadratic Bezier curve, a refined length of the quadratic Bezier curve associated with the positions of the external control points determined by the coarse determination; (ii) refining (536) by adjusting the positions of the external control points to minimize the difference between the known catheter spline length and the refined length of the Bezier curve; d) rendering (538) a shape of the flexible spline based on the quadratic Bezier curve defined by the first endpoint locations, the refined external control point locations, and the second endpoint locations.

[0114] Example 2: 2. The method of example 1, wherein the positions of the external control points are constrained to a predetermined path, and the coarse determination includes determining the positions of the external control points on the predetermined path such that the estimated length of the quadratic Bézier curve is equal to the known length of the flexible spline.

[0115] Example 3: The coarse determination of the position of the external control point is performed by the formula L s =(2L c +L p ) / 3, where L s is the known length of the spline, and L c is the length of the chord connecting the first end point position and the second end point position, and L p 3. The method of any one of Examples 1 or 2, wherein x is a length of a control line of the Bézier curve formed by the first end point position, the position of the outer control point, and the second end point position.

[0116] Example 4: 4. The method of any of Examples 2 or 3, wherein the predetermined path is a straight path intermediate and perpendicular to the chord connecting the first endpoint location and the second endpoint location.

[0117] Example 5: Making a rough decision is (i) iteratively selecting candidate locations for the control points; (ii) for each candidate location, calculating an estimated length of the quadratic Bezier curve, the estimated length being based on a length of a control line formed by the first endpoint location, the location of the control point, and the second endpoint location, and a length of a chord connecting the first endpoint location and the second endpoint location; (iii) comparing the estimated length of the quadratic Bezier curve to the known length of the catheter spline; (iv) identifying candidate locations for the control points where the difference between the known catheter spline length and the estimated length of the Bezier curve is less than a first threshold.

[0118] Example 6: The estimated length of the quadratic Bezier curve is given by the formula L est =(2L c +L p ) / 3, where L est is the estimated length of the quadratic Bézier curve, and L c is the length of the chord connecting the first end point position and the second end point position, and L p is a length of a control broken line formed by the first endpoint position, the control point position, and the second endpoint position.

[0119] Example 7: 7. The method according to any one of embodiments 1 to 6, wherein in the coarse determination, the candidate locations are constrained to a first predetermined region.

[0120] Example 8: 8. The method of any of examples 1 to 7, wherein in said refining the positions of said external control points, said positions of said external control points are constrained to a second predetermined region.

[0121] Example 9: 1. A system including a console, the console comprising: a) receiving first and second endpoint position data based on a first and second position sensor assembly mounted near a first end and a second end of a flexible spline at a distal tip of the catheter; b) performing a coarse determination of positions of external control points of a quadratic Bézier curve to approximate a shape of the Flexibility Spline, the quadratic Bézier curve being defined by a first point and a second point corresponding to the first and second endpoint locations and by the external control points, the coarse determination being based on a relationship between a known length of the Flexibility Spline and an estimated length of the quadratic Bézier curve, the estimated length of the quadratic Bézier curve in the coarse determination being calculated based on the length of a chord connecting the first endpoint location and the second endpoint location and the length of a control line formed by the first endpoint location, the positions of the control points, and the second endpoint location; c) determining the position of the external control point by (i) calculating a refined length of the quadratic Bézier curve associated with the positions of the external control points determined in step b) by numerical integration of the quadratic Bézier curve; (ii) refining by adjusting the positions of the external control points to minimize the difference between the known catheter spline length and the refined length of the Bezier curve; d) rendering a shape of the flexible spline based on the quadratic Bezier curve defined by the first endpoint locations, the refined external control point locations determined in step c), and the second endpoint locations.

[0122] Example 10. A non-transitory computer-readable medium storing instructions that, when executed by a processor, cause the processor to: a) receiving first and second endpoint position data based on a first and second position sensor assembly mounted near a first end and a second end of a flexible spline at a distal tip of the catheter; b) performing a coarse determination of locations of external control points of a quadratic Bézier curve to approximate a shape of the Flexibility Spline, the quadratic Bézier curve being defined by a first point and a second point corresponding to the first end location and the second end location, and by the external control points, the coarse determination being based on a relationship between a known length of the Flexibility Spline and an estimated length of the quadratic Bézier curve; c) determining the position of the external control point by (i) calculating a refined length of the quadratic Bézier curve associated with the positions of the external control points determined in step b) by numerical integration of the quadratic Bézier curve; (ii) refining by adjusting the positions of the external control points to minimize the difference between the known catheter spline length and the refined length of the Bezier curve; d) rendering a shape of the flexible spline based on the quadratic Bezier curve defined by the first endpoint locations, the refined external control point locations determined in step c), and the second endpoint locations.

[0123] Unless otherwise indicated, as will be apparent from this disclosure, it is understood that throughout this specification, discussions utilizing terms such as "processing," "computing," "comparing," "determining," "estimating," and the like refer to computer operations and / or processes that manipulate and / or transform data into other data, where such data may be represented as physical quantities, such as electronic quantities, and / or where such data represent physical objects. The term "computer" should be interpreted expansively to encompass any type of hardware-based electronic device having data processing capabilities.

[0124] The various illustrative logical blocks, modules, and algorithmic steps described in connection with the embodiments disclosed herein may be implemented as electronic hardware, computer software, or a combination of both. To clearly illustrate this interchangeability of hardware and software, various illustrative components, blocks, modules, and steps have been described above generally in terms of their functionality. Whether such functionality is implemented as hardware or software depends on the particular application and design constraints imposed on the overall system. The described functionality may be implemented in various ways for each particular application, and such implementation decisions should not be interpreted as causing any departure from the scope of the present disclosure.

[0125] It will also be understood that a system according to the present disclosure may be implemented, at least in part, on a suitably programmed computer. Similarly, the present disclosure contemplates a computer program readable by a computer for performing the methods of the present disclosure. The present disclosure further contemplates a non-transitory computer-readable memory tangibly embodying a program of instructions executable by a computer for performing the methods of the present disclosure.

[0126] [Embodiment] (1) A method for real-time tracking of a spline profile in a catheter distal tip assembly, comprising: a) receiving first and second endpoint position data based on a first and second position sensor assembly mounted near a first end and a second end of a flexible spline at a distal tip of the catheter; b) performing a coarse determination of positions of external control points of a quadratic Bézier curve to approximate a shape of the Flexibility Spline, the quadratic Bézier curve being defined by a first point and a second point corresponding to the first end position and the second end position, and by the external control points, the coarse determination being based on a relationship between a known length of the Flexibility Spline and an estimated length of the quadratic Bézier curve, the estimated length of the quadratic Bézier curve being calculated based on the length of a chord connecting the first end position and the second end position, and the length of a control line formed by the first end position, the positions of the control points, and the second end position; c) determining the positions of the control points by (i) calculating, by numerical integration of the quadratic Bezier curve, a refined length of the quadratic Bezier curve associated with the positions of the external control points determined by the coarse determination; (ii) refining by adjusting the positions of the external control points to minimize the difference between the known catheter spline length and the refined length of the Bezier curve; d) rendering the shape of the flexible spline based on the quadratic Bezier curve defined by the first endpoint location, the refined external control point location, and the second endpoint location. (2) The method of embodiment 1, wherein the positions of the external control points are constrained to a predetermined path, and the coarse determination includes determining the positions of the external control points on the predetermined path such that the estimated length of the quadratic Bezier curve is equal to the known length of the flexible spline. (3) The coarse determination of the location of the external control point is performed using the formula L s =(2L c +L p ) / 3, where L s is the known length of the spline, and L c is the length of the chord connecting the first end point location and the second end point location, and L pis the length of the control line of the Bezier curve formed by the first end point location, the location of the outer control point, and the second end point location. (4) The method of claim 2, wherein the predetermined path is a straight path intermediate and perpendicular to the string connecting the first end position and the second end position. (5) The method of embodiment 1, wherein in the coarse determination, the positions of the external control points are constrained to a first predetermined region.

[0127] (6) The method of claim 1, wherein in refining the positions of the external control points, the positions of the external control points are constrained to a second predetermined region. (7) A system including a console, the console comprising: a) receiving first and second endpoint position data based on a first and second position sensor assembly mounted near a first end and a second end of a flexible spline at a distal tip of the catheter; b) performing a coarse determination of positions of external control points of a quadratic Bézier curve to approximate a shape of the Flexibility Spline, the quadratic Bézier curve being defined by a first point and a second point corresponding to the first end position and the second end position, and by the external control points, the coarse determination being based on a relationship between a known length of the Flexibility Spline and an estimated length of the quadratic Bézier curve, the estimated length of the quadratic Bézier curve being calculated based on the length of a chord connecting the first end position and the second end position, and the length of a control line formed by the first end position, the positions of the control points, and the second end position; c) determining the positions of the external control points by (i) calculating a refined length of the quadratic Bézier curve associated with the positions of the external control points determined in step b) by numerical integration of the quadratic Bézier curve; (ii) refining by adjusting the positions of the external control points to minimize the difference between the known catheter spline length and the refined length of the Bezier curve; d) rendering the shape of the flexible spline based on the quadratic Bezier curve defined by the first endpoint location, the refined external control point locations determined in step c), and the second endpoint location. (8) A non-transitory computer-readable medium storing instructions that, when executed by a processor, cause the processor to: a) receiving first and second endpoint position data based on a first and second position sensor assembly mounted near a first end and a second end of a flexible spline at a distal tip of the catheter; b) performing a coarse determination of positions of external control points of a quadratic Bézier curve to approximate a shape of the Flexibility Spline, the quadratic Bézier curve being defined by a first point and a second point corresponding to the first end point location and the second end point location, and by the external control points, the coarse determination being based on a relationship between a known length of the Flexibility Spline and an estimated length of the quadratic Bézier curve; c) determining the positions of the external control points by (i) calculating a refined length of the quadratic Bézier curve associated with the positions of the external control points determined in step b) by numerical integration of the quadratic Bézier curve; (ii) refining by adjusting the positions of the external control points to minimize the difference between the known catheter spline length and the refined length of the Bezier curve; d) rendering the shape of the flexible spline based on the quadratic Bezier curve defined by the first endpoint location, the refined external control point locations determined in step c), and the second endpoint location.

Claims

1. A system comprising a console, the console comprising: a) receiving first and second endpoint position data based on a first and second position sensor assembly mounted near a first end and a second end of a flexible spline at a distal tip of the catheter; b) performing a coarse determination of positions of external control points of a quadratic Bézier curve to approximate a shape of the Flexibility Spline, the quadratic Bézier curve being defined by a first point and a second point corresponding to the first and second end positions and by the external control points, the coarse determination being based on a relationship between a known length of the Flexibility Spline and an estimated length of the quadratic Bézier curve, the estimated length of the quadratic Bézier curve being calculated based on the length of a chord connecting the first and second end positions and the length of a control line formed by the first end position, the positions of the control points, and the second end position; c) determining the positions of the external control points by (i) calculating a refined length of the quadratic Bézier curve associated with the positions of the external control points determined in step b) by numerical integration of the quadratic Bézier curve; (ii) refining by adjusting the positions of the external control points to minimize the difference between the known catheter spline length and the refined length of the Bezier curve; d) rendering the shape of the flexible spline based on the quadratic Bezier curve defined by the first endpoint location, the refined external control point locations determined in step c), and the second endpoint location.

2. A non-transitory computer-readable medium storing instructions that, when executed by a processor, cause the processor to: a) receiving first and second endpoint position data based on a first and second position sensor assembly mounted near a first end and a second end of a flexible spline at a distal tip of the catheter; b) performing a coarse determination of positions of external control points of a quadratic Bézier curve to approximate a shape of the Flexibility Spline, the quadratic Bézier curve being defined by a first point and a second point corresponding to the first end point location and the second end point location, and by the external control points, the coarse determination being based on a relationship between a known length of the Flexibility Spline and an estimated length of the quadratic Bézier curve; c) determining the positions of the external control points by (i) calculating a refined length of the quadratic Bézier curve associated with the positions of the external control points determined in step b) by numerical integration of the quadratic Bézier curve; (ii) refining by adjusting the positions of the external control points to minimize the difference between the known catheter spline length and the refined length of the Bezier curve; d) rendering the shape of the flexible spline based on the quadratic Bezier curve defined by the first endpoint location, the refined external control point locations determined in step c), and the second endpoint location.

3. 1. A method for real-time tracking of a spline profile in a catheter distal tip assembly, comprising: a) receiving first and second endpoint position data based on a first and second position sensor assembly mounted near a first end and a second end of a flexible spline at a distal tip of the catheter; b) performing a coarse determination of positions of external control points of a quadratic Bézier curve to approximate a shape of the Flexibility Spline, the quadratic Bézier curve being defined by a first point and a second point corresponding to the first and second end positions and by the external control points, the coarse determination being based on a relationship between a known length of the Flexibility Spline and an estimated length of the quadratic Bézier curve, the estimated length of the quadratic Bézier curve being calculated based on the length of a chord connecting the first and second end positions and the length of a control line formed by the first end position, the positions of the control points, and the second end position; c) determining the positions of the control points by (i) calculating, by numerical integration of the quadratic Bézier curve, a refined length of the quadratic Bézier curve associated with the positions of the external control points determined by the coarse determination; (ii) refining by adjusting the positions of the external control points to minimize the difference between the known catheter spline length and the refined length of the Bezier curve; d) rendering a shape of the flexible spline based on the quadratic Bezier curve defined by the first endpoint location, the refined external control point location, and the second endpoint location.

4. 4. The method of claim 3, wherein the positions of the external control points are constrained to a predetermined path, and wherein the coarse determination comprises determining the positions of the external control points on the predetermined path such that the estimated length of the quadratic Bezier curve is equal to the known length of the flexible spline.

5. The coarse determination of the location of the external control point is performed using the formula L ｓ = (2L ｃ +L ｐ ) / 3, where L ｓ is the known length of the spline, and L ｃ is the length of the chord connecting the first end point location and the second end point location, and L ｐ 4. The method of claim 3, wherein ∑ i = 1 i ...

6. 5. The method of claim 4, wherein the predetermined path is a straight path intermediate and perpendicular to the chord connecting the first end location and the second end location.

7. The method of claim 3 , wherein in the coarse determination, the locations of the external control points are constrained to a first predetermined region.

8. The method of claim 3 , wherein in the refining the positions of the external control points, the positions of the external control points are constrained to a second predetermined region.

Images