Determination of catheter shape

Abstract

Embodiments of the present disclosure may include receiving a plurality of impedance measurements from a plurality of electrodes disposed on a flexible tip of a catheter. The method may include receiving magnetic position measurements from a magnetic position sensor disposed on a shaft of the catheter. The method may include determining a relationship between individual electrodes of the plurality of electrodes disposed on the flexible tip of the catheter based on the impedance measurements received from the plurality of electrodes. The method may include predicting a shape of the flexible tip of the catheter based on the determined relationship between individual electrodes of the plurality of electrodes disposed on the flexible tip of the catheter. The method may include determining a shape of the catheter based on the magnetic position measurements and the predicted shape of the flexible tip.

Description

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims the benefit of U.S. Provisional Application No. 63 / 014,453, filed April 23, 2020, which is incorporated herein by reference as if fully set forth herein. Technical Field

[0003] The present disclosure generally relates to determining catheter shape. Background Art

[0004] Medical devices, catheters, and / or cardiovascular catheters, such as electrophysiology catheters, can be used in various diagnostic, therapeutic, mapping, and / or ablation procedures to diagnose and / or correct conditions such as atrial arrhythmias, including, for example, ectopic atrial tachycardia, atrial fibrillation, and atrial flutter. The medical device can be traversed through the patient's vasculature to a site where a diagnostic, therapeutic, mapping, and / or ablation procedure is performed to diagnose and / or correct a condition.

[0005] Sensors (e.g., electrodes, magnetic positioning sensors) can be placed on a medical device that can receive signals generated near the patient from a device. Based on the received signals, the orientation and / or position of the medical device within the heart can be calculated.

[0006] One technique for determining the position and orientation of a catheter within the body is to track multiple sensors on the catheter using a position sensing and navigation system (sometimes referred to as an orientation mapping system). The sensors may include electrodes disposed on the catheter that can provide voltage measurements associated with their exposure to an electric field generated by exciting pairs of electrodes on the outer surface of the body. The voltage measurements of the catheter electrodes can then be used to determine the position and orientation of the catheter electrodes within the coordinate system of the position sensing and navigation system. Other exemplary position sensing and navigation systems include magnetic systems.

[0007] To provide clinicians with information regarding the position and orientation of the catheter, the determined position and orientation of the catheter sensor is often used to render an image of the catheter relative to surrounding tissue, including cardiac tissue. However, one drawback of conventional systems is that the determined position and orientation of the catheter sensor may include errors due to errors associated with the data received from the catheter electrodes. In one example, the position of the catheter electrodes may be affected by offset and / or drift. For example, the impedance may slowly drift or even experience transient offsets due to drift and / or shift in the detection position of the medical device, such as due to changes in medication. Furthermore, the data received from the catheter electrodes may be inherently nonlinear, making it difficult to determine the position of the catheter in linear space when using nonlinear data. As a result, due to the errors and nonlinear nature of the data received from the catheter electrodes, the rendered shape of the catheter based on the determined position of the catheter electrodes may be distorted compared to its true mechanical shape. Summary of the Invention

[0008] Embodiments of the present disclosure include a method for determining a shape of a catheter. The method may include receiving a plurality of impedance measurements from a plurality of electrodes disposed on a flexible tip of the catheter. The method may include receiving magnetic position measurements from a magnetic position sensor disposed on a shaft of the catheter. The method may include determining a relationship between individual electrodes of the plurality of electrodes disposed on the flexible tip of the catheter based on the impedance measurements received from the plurality of electrodes. The method may include predicting a shape of the flexible tip of the catheter based on the determined relationship between individual electrodes of the plurality of electrodes disposed on the flexible tip of the catheter. The method may include determining the shape of the catheter based on the magnetic position measurements and the predicted shape of the flexible tip.

[0009] Embodiments of the present disclosure include a system for determining the shape of a catheter. The system may include a processor and a memory storing instructions on a non-transitory computer-readable medium, wherein the instructions are executable by the processor to receive a plurality of raw impedance measurements from a plurality of electrodes disposed on a flexible tip of the catheter. The system may include instructions executable by the processor to receive magnetic position measurements from a magnetic position sensor disposed on a shaft of the catheter. The system may include instructions executable by the processor to determine angles between respective electrodes of the plurality of electrodes disposed on the flexible tip of the catheter based on the raw impedance measurements received from the plurality of electrodes. The system may include instructions executable by the processor to predict the shape of the flexible tip of the catheter based on the determined angles between respective electrodes of the plurality of electrodes disposed on the flexible tip of the catheter. The system may include instructions executable by the processor to change a determined orientation of the flexible tip of the catheter based on the magnetic position sensor measurements. The system may include instructions executable by the processor to use the changed orientation of the flexible tip of the catheter to determine the shape of the catheter. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] Figure 1 is a schematic diagram of an exemplary system for performing one or more diagnostic or therapeutic procedures according to an embodiment of the present disclosure.

[0011] Figure 2A An isometric side view of an electrophysiology catheter is shown in accordance with an embodiment of the present disclosure.

[0012] Figure 2B A top view of a second EP catheter according to an embodiment of the present disclosure is shown.

[0013] Figure 3 A method for determining the shape of a catheter according to an embodiment of the present disclosure is shown.

[0014] Figure 4 Shown is a graphical depiction of electrostatic field lines associated with a particular domain, in accordance with an embodiment of the present disclosure.

[0015] Figure 5 A system for predicting the shape of a catheter according to an embodiment of the present disclosure is shown.

[0016] Figures 6A to 6D Parameters for defining the shape of a circular mapping catheter according to an embodiment of the present disclosure are shown.

[0017] Figure 7A An orthogonal projection of a two-dimensional catheter shape is shown, according to an embodiment of the present disclosure.

[0018] Figure 7B FIG. 4 shows a final catheter shape model according to an embodiment of the present disclosure, wherein: Figure 7A The orthogonal projections shown have been projected to provide the final catheter shape model.

[0019] Figures 8A to 8D Parameters for defining a catheter shape model of a high-density electrode mapping catheter according to an embodiment of the present disclosure are shown. DETAILED DESCRIPTION

[0020] Referring now to the drawings, wherein like reference numerals are used to identify like parts throughout the several views, Figure 1 is a diagrammatic overview of a catheter system in which the present invention may be practiced. The system may include various visualization, mapping, and navigation components known in the art, including, for example, the EnSite TM Velocity TM Cardiac mapping and visualization systems, as discussed further herein.

[0021] The system may be used in conjunction with or for various medical procedures, such as cardiac mapping and / or cardiac ablation procedures. In one embodiment, the medical positioning system 14 may include a magnetic field based system, such as the CARTO® system available from Biosense Webster. TM The magnetic field-based system may include, in part, a magnetic field-based system, such as the MediGuide from Abbott Laboratories, as generally indicated by reference to one or more of U.S. Patent Nos. 6,498,944, 6,788,967, and 6,690,963, the entire disclosures of which are incorporated herein by reference as if fully set forth herein. TM Technology system, and as generally shown by reference to one or more of the following disclosures: U.S. Patent Nos. 6,233,476, 7,197,354, and 7,386,339; U.S. Patent Application No. 14 / 208,120, filed on March 13, 2014, entitled “Medical Device Navigation System,” U.S. Provisional Patent Application No. 61 / 834,223, filed on June 12, 2013, entitled “Medical Device Navigation System,” and International Application No. PCT / IB2014 / 059709, filed on March 13, 2014, entitled “Medical Device Navigation System,” the disclosures of which are incorporated herein by reference in their entireties as if fully set forth herein. In yet another embodiment, the medical positioning system 14 may include a combination of a magnetic field-based system and an electric field-based system, such as, but not limited to, the systems described in co-pending U.S. patent application Ser. No. 13 / 231,284, filed on Sep. 13, 2011, entitled “Catheter Navigation Using Impedance and Magnetic Field Measurements,” and U.S. patent application Ser. No. 13 / 087,203, filed on April 14, 2011, entitled “System and Method for Registration of Multiple Navigation Systems to a Common Coordinate Frame,” or the CARTO system commercially available from Biosense Webster. TM3 systems, each of which is incorporated herein by reference in its entirety as if fully set forth herein. In some embodiments, the medical positioning system 14 may include or be used in conjunction with other common systems, such as, but not limited to, systems based on fluoroscopy, computed tomography (CT), and magnetic resonance imaging (MRI). For purposes of clarity and illustration only, the medical positioning system 14 will be described below as a hybrid system including magnetic and impedance tracking. Although reference is made to cardiac mapping of the heart, one or more aspects of the present disclosure may be applicable to other anatomical structures.

[0022] refer to Figure 1 , a catheter system includes a diagrammatic depiction of a heart 10 of a patient 11. The system includes the ability to receive multiple catheter positions as the distal end of the catheter is swept around and within the chambers of the heart. To this end, Figure 1 An exemplary catheter positioning system of the type based on externally applied orthogonal electric fields is shown, which is used to determine the position of one or more catheter position sensors. Such systems may include impedance positioning systems and / or hybrid systems of magnetic and impedance tracking, such as the EnSite TM NavX TM Electroanatomical mapping system, EnSite TM Velocity TM Electroanatomical Mapping Systems and EnSite Precision TM Electroanatomical mapping systems, all of which are commercially available from Abbott Laboratories or as generally disclosed by reference to the following: U.S. Patent No. 7,263,397 (the '397 patent), or U.S. Patent Publication No. 2007 / 0060833A1, U.S. Application No. 11 / 227,580, filed September 15, 2005 (the '580 application), or U.S. Publication No. 2018 / 0296111A1, U.S. Application No. 15 / 953,155, filed April 13, 2018 (the '155 application). The '397 patent, the '580 application, and the '155 application are all incorporated herein by reference as if fully set forth herein. Various EnSite TM The system is based on the principle that when an electric current is passed through the chest cavity, a voltage drop is generated across an internal organ (e.g., the heart), and this voltage drop can be measured and used to determine the position of the medical device within the body. However, it should be understood that this embodiment is merely exemplary and non-limiting in nature. Other technologies for determining the orientation of a catheter in 3D space, such as MediGuide TM Systems that can be used to implement the present invention include, for example, Biosense Webster's CARTO TM Navigation and positioning systems, or Northern Digital's Systems, both of which utilize magnetic fields rather than electric fields. Thus, as used herein, a sensor is configured to generate a signal indicative of catheter position information and may include one or more position sensors. The position sensor may include, for example, one or more electrodes configured to detect one or more characteristics of an electric field in the case of an impedance-based positioning system, or one or more coils (e.g., wire windings) configured to detect one or more characteristics of a magnetic field in the case of a magnetic field-based positioning system.

[0023] It should also be understood that in some positioning systems, one or more position sensors may collectively define a sensor. One or more position sensors may be provided at the distal end of the catheter, and the positioning system may be configured to obtain position information from the one or more position sensors. The positioning system may use not only the received position information, but also the geometric relationship between the one or more position sensors providing the position information and the distal position on the catheter (for example, a piece of geometric information may be the distance from the ring electrode to the tip) to calculate the distal position of the catheter. Finally, the positioning system may use the calculated position as if it were collected directly. Similarly, in a magnetic field-based positioning embodiment, there may be a geometric relationship between the catheter tip and the magnetic coil, wherein the positioning system is configured to use the calculated tip position (i.e., calculated based on the magnetic coil signal and predetermined knowledge about the geometric relationship between the coil and the tip) as if such a position were collected directly. Of course, other variations are also possible.

[0024] Continue to refer Figure 1 In the illustrated embodiment of the impedance-based positioning system, three sets of surface electrodes are shown (e.g., applied via patches): X-axis electrodes 12, 14; Y-axis electrodes 18, 19; and Z-axis electrodes 16, 22. In some embodiments, an additional surface electrode 21 may be used (e.g., applied via an "abdominal" patch). The surface electrodes are each connected to a switch 24. A representative catheter 13 is shown having a single distal electrode 17, which may be referred to herein as a "wandering" or "measuring" electrode. In some embodiments, the catheter 13 may be a coronary sinus catheter or a right ventricular apical catheter. In this embodiment, the electrode 17 may define a position sensor, but as mentioned above, many variations are possible, and the catheter 13 may include multiple position sensors, as discussed further herein. Figure 1 Also shown is a second separate catheter 29 having a fixed reference electrode 31 which can be stabilized on the heart 10 for calibration purposes.

[0025] Figure 1Also shown are a computer system 20, a signal generator 25, an analog-to-digital converter 26, and a low-pass filter 27. The computer system 20 can perform the various functions described herein using software, hardware, firmware, and / or logic. The computing system 20 can be a combination of hardware and instructions to share information. For example, the hardware may include processing resources 32 and / or memory resources 33 (e.g., a non-transitory computer-readable medium (CRM) database, etc.). As used herein, the processing resources 32 may include multiple processors capable of executing instructions stored by the memory resources 33. The processing resources 32 may be integrated into a single device or distributed across multiple devices. The instructions (e.g., computer-readable instructions (CRI)) may include instructions stored on the memory resources 33 and executable by the processing resources 32 for aligning the heart model.

[0026] The computer system 20 is configured to control the signal generator 25 according to a predetermined strategy to selectively stimulate each pair of surface electrodes. In operation, the computer system 20 is configured to obtain raw patch data (i.e., voltage readings) through the filter 27 and the AD converter 26, and use the raw patch data to determine the raw electrode position coordinates in three-dimensional space (X, Y, Z) of the catheter electrode (e.g., the wandering electrode 17 mentioned above) located within the heart 10 or a chamber thereof. In some embodiments, upon receiving such electrode position coordinates, the phase of the cardiac cycle of the patient 11 can be measured or otherwise determined. To this end, in one embodiment, most or all of the conventional twelve (12) ECG leads coupled to the body surface electrodes and generally identified by the reference numeral 15 are provided to support the acquisition of an electrocardiogram (ECG) of the patient 11.

[0027] Alternatively, a reference electrode located at a fixed position in the heart 10, such as the fixed reference electrode 31, can be used to provide a relatively stable signal (e.g., placed at the coronary sinus) that can be analyzed to determine the cardiac phase of the heart 10 in the cardiac cycle. More specifically, another catheter (in addition to a mobile or wandering catheter) having an electrode can be placed and maintained at a constant position relative to the heart 10 to obtain a relatively stable signal indicative of the cardiac phase. As shown, the ECG lead 15 is directly coupled to the computer system 20 for acquisition and subsequent processing to obtain the phase of the heart 10 in the cardiac cycle. The ECG lead 15 can also be provided to other systems (not shown).

[0028] As previously mentioned, embodiments of the present disclosure may be used with magnetic field-based systems. Some embodiments may include a main electronic control unit (e.g., one or more processors) with various input / output mechanisms, a display 23, an optional image database, a positioning system such as a medical positioning system (MPS) (electromagnetic sensor tracking system), an electrocardiogram (ECG) monitor, one or more MPS position sensors (e.g., patient reference sensors), and an MPS-enabled medical device (e.g., an elongated catheter or introducer) that itself includes one or more of the aforementioned MPS position sensors. As discussed, in some embodiments, the medical positioning system may include a magnetic field-based system, such as, for example, the MediGuide technology system from Abbott Laboratories, and as generally shown by reference to one or more of the following disclosures: U.S. Patent Nos. 6,233,476, 7,197,354, and 7,386,339; U.S. Patent Application No. 14 / 208,120, filed on March 13, 2014, entitled “Medical Device Navigation System,” U.S. Provisional Patent Application No. 61 / 834,223, filed on June 12, 2013, entitled “Medical Device Navigation System,” and International Application No. PCT / IB2014 / 059709, filed on March 13, 2014, entitled “Medical Device Navigation System,” the disclosures of which are incorporated herein by reference in their entireties as if fully set forth herein.

[0029] Embodiments may include input / output mechanisms that may include conventional means for interfacing with a computer-based control unit (e.g., keyboard, mouse, tablet, foot pedal, switches, etc.) Embodiments may also include a display 23 that may also include conventional means.

[0030] Embodiments may be used for navigation applications using imaging of regions of interest. Thus, the magnetic field-based system may optionally include an image database. The image database may be configured to store image information related to the patient's body, for example, a region of interest surrounding a target site of a medical device and / or multiple regions of interest along a navigation path expected to be traversed by the device to reach the target site. The image data in the image database may include known image types, including (1) one or more two-dimensional still images acquired at separate times in the past; (2) multiple related two-dimensional images acquired in real time from an image acquisition device (e.g., fluoroscopic images from an X-ray imaging device), wherein the image database acts as a buffer (real-time fluoroscopic); and / or (3) a sequence of related two-dimensional images defining an image playback (CL), wherein each image in the sequence has at least an ECG timing parameter associated therewith that is sufficient to allow the sequence to be played back based on the acquired real-time ECG signal obtained from the ECG monitor. It should be understood that the foregoing is merely exemplary and non-limiting in nature. For example, the image database may also include three-dimensional image data. It should also be understood that images may be acquired by any imaging modality now known or later developed (eg, X-ray, ultrasound, computed tomography, magnetic resonance imaging, etc.).

[0031] The MPS can be configured to function as a positioning system and thereby determine positioning (positioning) data about one or more MPS position sensors, one or more medical devices, and / or one or more patient reference sensors (PRS), and output corresponding position readings. The position readings can each include at least one or both of position and orientation (P&O) relative to a reference coordinate system, which can be a coordinate system of the MPS. For example, the P&O can be expressed as the position (i.e., coordinates on the X, Y, and Z axes) and orientation (i.e., azimuth and elevation) of a magnetic field sensor in a magnetic field relative to a magnetic field generator or transmitter.

[0032] The MPS determines the corresponding position (i.e., P&O) in a reference coordinate system based on capturing and processing signals received from magnetic field sensors, which are arranged in a controlled low-intensity AC magnetic field. From an electromagnetic perspective, as contemplated herein, these sensors generate a voltage that is induced on a coil located in a varying magnetic field. The sensors are therefore configured to detect one or more characteristics of the magnetic field in which they are located and generate an indication signal that is further processed by the MPS to obtain the corresponding P&O of the sensor. Exemplary design features, as well as manufacturing processes and methods for sensors and medical devices incorporating such sensors, can be found in U.S. Patent No. 8,636,718, the entire contents of which are incorporated herein by reference.

[0033] The MPS sensor, and optionally additional MPS sensors in other embodiments, may be associated with an MPS-enabled medical device. Another MPS sensor, a patient reference sensor (PRS), is configured to provide a positional reference of the patient's body, thereby allowing motion compensation for the patient's whole-body motion and / or breathing-induced motion. The PRS may be attached to the patient's manubrium, a stable location on the chest, or other location that is relatively stably positioned. Similar to the MPS position sensor, the PRS is configured to detect one or more characteristics of the magnetic field in which it is located, wherein the MPS provides a position reading (e.g., a P&O reading) that indicates the position and orientation of the PRS in a reference coordinate.

[0034] Electrocardiogram (ECG) monitor is configured to continuously detect the electrical timing signal of the heart organ by using a plurality of ECG electrodes (not shown), and these ECG electrodes can be fixed to the outside of the patient's body from the outside. The timing signal usually corresponds to a specific time of the cardiac cycle. Usually, the ECG signal can be used by the control unit for ECG synchronous playback (image playback) of the previously captured image sequence stored in the database. Both the ECG monitor and the ECG electrodes can include conventional components.

[0035] The magnetic field-based system can be incorporated into or associated with a fluorescence imaging system that may include commercially available fluorescence imaging components, such as an X-ray source, a C-arm, and / or an X-ray image intensifier or detector (i.e., a "cath lab"). The MPS (electromagnetic sensor tracking system) includes a magnetic transmitter assembly (MTA) (electromagnetic field generator) and a magnetic processing core for determining position and orientation (P&O) readings. The MTA is configured to generate a magnetic field in and around the patient's chest in a predefined three-dimensional space identified as a motion frame.

[0036] As described above, the MPS sensors are configured to sense one or more characteristics of the magnetic field while the sensor is within the motion frame, and each sensor generates a corresponding signal that is provided to the magnetic processing core. The processing core, responsive to these detected signals, is configured to calculate a corresponding P&O reading for each MPS sensor within the motion frame. The processing core can detect when an MPS sensor leaves the motion frame. Thus, the MPS can track each sensor in real time in three-dimensional space.

[0037] The actual volume of the motion frame can be stored, for example, in a processing core, and the processing core can determine the position and orientation of each sensor relative to the boundary of the motion frame. Alternatively, the actual volume of the motion frame can be stored, for example, in a master control, and the master control can determine the position and orientation of each sensor relative to the boundary of the motion frame. Thus, the system can assess (e.g., in the processing core or in the master control) whether a sensor is within the motion frame, at the boundary of the motion frame, or outside the motion frame. Based on this information, the motion frame and the sensors can be displayed on a display in relation to each other, as described in more detail elsewhere herein.

[0038] In some alternative embodiments, the MTA can be located below the patient table, between the X-ray source and the patient table. For example, the MTA can be connected to the patient table. In some embodiments, as discussed herein, the MTA can be a mobile device that can be placed on the patient's chest and used to generate a magnetic field for tracking the subject.

[0039] The positional relationship between the image coordinate system and the MPS reference coordinate system (electromagnetic tracking coordinate system) can be calculated based on the known optical and magnetic calibration of the system (e.g., established during setup), because in such embodiments, the positioning system and the imaging system can be considered fixed relative to each other. However, for other embodiments using other imaging modalities, including embodiments where image data is acquired at an earlier time and then imported from an external source (e.g., imaging data stored in a database), it may be necessary to perform a registration step to align the MPS coordinate system with the image coordinate system so that the MPS position readings can be properly coordinated with any particular image being used.

[0040] Figure 2A An electrophysiology catheter 40A is shown according to an embodiment of the present disclosure. The electrophysiology catheter 40A may be used in an electrophysiology procedure to help a physician understand the nature of an abnormal heart rhythm (e.g., an arrhythmia) and may include features as further discussed in WO 2017 / 177121, which is incorporated herein by reference as if fully set forth herein. The procedure is performed by inserting an electrophysiology catheter 40A that measures electrical activity through a blood vessel that enters the heart. Each electrophysiology catheter 40A may include several electrodes 46-1A, 46-2A, ..., 46-12A that are connected to a computer system (e.g., a heart rate monitor) via a connection box. Figure 1 In the computer system 20 in FIG. , electrodes 46-1A, 46-2A, ..., 46-12A are collectively referred to as electrodes 46A. Electrode 46A may be disposed on a flexible tip portion 44A, which may be a rounded tip, as shown. However, in some embodiments, the tip may be formed in other shapes.

[0041] The electrophysiology catheter 40A may include a magnetic position sensor 56, which in some embodiments is disposed in and / or on the shaft 42A. The electrodes may detect one or more characteristics of the electric field in which the electrodes 46A are disposed. As previously discussed herein, Figure 1 The electric field may be generated by surface electrodes (e.g., patch electrodes) placed externally on the patient. Based on the impedance associated with the signal received from electrode 46A, the position (e.g., coordinates) of electrophysiology catheter 40A may be determined. In some embodiments, electrophysiology catheter 40A may be an Advisor® manufactured by Abbott Laboratories. TM FL circular mapping catheter, Sensor Enabled TM , but in some embodiments, the EP catheter 40A can be another EP catheter. The catheter 40A can be used with the EnSite TM Velocity TM Electroanatomical Mapping System, EnSite Precision TM Electroanatomical mapping system and / or MediGuide TM The system may be used in conjunction with other types of systems, such as those mentioned herein.

[0042] Figure 2B is a top view of a second electrophysiology catheter 101 according to an embodiment of the present disclosure. Electrophysiology catheters are also referred to herein as high-density electrode catheters 101. In some embodiments, the high-density electrode catheter 101 may include a flexible tip 110 that forms a flexible array of electrodes 102. This planar array (or "paddle-like" configuration) of electrodes 102 includes four side-by-side, longitudinally extending arms 103, 104, 105, 106 that form a flexible frame on which the electrodes 102 are arranged. The four electrode-carrying arms may include a first outer arm 103, a second outer arm 106, a first inner arm 104, and a second inner arm 105, which may be connected at the distal end by a distal connection 109, but this is not required. The arms may be laterally separated from each other.

[0043] Each of the four arms may carry a plurality of electrodes 102. For example, each of the four arms may carry electrodes 102 spaced apart along the length of each of the four arms. Figure 2B The illustrated high-density electrode catheter 101 shows four arms, but the high-density electrode catheter 101 may include more or fewer arms. Figure 2BThe illustrated high-density electrode catheter 101 shows 18 electrodes (e.g., 5 electrodes on the first lateral arm 103 and the second lateral arm 106 and 4 electrodes on the first medial arm 104 and the second medial arm 105), but the catheter may include more or fewer than 18 electrodes. Furthermore, the first lateral arm 103 and the second lateral arm 106 may include more or fewer than 5 electrodes and the first medial arm 104 and the second medial arm 105 may include more or fewer than 4 electrodes.

[0044] In some embodiments, electrodes 102 can be used for diagnostic, therapeutic, and / or mapping procedures. For example, but not limited to, electrodes 102 can be used for electrophysiological studies, pacing, cardiac mapping, and ablation. In some embodiments, electrodes 102 can be used to perform unipolar or bipolar ablations. The unipolar or bipolar ablations can form specific lesion lines or patterns. In some embodiments, electrodes 102 can receive electrical signals from the heart, which can be used for electrophysiological studies. In some embodiments, electrodes 102 can perform position or location sensing functions associated with cardiac mapping.

[0045] In some embodiments, the high-density electrode catheter 101 may include a catheter shaft 107. The catheter shaft 107 may include a proximal end and a distal end. The distal end may include a connector 108 that couples the distal end of the catheter shaft 107 to the proximal end of the planar array. The catheter shaft 107 may define a catheter shaft longitudinal axis aa, such as Figure 2B As shown, the first outer arm 103, the first inner arm 104, the second inner arm 105, and the second outer arm 106 can extend along the catheter shaft longitudinal axis aa and generally parallel to the catheter shaft longitudinal axis aa. The catheter shaft 107 can be made of a flexible material so that it can be passed through the tortuous vasculature of a patient. In some embodiments, the catheter shaft 107 can include one or more ring electrodes 111 arranged along the length of the catheter shaft 107 and one or more magnetic position sensors 116 located in or along the shaft 107. In one example, the ring electrodes 111 can be used for diagnostic, therapeutic, and / or mapping procedures.

[0046] Embodiments of the present disclosure can generate a visual representation of a catheter. As described above, a catheter can have a catheter shaft and a flexible tip portion comprising a plurality of electrodes. The flexible tip portion can typically be flexible enough to conform to the patient's tissue, thereby allowing some or all of the plurality of electrodes disposed on the flexible tip portion to contact the patient's tissue. However, when attempting to determine a visual representation of the flexible tip portion, and catheters in general, the flexible nature of the tip portion can prove problematic. The electrodes on the flexible tip portion can shift and / or drift in the impedance field generated by one or more electrode patches in contact with the patient's body, which can result in a deviation between the impedance-calculated position of the electrodes and their actual position. Various methods have been used to calculate the positions of the plurality of electrodes disposed on the flexible tip portion, particularly impedance transformations, which provide a relationship between impedance position and real-world position. However, such transformations are not easy to find and are time- and position-dependent.

[0047] Embodiments of the present disclosure may determine a visual representation of the flexible tip and catheter as a whole by using raw impedance positions derived from the electric field inside the heart, by using angles between the raw impedance positions, and by applying characteristics of the electric field in which electrodes are arranged on the flexible tip of the catheter.

[0048] Figure 3 A method 120 for determining the shape of a catheter according to an embodiment of the present disclosure is shown. In some embodiments, the method may include receiving 122 a plurality of impedance measurements from a plurality of electrodes disposed on a flexible tip portion of the catheter. Figure 2A and 2B The discussion can be made from the Figure 2A The electrodes 46-1A, 46-2A, ..., 46-10A on the catheter 40A shown receive a plurality of impedance measurements and / or may receive a plurality of impedance measurements from electrodes 102-1, 102-2, ..., 102-18 disposed on the catheter 40A. Figure 2B On the flexible tip portion 110 of the high-density electrode catheter 101 in the.

[0049] The method may include receiving 124 magnetic position measurements from a magnetic position sensor disposed on a shaft of the catheter. For example, the catheter shaft 42A ( Figure 2A ) may include a magnetic position sensor 56, and the catheter shaft 107 ( Figure 2B ) may also include a magnetic position sensor 116 from which magnetic position measurements may be received.

[0050] The method 120 may include determining 126 a relationship between individual electrodes in a plurality of electrodes disposed on the flexible tip of the catheter based on impedance measurements received from the plurality of electrodes. In some embodiments, determining the relationship between individual electrodes in the plurality of electrodes disposed on the flexible tip of the catheter may include determining an angle between individual electrodes in the plurality of electrodes. In one example, the angle between any number of electrodes disposed on the flexible tip of the catheter may be determined. In some embodiments, the angle between at least three electrodes disposed on the flexible tip of the catheter may be determined. In some embodiments, three electrodes may be the minimum number of electrodes for determining the angle between the electrodes. In some embodiments, the angle may be determined using several pairs of electrodes to measure bend, yaw, twist, etc. of the flexible tip of the catheter using several pairs of electrodes.

[0051] In some embodiments, the impedance measurements used to determine the angle between each of the plurality of electrodes disposed on the flexible tip of the catheter can be raw impedance measurements. In some embodiments, using raw impedance can allow fewer calculations to be performed when determining the angle between the electrodes. As a result of using raw impedance, the positions of the electrodes 46A, 102 can be offset relative to their actual positions. However, it can be assumed that the position of each electrode 46A, 102 has shifted by approximately the same amount, thereby determining the general shape of the flexible tip, even if it has experienced offset and / or drift. In some embodiments, before determining the angle between the electrodes, the raw impedance measurements can be transformed from the impedance domain to the magnetic domain by using local field scaling, as discussed further herein.

[0052] The field in which the electrodes 46A, 102 are arranged can be considered an electrostatic field, which can be described by Poisson's formula using Laplace's equation when no charge changes occur inside. In addition, it can be assumed that no magnetic field acts on the volume in which the electrodes 46A, 102 are arranged. Therefore, there may be no curl in the electrostatic field because the magnetic field can act as eddy currents of the electric current. In some embodiments, the size (e.g., longitudinal length and / or lateral width) of the flexible tip of the catheter 40A, 101 can be approximately 2 centimeters. However, in some embodiments, the size can be greater or less than 2 centimeters. Because the size of the flexible tip of the catheter 40A, 101 is relatively small, the characteristics of the electrostatic field can remain relatively uniform throughout the space in which the flexible tip of the catheter is arranged. For example, referring to Figure 4 , Figure 4is a graphical depiction 140 of electrostatic field lines 142 relative to a particular domain 144 within which minimal curl exists. In some embodiments, due to the relatively small size of the flexible tip of the catheter, the local field scaling can be assumed to be constant across the flexible tip. For example, as discussed further herein, impedance measurements received from electrodes 46A, 102 can be transformed from the impedance domain to the magnetic domain using local field scaling. The scaling can be assumed to be constant across the relatively small size of the flexible tip of the catheter.

[0053] like Figure 4 As shown, the x-axis and y-axis represent distance, in this case in centimeters. The domain 144 is approximately Figure 2A and 2B The dimensions of the flexible tip 44A, 110 are shown. Figure 4 As shown, the smallest change in the direction of the electrostatic field exists within a relatively small domain 144, which is shown as approximately 2 cm x 2 cm, but the domain can be larger or smaller depending on the size of the flexible tip. Therefore, even if the data received from the electrodes 46A, 102 disposed on the flexible tip 44A, 110 is raw impedance data, the angle between each of the electrodes 46A, 102 can be accurately determined.

[0054] In some embodiments, in the absence of a magnetic field acting on domain 144, the curl in the electrostatic field within domain 144 can be assumed to be zero, which can help reduce the complexity of determining the angle between each of the multiple electrodes. For example, the directional change of the electrostatic field represented by arrow 142 is gradual within the measurement domain 144 relative to the catheter being used. For example, there are no bends, loops, twists, or other types of changes in the electrostatic field potential lines, which are the sources of the emitted electrostatic field and converge at the electrostatic field sink. By converting impedance to position based on Ohm's law, the total impedance measured is a function of the path length and the impedance per unit length, which maintains the above-mentioned assumption of minimal directional change of the electrostatic field within the measurement domain 144.

[0055] Due to the minimal change in direction of the electrostatic field, it can be determined Figure 2A and 2B The angles between any combination of electrodes 46A, 102 shown are used to determine bend, yaw, flexion, and twist, in conjunction with the flexible tip portions 44A, 110 of the catheters 40A, 101. Figures 6A to 6D and Figures 8A to 8D These parameters are discussed further in the References Figure 2A , the flexible tip portion 44A can undergo bending in either direction of arrow 48. For example, referring to FIG. Figure 2A4, the flexible tip portion 44A, which is traversed by line 48, can bend left or right relative to the page in either direction of arrow 48. The flexible tip portion 110 can undergo out-of-plane bending, wherein the flexible tip portion 44A moves in the direction of arrow 50, thereby forming a spiral around the bend of the loop of the catheter. For example, referring to FIG. Figure 2A , the flexible tip portion 44A through which arrow 50 passes can move to the left along the page, thereby forming a spiral in the flexible tip portion 44A. When the portion of the flexible tip portion 44A through which arrow 52 passes moves in either direction of arrow 52, the flexible tip portion 44A can experience a twist in the direction of arrow 52. The flexible tip portion 110 can experience in-plane bending, wherein the flexible tip portion 44A moves in the direction of arrow 54, causing in-plane buckling of the loop of the catheter. For example, referring to FIG. Figure 2A , the flexible tip portion 44A passed by arrow 54 can be moved to the right along the page so that the flexible tip portion 44A of the catheter bends within a plane.

[0056] refer to Figure 2B , the flexible tip portion 110 can undergo bending in either direction of arrows 112a, 112b. Figure 2B , the flexible tip portion 110 may bend into (e.g., in the direction of arrow 112a) or away from (e.g., in the direction of arrow 112b) the page. The flexible tip portion 110 may undergo flexion, wherein the flexible tip portion 110 flexes about the longitudinal axis aa. For example, referring to FIG. Figure 2B 114a or 114b, wherein the flexible tip portion 110 is twisted about the longitudinal axis in a first direction (e.g., arrow 114a) or in a second direction (e.g., arrow 114b). The ... Figure 2B , the flexible tip portion 110 may bend upward or downward relative to the page along a first direction of arrow 115a or along a second direction of arrow 115b.

[0057] In some embodiments, using raw impedance data from electrodes when determining the angle between electrodes can result in noisy data. For example, the position of an electrode determined using the raw impedance data may sometimes be inconsistent, causing the position of the electrode to jump relative to the position of other electrodes. Therefore, the method of the present disclosure may include filtering raw impedance measurements received from a plurality of electrodes arranged on a flexible tip portion of a catheter. In some embodiments, if the raw impedance data is not filtered, an incorrect shape of the flexible tip portion of the catheter may be determined. In some embodiments, filtering the raw impedance measurements received from the plurality of electrodes may include filtering the raw impedance measurements using a low-pass filter. In some embodiments, prior to filtering, the raw impedance data may be transformed from the impedance domain to the magnetic domain by using local field scaling, as further discussed herein.

[0058] Further references Figure 3 In some embodiments, method 122 may include predicting 128 a shape of the flexible tip portion of the catheter based on the determined relationship between each of the plurality of electrodes disposed on the flexible tip portion of the catheter. In some embodiments, the method may include predicting an orientation of each of the plurality of electrodes disposed on the flexible tip portion 44A, 110 of the catheter. For example, the angle between the electrodes 46A, 102 disposed on the flexible tip portion may change based on the bending, yaw, flexion, and twisting that the flexible tip portion 44A, 110 of the catheter is experiencing. As described above, to determine changes in the angle between the electrodes, it is helpful to obtain raw impedance data from at least three electrodes, as it is difficult to determine an angular trend between only two electrodes. Based on the changing angles between the electrodes, the shape of the flexible portion of the catheter may be determined.

[0059] In some embodiments, method 122 may include predicting the shape of the flexible tip of the catheter by calculating the shape of the flexible tip using angles between respective electrodes of a plurality of electrodes associated with a shape model of the flexible tip. As described above, the shape model of the flexible tip may account for bending, yaw, buckling, and / or twisting. As further discussed herein, embodiments of the present disclosure may include predicting the shape model of the flexible tip of the catheter.

[0060] Figure 5A system for predicting the shape of a catheter according to an embodiment of the present disclosure is shown. In some embodiments, raw impedance data can be received from which electrode positions and a frame curve can be calculated. In one example, raw impedance data can be received from one or more electrodes, as represented by arrow 152 leading to block 154. In some embodiments, as discussed, at block 154, a low-pass filter 154 can be applied to the raw impedance data 152. In some embodiments, at block 156, the electrode positions can be transformed into magnetic space. For example, at block 156, the filtered raw impedance data can be transformed into magnetic data using an impedance transformation model.

[0061] In some embodiments, the impedance transformation model may include transforming the raw impedance measurements from the impedance domain to the magnetic domain by using local field scaling 164. The local field scaling 164 may utilize a rigid body transformation that may include one or more equations that model the distance between one or more electrode pairs. The constraints of the rigid body transformation may include a known distance between electrodes on the flexible tip of the catheter. In one example, a rigid transformation of a point from the impedance domain to the magnetic domain may be performed using a rigid body transformation where the constraints are the known distance between electrodes along a spline or a circular loop of the flexible tip of the catheter. However, any type of distance between electrodes on a shaped flexible tip may be used. For example, embodiments of the present disclosure are not limited to catheters having flexible tips, such as those with respect to Figure 2A and 2B Those shown and discussed above. In one example, a local field scale 164 associated with the raw impedance measurement can be determined, and the raw impedance measurement can be converted to a magnetic position by scaling the raw impedance measurement based on the local field scale 164. Once the local scaling is complete, the raw impedance measurement can be adjusted to a coarse magnetic position by scaling along the x, y, and z axes. To account for differences in the data, the measurement can be filtered (e.g., by a low-pass filter 154), as discussed herein.

[0062] Some embodiments of the present disclosure include determining a catheter shape model 158, which is discussed further below. As described above, the angles between each of the plurality of electrodes can be used to calculate the shape of the flexible tip of the catheter in relation to the catheter shape model 158. The shape model 158 can be used to calculate both electrode positions 160 and a frame curve 162. In one example, the electrode positions can be determined based on the determined shape of the flexible tip. In some embodiments, the electrode positions can be combined with the frame curve generated by the catheter model and displayed. In some embodiments, the catheter model includes a determined shape model of the flexible tip, as discussed further herein.

[0063] Further references Figure 3, the method 120 may include determining 130 the shape of the catheter based on the magnetic position measurements and the predicted shape of the flexible tip. Figure 2A and 2B Magnetic position measurements can be obtained from magnetic position sensors 56, 116. In some embodiments, the positional relationship between catheter shaft 42A, 107 and flexible tip 44A, 110 can be known. Electrode positions can be determined based on raw impedance data; therefore, the data may be subject to offset and drift. In some embodiments, the determined position of the electrodes, which can be converted into magnetic position data, can be offset so that the determined position of the electrodes is properly aligned with the position of the magnetic position sensors.

[0064] For example, in some embodiments, method 120 may include determining the shape of the catheter using angles between respective electrodes of the plurality of electrodes and magnetic position measurements associated with a shape model of the flexible tip. In some embodiments, position and orientation measurements may be received from a magnetic position sensor disposed on the catheter, and the position and orientation measurements may be used to determine the shape of the catheter using angles between respective electrodes of the plurality of electrodes and the magnetic position and orientation measurements.

[0065] In some embodiments, determining the shape of the catheter can include changing the shape of the flexible tip of the catheter relative to the shaft of the catheter based on position and orientation measurements received from the magnetic position sensor. In some embodiments, the shape of the flexible tip can be first determined using raw impedance data associated with a shape model of the flexible tip received from the electrodes. The determined position of the catheter shaft can then be used to correctly position the determined shape of the flexible tip. For example, the determined shape of the flexible tip can be correctly positioned based on the position and orientation measurements received from the magnetic position sensor. Therefore, determining the shape of a catheter including the flexible tip and the catheter shaft can include changing the determined shape of the flexible tip of the catheter relative to the shaft of the catheter based on the position and orientation measurements received from the magnetic position sensor.

[0066] Determining the shape model of the flexible tip may include determining different shape models for catheters having different types of flexible tips. Figure 2A The catheter shown determines a first shape model, which can be Figure 2B Different shape models are determined for the catheters shown because the two catheters have different flexible tips. Shape models can be determined for other types of flexible tips in a similar manner.

[0067] In the case of circular mapping catheters, e.g. Figure 2A The catheter shown (e.g., Advisor available from Abbott Laboratories) TMVL mapping catheters), the catheter can be modeled based on the physical behavior of the catheter shape. This approach can involve using the mechanical properties of a simple wire spring to develop a numerical bending model. The circular mapping catheter shape can be divided into three main parts, such as Figure 2A The three parts may include a rigid shaft 42A, a knee 58 pre-bent at 90 degrees, and a loop 60 (also pre-bent at a given angle within the plane of the loop). The defined catheter shape model allows for four different motions, also incorporating Figures 6A to 6B These motions are described and discussed. The four different motions include bending about the forward axis of the catheter 40A from the knee 58 in either direction of arrow 48 (e.g., bending); bending about the lateral axis of the catheter 40A from the knee 58 in either direction of arrow 52 (e.g., twisting); bending in-plane about the bend of the catheter's loop 60 in the direction of arrow 52 (e.g., looping); and bending out of plane about the bend of the catheter's loop in the direction of arrow 50 (e.g., spiraling).

[0068] For the bending and twisting of the loop portion of the catheter, the Euler-Bernoulli beam theory can be used, and the portion to which this theory applies can be the top of the knee 58 to the first and second quadrants of the loop 60 that extend approximately to the electrode 46-5A. For the angle of the loop 60, the Euler-Bernoulli beam theory can be used, and the portion to which this theory applies can be the entire loop 60 from the knee 58 to the distal end where the electrode 46-10A is located. For the helical angle, the torsion theory in mechanics can be used, and the portion to which this theory applies can be the entire loop 60 from the knee 58 to the distal end where the electrode 46-10A is located.

[0069] The theory of torsion can be used as follows. In the field of solid mechanics, torsion can be defined as the twisting of an object due to an applied torque. Torsion can be expressed in Pascals (Pa), which is the SI unit of Newtons per square meter, or pounds per square inch (psi), while torque is expressed in Newton meters (N·m) or foot-pounds-force (ft·lbf). In a section perpendicular to the axis of torque, the resultant shear stress in the section may be perpendicular to the radius. In non-circular cross sections, twisting may be accompanied by a deformation called warping, in which the cross section does not remain flat. For an axis of uniform cross section not subject to warping, torsion can be expressed as:

[0070]

[0071] Where T is the applied torque or torsional moment in Nm; Tau is the maximum shear stress at the outer surface; J Tis the torsional constant of the cross section, which is approximately the second moment of area about the neutral axis; r is the distance between the axis of rotation and the farthest point in the cross section (at the outer surface); l is the length of the object applying or exceeding the torque; -(phi) is the twist angle in radians; G– is the shear modulus, also known as the modulus of rigidity.

[0072] The shear stress at a point inside the shaft can be expressed as:

[0073]

[0074] The twist angle can be found using the following equation:

[0075]

[0076] For circular cross sections, the same formula applies, and the moment of inertia of a circular cross section can be defined as:

[0077]

[0078] The above relationship can be expressed as:

[0079]

[0080] Among them, GI p is defined as torsional stiffness. Twist angle Can be expressed as

[0081]

[0082] in The unit of measurement is radians. Torsional flexibility can be expressed as

[0083]

[0084] And the torsional stiffness is expressed as

[0085]

[0086] In addition to torsion, bending about two perpendicular axes can also be considered, and the stresses induced by these bends can be combined using the superposition rule. The equations describing the bending of a conduit during bending and twisting can be derived using the Euler-Bernoulli beam element. The Euler-Bernoulli equations describe the relationship between the deflection of a beam and the applied load. The following formula describes the bending curve caused by a distributed load q.

[0087]

[0088] The curve w(x) describes the deflection of the beam along the z direction at some location x (recall that the beam is modeled as a one-dimensional object). q is the distributed load, which is the force per unit length (similar to how pressure is force per unit area); it can be a function of x, w, or other variables.

[0089] In the above equation, E is the elastic modulus and I is the second moment of area of the cross section of the beam. I can be calculated relative to an axis passing through the centroid of the cross section and perpendicular to the applied load. Specifically, for a beam with its axis oriented along x and the load along z, the cross section of the beam is in the YZ plane and the associated second moment of area is

[0090] I=∫∫z 2 dgdz,

[0091] The continuous derivatives of the deflection w have important physical meaning: dw / dx is the slope of the beam, and M is the bending moment in the beam.

[0092]

[0093] The Euler-Bernoulli theorem can be extended to cases of large deflections, and instead of integrating the deflection along the x-axis of the beam, the slope can be integrated piecewise. The moment at each section can be calculated using the distance from the distal end and the normal force acting on it. The catheter can be modeled as a circular beam with a load at the end, and the bending angle of each segment can be integrated by superposition of mutually perpendicular components. Since the catheter is pre-bent at the knee and loop sections, the shape of the catheter can be composed of an undeformed shape (pre-bend) and a deformed shape, which is a result of the three bending components. After numerically integrating the catheter shape along the spine of the catheter, the electrode position and catheter wire position on this shape can be calculated, which can be performed using the Frenet-Serret formula, as described below.

[0094] In differential geometry, the Fresnet-Séret formula describes the equation These formulas describe the kinematic properties of a particle moving along a continuously differentiable curve, or the geometric properties of the curve itself, independent of any motion. More specifically, these formulas describe the derivatives of the so-called unit tangent vector, the unit normal vector, and the unit binormal vector with respect to each other. The vector notation and linear algebra currently used to write these formulas were not available at the time of their discovery.

[0095] The unit tangent vector, the unit normal vector, and the unit binormal vector, often referred to as T, N, and B, or collectively as the Frenet-Cerret frame or TNB frame, together form the span The orthogonal basis is defined as follows. T is a unit vector tangent to the curve and pointing in the direction of motion; N is the unit normal vector, which is the derivative of T with respect to the arc length parameter of the curve divided by its length; and B is the unit binormal vector, which is the cross product of T and N.

[0096] The Frenet-Seret formula is:

[0097]

[0098] Here, d / ds is the derivative with respect to arc length, κ is the curvature, and τ is the twist of the curve. The two scalars κ and τ effectively define the curvature and twist of a space curve. The associated set of T, N, B, κ, and τ is known as the Fresnet-Cerret mechanism. Curvature measures whether a curve is a straight line, while twist measures whether it is a plane.

[0099] The unit tangent vector, the unit normal vector, and the unit binormal vector, often referred to as T, N, and B, or collectively as the Frenet-Cerret frame or TNB frame, together form the span The orthogonal basis is defined as follows. T is a unit vector tangent to the curve and pointing in the direction of motion; N is the unit normal vector, which is the derivative of T with respect to the arc length parameter of the curve divided by its length; and B is the unit binormal vector, which is the cross product of T and N.

[0100] The Fresnet–Seret formula is also known as the Fresnet–Seret theorem and can be expressed more concisely using matrix notation.

[0101]

[0102] This matrix is stored segment by segment along the spine of our catheter and is used to extract the positions and curves of the electrodes. As described above, the Fresne-Seret frame moving along the helix is represented by T, which is a unit vector tangent to the curve of the helix and pointing in the direction of motion; N is the unit normal vector, the derivative of T with respect to the arc length parameter of the helix curve divided by its length; and B is the unit binormal vector, the cross product of T and N. This model can then be compared with data from multiple sources (e.g., synthetic data, water tank data, animal test data). In embodiments of the present disclosure, the match between the synthetic data and the calculated shapes validates the numerical model and shows small errors for all measured positions and electrodes.

[0103] Figures 6A to 6D Parameters for defining the shape of a circular mapping catheter according to an embodiment of the present disclosure are shown. Figure 6A As shown, the catheter shape model can take into account the bending of the flexible tip portion 176A of the catheter 170A about the forward axis cc of the catheter 170A starting from the knee 182A of the catheter 170A. The bending shown of the flexible tip portion 176A of the catheter 170A is also relative to Figure 2AAs shown by arrow 52, catheter 170A includes a catheter shaft 172A connected to a flexible tip portion 176A formed by a ring-shaped distal end 174A. The ring-shaped distal end 178A includes a plurality of electrodes 178A, only one of which is labeled for ease of illustration, and the catheter shaft 172A also includes a plurality of electrodes 180A, only one of which is labeled.

[0104] like Figure 6B As shown, the catheter shape model can take into account the bending of the flexible tip portion 176B of the catheter 170B about the lateral axis dd of the catheter 170B starting from the knee 182B of the catheter 170B. The bending shown of the flexible tip portion 176B of the catheter 170B is also relative to Figure 2A As shown by arrow 48, catheter 170B includes a catheter shaft 172B connected to a flexible tip 176B formed by a ring-shaped distal end 174B. The ring-shaped distal end 178B includes a plurality of electrodes 178B, only one of which is labeled for ease of illustration, and the catheter shaft 172B also includes a plurality of electrodes 180B, only one of which is labeled.

[0105] like Figure 6C As shown, the catheter shape model can take into account the bending of the flexible tip portion 176C of the catheter 170C in a plane around the bend of the annular distal end 176C of the catheter 170C. The bending shown of the flexible tip portion 176C of the catheter 170C is also relative to Figure 2A As shown by arrow 54, catheter 170C includes a catheter shaft 172C connected to a flexible tip 176C formed by a ring-shaped distal end 174C. The ring-shaped distal end 178C includes a plurality of electrodes 178C, only one of which is labeled for ease of illustration, and the catheter shaft 172C also includes a plurality of electrodes 180C, only one of which is labeled.

[0106] like Figure 6D As shown, the catheter shape model can take into account the bending of the flexible tip portion 176D of the catheter 170D out of plane around the bend of the annular distal end 176D of the catheter 170D. The bending shown of the flexible tip portion 176D of the catheter 170D is also relative to Figure 2A As shown by arrow 50, catheter 170D includes a catheter shaft 172D connected to a flexible tip 176D formed by a ring-shaped distal end 174D. The ring-shaped distal end 178D includes a plurality of electrodes 178D, only one of which is labeled for ease of illustration, and the catheter shaft 172D also includes a plurality of electrodes 180D, only one of which is labeled. The catheter shape model generated for the circular mapping catheter has a display error of less than 1 mm when used with the synthetic dataset.

[0107] In the case of high-density electrode mapping catheters, e.g. Figure 2B The catheter shown (e.g., Advisor available from Abbott TM Mesh high-density mapping catheters), modeling the catheter based on the physical behavior of the catheter shape. To develop this scheme, finite elements were used, and insights were gained about how forces and constraints are applied to achieve the deformed shape. The finite element method (FEM) is a numerical method used to solve problems in engineering and mathematical physics. Typical problem areas of interest include structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. The analytical solution to these problems usually requires solving boundary value problems of partial differential equations. The finite element method formulation of the problem produces a system of algebraic equations. The method approximates the unknown function over a domain. To solve this problem, it subdivides a large system into smaller, simpler parts, which are called finite elements. The simple equations modeling these finite elements are then combined into a larger system of equations to model the entire problem. FEM then uses variational methods from variational calculus to approximate the solution by minimizing the associated error function.

[0108] The solution of the method may include (1) dividing the domain of the problem into a set of subdomains, where each subdomain is represented by a set of element equations of the original problem, and then (2) systematically recombining all of the element equations into a global system of equations for the final calculation. The global system of equations has known solution techniques and can be calculated to obtain numerical answers based on the initial values of the original problem. Given a set of known deflections on a shape, embodiments of the present disclosure can obtain applied forces and positions. In some embodiments, a set of solutions can be constructed, each with a small deviation from the last, until the final shape is reached. Using a single FEM solution may not be feasible because the construction of the global stiffness matrix assumes a known geometry, and it may not be possible to calculate this geometry using the initial state of the shape.

[0109] In some embodiments, a simplified numerical model can be developed based on insights gained from the finite element model: the shape of the catheter in contact with the wall, and the forces applied perpendicular to the contact wall. Furthermore, modeling the catheter stiffness reveals that some axes are stiffer than others, making certain motions less likely to occur. For example, the catheter is less likely to bend in yaw because its moment of inertia is likely much higher in yaw, and it is more likely to slip from its contact point. Regarding twisting, pure twisting by itself may not occur when the catheter shape is unbent; therefore, some bending and yaw can be combined with twisting to maintain the shape in contact with the heart wall.

[0110] Solving the numerical model can be limited to understanding the four parameters that influence the final form of the conduit: bending, yaw, twisting, and buckling, as discussed further in this article. Equations describing the bending of the conduit along its spine are derived using Euler-Bernoulli beam elements. These equations apply to both bending and yaw, with different stiffness values applied to each. The Euler-Bernoulli equations describe the relationship between the deflection of the beam and the applied load. The following formula describes the bending curve caused by the distributed load q.

[0111] The Euler-Bernoulli equation describes the relationship between the deflection of a beam and the applied load. The following equation describes the deflection curve caused by a distributed load q.

[0112]

[0113] The curve w(x) describes the deflection of the beam along the z direction at some location x (recall that the beam is modeled as a one-dimensional object). q is the distributed load, which is the force per unit length (similar to how pressure is a force per unit area); it can be a function of x, w, or other variables. In the above equation, E is the elastic modulus and I is the second moment of area of the beam's cross section. Specifically, I is calculated with respect to an axis passing through the centroid of the cross section and perpendicular to the applied load. For a beam with its axis oriented along x and the load along z, the beam's cross section is in the YZ plane, and the associated second moment of area is

[0114] I=∫∫z 2 dydz,

[0115] The continuous derivatives of the deflection w have important physical meaning: dw / dx is the slope of the beam, and M is the bending moment in the beam.

[0116]

[0117] The Euler–Bernoulli theorem can be extended to large deflections. Instead of integrating the deflection along the beam's x-axis, the slope can be integrated piecewise. The moment at each section can be calculated using the distance from the far end and the normal force acting on it.

[0118] A theorem for torsion can be used to describe the torsion of a beam in solid mechanics. In solid mechanics, torsion is the twisting of an object due to an applied torque. Torque is expressed in Pascals (Pa), the SI unit of Newtons per square meter, or pounds per square inch (psi), while torque is expressed in Newton meters (N·m) or foot-pounds-force (ft·lbf). In a section perpendicular to the axis of torque, the resultant shear stress in that section can be perpendicular to the radius.

[0119] In non-circular cross-sections, twisting is accompanied by a deformation called warping, in which the cross-section does not remain planar. For an axis of uniform cross-section not subject to warping, torsion can be expressed as:

[0120]

[0121] Where T is the applied torque or torsional moment in Nm; Tau is the maximum shear stress at the outer surface; J T is the torsional constant of the cross section, which is approximately the second moment of area about the neutral axis; r is the distance between the axis of rotation and the farthest point in the cross section (at the outer surface); l is the length of the object to which the torque is applied; (phi) is the twist angle in radians; G is the shear modulus, also known as the modulus of rigidity.

[0122] The shear stress at a point inside the shaft can be expressed as:

[0123]

[0124] The twist angle can be found using the following equation:

[0125]

[0126] Although for Advisor TM For high-density mesh mapping catheters, numerical integration of the twist is not mandatory, but the integration step can also be used to integrate the twist, as this allows changing the torsional stiffness J along the spine. T , thus achieving higher accuracy of the solution. TM Mesh high-density mapping catheters are also well-suited for the Darboux frame approach for modeling electrodes and curves on the paddle, as described below. Pure twisting may not exist on the catheter. The forces on the catheter are caused by the interface with the heart wall, and the final shape is the result of a no-slip constraint between the paddle of the high-density electrode mapping catheter and the heart wall, so twisting can be combined with bending and / or yaw.

[0127] After numerically integrating the catheter shape along the spine of the catheter, the electrode positions and catheter wire positions on the shape can also be calculated. To calculate the electrode positions and catheter wire positions on the shape, the Darboux frame method can be used. In differential geometry of surfaces, a Darboux frame can be defined as a natural motion frame constructed on a surface. The Darboux frame can be similar to the Fresne-Seret frame applied to surface geometry. The Darboux frame exists at any non-umbilical point of a surface embedded in Euclidean space. To use the Darboux frame method on an embedded curve, S can be a three-dimensional Euclidean space E. 3A directed surface in S. The construction of a Darboux frame on S begins by considering the frame moving along a curve in S and then specializes when the curve moves along the principal curvature. At each point p of the directed surface, the unit normal vector u(p) can be attached in a unique way, provided an orientation is chosen for the normal at any particular fixed point. If γ(s) is a curve in S, parameterized by arc length, then the Darboux frame for γ can be defined as

[0128] T(s)=γ′(s), (unit tangent vector)

[0129] u(s)=u(γ(s)), (unit normal vector)

[0130] t(s)=u(s)×T(s), (tangent normal vector)

[0131] The triple T, t, u defines a positive orthonormal basis attached to each point of the curve: the natural motion frame along the embedded curve.

[0132] Although for Advisor TM For high-density mesh mapping catheters, numerical integration of the twist is not mandatory, but the integration step can also be used to integrate the twist, as this allows changing the torsional stiffness J along the spine. T , thus achieving higher solution accuracy. It is also well-suited to the Darboux frame method for modeling electrodes and curves on the paddle, as described below. Observationally, pure torsion on the catheter has not been confirmed. For example, the forces on the catheter are caused by the interface with the heart wall, and the final shape is the result of the no-slip constraint between the paddle portion of the high-density electrode mapping catheter and the heart wall. Therefore, torsion can be combined with bending and often yaw.

[0133] The Darboux frame of a curve may not produce a natural moving frame on the curve, since it still depends on the initial choice of the tangent vector. To obtain a moving frame on a surface, the Darboux frame of γ can be compared with its Freune–Cerret frame.

[0134] T(s) = γ′(s), (unit tangent vector, as above)

[0135] (Frenet normal vector)

[0136] B(s)=T(s)×N(s), (Frenet binormal vector)

[0137] Since the tangent vector is the same in both cases, there is a unique angle α such that a rotation in the planes of N and B produces the pair t and u.

[0138]

[0139] Taking the derivative and applying the Fresnet-Seret formula yields

[0140]

[0141] Among them, κ g is the geodesic curvature of the curve, κ n is the normal curvature of the curve, and τ rj is the relative twist of the curve (also known as geodesic twist). Using the above scheme, the catheter shape can be calculated using numerical integration along the spine of the catheter operating under bending, yaw, and twist, and the final catheter shape can be obtained using the Darboux frame method. Electrode positions and catheter frame curves can be calculated by orthogonally projecting the two-dimensional catheter shape and electrodes onto a deformed Darboux frame to provide a catheter shape model.

[0142] Figure 7A 190A is shown in the figure.As shown, the orthogonal projection 190A of the two-dimensional catheter shape includes electrode positions 192-1, 192-2, ..., 192-16 (hereinafter referred to as electrode positions 192), and the distance 194 between each electrode position in the electrode positions 192.As shown, the distance between each electrode position in the electrode positions 192 along the flexible tip 196 remains unchanged along the spine of the catheter, which represents the behavior of a physical catheter. However, the spacing between the electrode positions 192-1, 192-2, 192-3, 192-4 and the electrode positions 192-13, 192-14, 192-15, 192-16 on the side of the flexible tip 196 does not remain the same, because the distance between the two sides of the flexible tip 196 may change relative to the size of the force applied to either side.For example, the flexible tip may experience distortion and / or buckling, causing the distance between the electrodes arranged on either side of the flexible tip 196 to change. As shown, electrode locations 192-17, 192-18 are associated with electrodes disposed on the shaft of the catheter and are included in the orthogonal projections.

[0143] Figure 7B The final catheter shape model 190B is shown, where Figure 7A The orthogonal projection 190A is shown having been projected onto a pattern frame 198 to provide a final catheter shape model 190B. Although not shown, Figure 7A The illustrated shaft electrode positions 192-17, 192-18 may also be projected onto a beacon frame 198. The catheter shape model 190B may be used to model the bending, yaw, twist, and buckling of a physical catheter, as discussed further herein.

[0144] Figures 8A to 8D Parameters used to define the catheter shape model of a high-density electrode mapping catheter are shown. Figure 8AAs shown, the catheter shape model 210A can take into account the bending of the flexible tip portion 212A of the catheter about the x-axis defined by line ee. The bending of the flexible tip portion 212A of the catheter is also shown relative to Figure 2B As shown in the figure, the catheter shape model 210A includes a flexible tip portion 212A, which includes multiple electrode positions 214A. Although the catheter shape model 210A includes multiple electrode positions 214A, for ease of illustration, only the electrode position 214A is labeled.

[0145] The catheter shape model 210A also includes frame curves 216A-1, 216A-2, 216A-3, and 216A-4 projected using the Darboux frame method. The catheter shape model 210A is also shown to include catheter shaft electrode positions 218A-1 and 218A-2. In some embodiments, the catheter shaft electrode positions 218A-1 and 218A-2 can be determined using magnetic position sensor positions 220A-1 and 220A-2, also shown in the catheter shape model 210A. The magnetic position sensor positions 220A-1 and 220A-2 can be obtained using magnetic position sensors disposed on the shaft of the catheter shown in the catheter shape model 210A. For reference, the undeflected electrode position 222A is shown as a box to display the deflection difference and representation between the undeflected state represented by the undeflected electrode position 222A and the electrode orientation 214A included in the catheter shape model 210A reflecting the curvature of the flexible tip 212A.

[0146] like Figure 8B As shown, the catheter shape model 210B can take into account the twisting of the flexible tip portion 212B of the catheter along the spine of the catheter and about the y-axis defined by the line ff. The bending of the flexible tip portion 212B of the catheter is also relative to Figure 2B As shown in the figure, the catheter shape model 210B includes a flexible tip portion 212B, which includes multiple electrode positions 214B. Although the catheter shape model 210B includes multiple electrode positions 214B, for ease of illustration, only the electrode position 214B is labeled.

[0147] The catheter shape model 210B also includes frame curves 216B-1, 216B-2, 216B-3, and 216B-4 projected using the Darboux frame method. The catheter shape model 210B is also shown to include catheter shaft electrode positions 218B-1 and 218B-2. In some embodiments, the catheter shaft electrode positions 218B-1 and 218B-2 can be determined using magnetic position sensor positions 220B-1 and 220B-2, also shown in the catheter shape model 210B. The magnetic position sensor positions 220B-1 and 220B-2 can be obtained using magnetic position sensors disposed on the shaft of the catheter shown in the catheter shape model 210B. For reference, an undeflected electrode position 222B is shown as a box to illustrate the deflection difference between the undeflected state represented by the undeflected electrode position 222B and the electrode position 214B included in the catheter shape model 210B, which reflects the distortion of the flexible tip 212B.

[0148] like Figure 8C As shown, the catheter shape model 210C can take into account the yaw of the flexible tip portion 212C of the catheter about the z-axis defined by line gg. The yaw of the flexible tip portion 212C of the catheter is also shown relative to Figure 2B As shown in the figure, the catheter shape model 210C includes a flexible tip portion 212C, which includes multiple electrode positions 214C. Although the catheter shape model 210C includes multiple electrode positions 214C, for ease of illustration, only the electrode position 214C is labeled.

[0149] The catheter shape model 210C also includes frame curves 216C-1, 216C-2, 216C-3, and 216C-4 projected using the Darboux frame method. The catheter shape model 210C is also shown to include catheter shaft electrode positions 218C-1 and 218C-2. In some embodiments, the catheter shaft electrode positions 218C-1 and 218C-2 can be determined using magnetic position sensor positions 220C-1 and 220C-2, also shown in the catheter shape model 210C. The magnetic position sensor positions 220C-1 and 220C-2 can be obtained using magnetic position sensors disposed on the shaft of the catheter shown in the catheter shape model 210C. For reference, an undeflected electrode position 222C is shown as a box to illustrate that the undeflected state represented by the undeflected electrode position 222C includes deflection differences between electrode positions 214C in the catheter shape model 210C, which reflect the yaw of the flexible tip 212C.

[0150] like Figure 8D As shown, the catheter shape model 210D can take into account the bending of the flexible tip portion 212D of the catheter about the z-axis defined by the line hh. The bending shown of the flexible tip portion 212D of the catheter is also relative to Figure 2B 113a and 113b. As shown, catheter shape model 210D includes a flexible tip portion 212D, which includes multiple electrode locations 214D. Although catheter shape model 210D includes multiple electrode locations 214D, for ease of illustration, only electrode location 214D is labeled. Catheter shape model 210D also includes frame curves 216D-1, 216D-2, 216D-3, and 216D-4 projected using the Darboux frame method.

[0151] The catheter shape model 210D is also shown as including catheter shaft electrode positions 218D-1, 218D-2. In some embodiments, the catheter shaft electrode positions 218D-1, 218D-2 can be determined by magnetic position sensor positions 220D-1, 220D-2, also shown in the catheter shape model 210D. The magnetic position sensor positions 220D-1, 220D-2 can be obtained by magnetic position sensors disposed on the shaft of the catheter shown in the catheter shape model 210D. For reference, an undeflected electrode position 222D is shown as a box to illustrate the deflection difference between the undeflected state represented by the undeflected electrode position 222D and the electrode position 214D included in the catheter shape model 210D, which reflects the yaw of the flexible tip 212D.

[0152] Further references Figure 1 , embodiments of the present disclosure may include a computer system 20 configured to determine the shape of a catheter (e.g., catheter 13). In some embodiments, the system 20 may include computer-readable instructions executable by a processing resource 32 to receive a plurality of raw impedance measurements from a plurality of electrodes 17 disposed on a flexible tip portion of the catheter 13. As discussed herein, embodiments of the present disclosure may use raw impedance measurements received from the plurality of electrodes 17, which may be subject to offset and drift. Using raw impedance measurements may reduce the amount of processing resources used to refine impedance data, which may be used by other methods of determining the shape of the catheter.

[0153] In some embodiments, the instructions may be executed to obtain a magnetic position sensor ( Figure 1) receives magnetic position measurements. Based on the raw impedance measurements received from the plurality of electrodes, the angles between the individual electrodes of the plurality of electrodes arranged on the flexible tip of the catheter can be determined. Depending on the type and / or amount of deflection of the flexible tip of the catheter 13, the angles between the electrodes can vary relative to each other, which can provide an indication of the specific shape of the flexible tip. Although offset and / or drift may be associated with the impedance measurements, the electrostatic field in which the electrodes are located can be generally uniform so that the electrostatic field does not have a particularly different effect on one electrode than on another electrode in the domain size of the flexible tip. For example, if offset and / or drift occurs, the effect on all of the plurality of different electrodes can be relatively uniform, which can allow the shape of the flexible tip to be accurately calculated based on the relationship (e.g., angle) between the individual electrodes in the electrodes.

[0154] In some embodiments, even though offset and / or drift may affect each impedance measurement in a generally consistent manner, the impedance measurements may still be subject to offset and / or drift. Thus, embodiments of the present disclosure may alter the determined position of the flexible tip of a catheter based on magnetic position sensor measurements. The magnetic position sensor, which may be disposed in the catheter shaft, remains within a known position and / or orientation of the flexible tip, and therefore also within a known position and / or orientation of the electrodes disposed on the flexible tip. Thus, the magnetic position sensor measurements may be used as a reference point to alter the determined orientation of the flexible tip.

[0155] In some embodiments, the orientation of the shaft of the catheter can be determined based on the magnetic position sensor measurement value.Then, the definite orientation of the flexible tip portion of the catheter can be changed based on the definite orientation of the magnetic position sensor measurement value and / or the shaft of the catheter. In one example, the definite orientation of the flexible tip portion of the catheter is changed so that the definite orientation of the flexible tip portion is aligned with the definite orientation of the shaft of the catheter. In some embodiments, the orientation of the change of the flexible tip portion of the catheter can be used to determine the shape of the catheter as a whole (for example, including the shaft and the flexible tip portion of the catheter). In one example, the definite shape of the catheter can be displayed on a display 23 (for example, a graphical user interface) to a doctor who performs treatment and / or diagnostic operations on a patient.

[0156] Embodiments of various devices, systems and / or methods are described herein. Many specific details are set forth to provide a thorough understanding of the overall structure, function, manufacture, and use of the embodiments as described in the specification and illustrated in the drawings. However, it will be understood by those skilled in the art that the embodiments may be practiced without these specific details. In other cases, well-known operations, parts, and elements are not described in detail to avoid obscuring the embodiments described in the specification. It will be understood by those of ordinary skill in the art that the embodiments described and illustrated herein are non-limiting examples, and it will be understood that the specific structural and functional details disclosed herein may be representative and do not necessarily limit the scope of the embodiments, which scope is limited only by the appended claims.

[0157] References throughout this specification to "various embodiments," "some embodiments," "one embodiment," or "an embodiment" mean that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment. Thus, appearances of the phrases "in various embodiments," "in some embodiments," "in one embodiment," or "in an embodiment" throughout this specification are not necessarily all referring to the same embodiment. Furthermore, particular features, structures, or characteristics may be combined in any suitable manner in one or more embodiments. Thus, particular features, structures, or characteristics illustrated or described in connection with one embodiment may be combined, in whole or in part, with features, structures, or characteristics of one or more other embodiments without limitation, as long as such combination is not illogical or nonfunctional.

[0158] It should be understood that the terms "proximal" and "distal" may be used throughout this specification with reference to the end of an instrument that a clinician manipulates to treat a patient. The term "proximal" refers to the portion of the instrument closest to the clinician, while the term "distal" refers to the portion farthest from the clinician. It will also be understood that, for simplicity and clarity, spatial terms such as "vertical," "horizontal," "upper," and "lower" may be used herein with respect to the illustrated embodiments. However, surgical instruments may be used in many orientations and positions, and these terms are not intended to be limiting or absolute.

[0159] Although at least one embodiment for determining the shape of the conduit has been described above with a certain degree of particularity, those skilled in the art may make many changes to the disclosed embodiments without departing from the spirit or scope of the present disclosure. All directional references (e.g., up, down, upward, downward, left, right, leftward, rightward, top, bottom, above, below, vertical, horizontal, clockwise and counterclockwise) are only used for identification purposes to help the reader understand the present disclosure, and do not constitute a restriction, particularly regarding the position, orientation or use of the device. Connection references (e.g., fixing, attaching, coupling, connecting, etc.) should be broadly interpreted and may include intermediate members between the connections of elements and relative motion between elements. Therefore, a connection reference does not necessarily mean that two elements are directly connected and have a fixed relationship to each other. It is intended that all contents contained in the above description or shown in the accompanying drawings be interpreted as being merely illustrative and non-restrictive. Changes in details or structure may be made without departing from the spirit of the present disclosure defined in the appended claims.

[0160] Any patent, publication, or other public material allegedly incorporated herein by reference is hereby incorporated in whole or in part only to the extent that the incorporated material does not conflict with existing definitions, statements, or other public material set forth in this disclosure. Therefore, to the extent necessary, the disclosure as expressly set forth herein supersedes any conflicting material incorporated herein by reference. Any material, or portion thereof, allegedly incorporated herein by reference that conflicts with existing definitions, statements, or other public material set forth herein will be incorporated only to the extent that no conflict arises between the incorporated material and the existing public material.

Claims

1. A method for determining a shape of a catheter, the method comprising: receiving a plurality of impedance measurements from a plurality of electrodes disposed on a flexible tip portion of the catheter; receiving magnetic position measurements from a magnetic position sensor disposed on a shaft of the catheter; determining an angle between respective electrodes of a plurality of electrodes disposed on a flexible tip portion of the catheter based on impedance measurements received from the plurality of electrodes; using the determined angle to predict a shape of a flexible tip portion of the catheter; as well as A shape of the catheter is determined based on the magnetic position measurements and the predicted shape of the flexible tip.

2. The method according to claim 1, wherein Predicting a shape of the flexible tip of the catheter is based on angles between respective electrodes of the plurality of electrodes associated with a shape model of the flexible tip.

3. The method according to claim 2, wherein: The shape model of the flexible tip takes into account bending, yaw, buckling, and twisting of the flexible tip. 4 . The method of claim 1 , further comprising receiving orientation measurements from a magnetic position sensor disposed on the catheter.

5. The method according to claim 4, wherein Determining the shape of the catheter includes changing the shape of a flexible tip of the catheter relative to an orientation of a shaft of the catheter, wherein the orientation of the shaft is based on position and orientation measurements received from the magnetic position sensor.

6. The method according to claim 1, wherein The plurality of impedance measurements used to determine angles between respective electrodes of a plurality of electrodes disposed on the flexible tip portion of the catheter are raw impedance measurements. 7 . The method of claim 6 , further comprising filtering raw impedance measurements received from a plurality of electrodes disposed on the flexible tip of the catheter.

8. The method according to claim 6, wherein: The method includes transforming the raw impedance measurements from the impedance domain to the magnetic domain using a rigid body transformation, wherein constraints of the rigid body transformation include a known distance between electrodes on the flexible tip.

9. The method according to claim 8, wherein The method further comprises: determining a local field scaling associated with the raw impedance measurement; and The raw impedance measurements are converted to magnetic positions by scaling the raw impedance measurements based on the local field scaling.

10. The method according to claim 9, wherein: The local field scaling is constant across the flexible tip of the catheter.

11. The method according to claim 1 , wherein: The catheter is a mapping catheter; and The flexible tip portion of the catheter on which the plurality of electrodes are disposed is rounded.

12. The method of claim 1, wherein: The catheter is a mapping catheter; and The flexible tip portion of the catheter on which the plurality of electrodes are disposed is paddle-shaped.

13. The method of claim 1, further comprising predicting the position of each of a plurality of electrodes disposed on the flexible tip of the catheter.

14. A system for determining a shape of a catheter, the system comprising: An electronic control unit comprising a processor and a memory, wherein the memory stores instructions executable by the processor to perform the following operations: receiving a plurality of raw impedance measurements from a plurality of electrodes disposed on a flexible tip portion of the catheter; receiving magnetic position measurements from a magnetic position sensor disposed on a shaft of the catheter; determining angles between respective electrodes of a plurality of electrodes disposed on a flexible tip portion of the catheter using raw impedance measurements received from the plurality of electrodes; predicting a shape of the flexible tip of the catheter using the determined angles between respective electrodes of a plurality of electrodes disposed on the flexible tip of the catheter; as well as A shape of the catheter is determined, wherein determining the shape of the catheter includes changing a shape of a flexible tip of the catheter based on the magnetic position measurements.

15. The system of claim 14, further comprising instructions executable by the processor to determine an orientation of the shaft of the catheter based on magnetic position sensor measurements.

16. The system according to claim 15, wherein: The shape of the flexible tip is altered based on the magnetic position measurements such that the determined orientation of the flexible tip is aligned with the determined orientation of the shaft of the catheter.

17. The system of claim 14, further comprising instructions executable by the processor to: determining a local field scaling associated with the raw impedance measurement; and The raw impedance measurements are converted to magnetic positions by scaling the raw impedance measurements based on the local field scaling.

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