Positioning device and method

Abstract

A method for determining the position and orientation of a positioning device having a magnet attached to an oscillating element. The method includes exciting the magnet using one of an external force or a torque, resulting in composite oscillatory motion of the magnet. The compound motion includes rotation and translation of a magnetic moment of the magnet about an axis of rotation, and the axis of rotation is located at an offset distance from a center of the magnetic moment of the magnet. The method includes sensing a magnetic field generated by the magnet using at least one sensor. The method includes determining a position and orientation of the positioning device from the sensing.

Description

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims the priority of German patent application 10 2022 120 495.2 filed on August 12, 2022. The entire disclosure content of German patent application 10 2022 120 495.2 is hereby incorporated herein by reference. Technical Field

[0003] The present invention relates to systems and methods for determining the position and orientation of a positioning device. Background Art

[0004] Localization and tracking of medical robots or tools is necessary for successful in vivo surgery and diagnosis. In particular, methods and devices that can be used without paying special attention to noise interference or signal absorption from biological tissue are the focus of current research.

[0005] Wireless biomedical devices such as endoscopic capsules and tissue markers require reliable localization and tracking using trackers with high spatial and temporal resolution to increase the success of medical procedures or diagnoses.

[0006] Over the years, many localization methods have been developed. However, these localization methods have many disadvantages. For example, harmful radiation from X-rays or computed tomography (CT) or easily interfered magnetic resonance imaging (MRI) are well-established localization techniques for medical robots and tools. However, they cannot be used during typical surgical operations because they require special rooms, large machinery and careful preparation. Millimeter-sized electromagnetic (EM) trackers can be embedded in, for example, diseased tissue under local imaging guidance and tracked in 3D for more efficient radiotherapy. Other trackers, such as trackers with embedded sensors, can provide high spatial resolution, but they are usually too large for feasible applications in the human body.

[0007] From the millimeter to the nanometer scale, robots have gained tremendous attention in the past few decades due to increasingly sophisticated manufacturing techniques, including multifunctional materials and design methods. These robots have been used in medical applications. Current research aims at multifunctionality, miniaturization, device autonomy, energy efficiency, and biocompatibility. While highly developed macroscopic devices such as endoscopes and catheters are in daily clinical use, wireless millimeter-to-nanometer devices are treated with caution due to insufficient position feedback and inaccurate control.

[0008] Ultrasound (US) systems have also been successfully demonstrated for localization of small devices. In vivo applications of such US systems suffer from distortion due to the inhomogeneous wave propagation properties of different biological materials (e.g., bones, organs, muscles), do not provide complete spatial information, and US sources are difficult to implement into millimeter-scale devices.

[0009] Electromagnetic (EM) waves at low frequencies and at radio frequencies (RF) between a few kHz and GHz have very low attenuation in biological materials and do not exhibit harmful effects, making them suitable for use as trackers in human applications. Spatial resolutions below 2 mm and temporal resolutions of 10 Hz have been achieved using multiple embedded coils, each of which has a relatively large size of 8 mm in length. Using highly sophisticated chip designs, integrated sensor circuits have been designed to measure 3D magnetic field gradients on a plate with submillimeter resolution at 10 Hz. However, despite the large penetration depth and high accuracy of RF methods, they are susceptible to magnetic objects in the vicinity of the tracker. Currently, the permanent magnets embedded in the trackers must be relatively large (>6 mm 3 ) to produce measurable fields in deep biological tissue, but is ideal for the purpose of magnetic actuation.

[0010] Magnetic resonance imaging (MRI), widely used in the medical field, is a localization technique that allows in vivo scanning of tissue in 3D. However, MRI suffers from a low temporal resolution above 1 Hz at an equally limited spatial resolution, which makes MRI unsuitable for tracking of sub-millimeter markers.

[0011] Sensors within magnetic fields were studied by Plotkin and Paperno in "3-D Magnetic Tracking of a Single Subminiature Coil with a Large 2-D Array of Uniaxial Transmitters," IEEE Transactions on Magnetics, September 2003, Vol. 5, p. 3295. The authors report on the development of magnetic sensors that measure the magnetic field generated by an external electromagnetic coil. Magnetic devices require a wired connection for energy supply or energy reception and are easily interfered with by medical devices and ferromagnetic objects.

[0012] Atuegwu and Galloway describe a magnetic tracking system in their study "Volumetric characterization of the Aurora magnetic tracker system for image-guided transorbital endoscopic procedures" in Physics in Medicine & Biology, 2008, Vol. 53, pp. 4355-4368. A magnetic tracking system is used for image-guided procedures. The magnetic tracking system comprises a field generator and a coil sensor. The field generator comprises a coil that generates an electromagnetic field. The coil sensor measures the voltage induced by the generated magnetic field in the coil. The induced voltage is then used to calculate the position and orientation of the coil sensor. The coil sensor requires a wired connection for energy supply. The coil is easily disturbed by medical devices and ferromagnetic objects.

[0013] Sharma et al. disclose a wireless tracking system using a magnetic field gradient in "Wireless 3D Surgical Navigation and Tracking System With 100 μm Accuracy Using Magnetic-Field Gradient-Based Localization" IEEE Transactions on Medical Imaging, August 2021, Vol. 40, No. 8, pp. 2066-2078. The tracking system is actuated in the human body during surgical and diagnostic procedures. The tracking system includes a microchip, a magnetic sensor, and an inductor coil. The tracking system is sensitive to the surrounding magnetic field, and the implantable microchip is large.

[0014] A sensed magnetic field generator is described by Fernandez et al. in "High-Accuracy Wireless 6DOF Magnetic Tracking System Based on FEM Modeling", IEEE International Conference on Electronics, Circuits and Systems (ICECS), 2018, 25, pp. 413-416. The authors disclose a magnetic tracking system based on a simplified position estimation algorithm. The magnetic tracking system includes a fixed field generator module for generating a known static magnetic field. The magnetic tracking system also includes a movable receiver module for sensing the generated field, for processing the values ​​of the coordinates of the generated magnetic field, and for transmitting the estimated position and orientation of the marker point. The magnetic tracking system is based on a wired approach.

[0015] Chinese patent application No. CN102274024A discloses a dual magnetic bar rotation search, positioning and tracking system based on a microprocessor, which includes two magnetic bars, a magnetic bar excitation circuit, a rotation device, a magnetoresistive sensor, a signal conditioning circuit, an ADC sampling circuit and a control processing unit. The magnetic bar includes an electromagnetic coil. The magnetic bar excitation circuit generates a magnetic field to excite the electromagnetic coil. The rotation device includes a horizontal rotation stepper motor and a vertical rotation stepper motor, and the two sets of rotation devices respectively control the two magnetic bars to rotate freely in the horizontal direction and the vertical direction.

[0016] Many studies have been conducted on systems that include permanent magnets for determining the position and orientation of positioning devices. Son et al., "A 5-D Localization Method for a Magnetically Manipulated Untethered Robot Using a 2-D Array of Hall-Effect Sensors", EEE / ASME Transactions on Mechatronics, 2016, Vol. 21, No. 2, pp. 708-716, disclose a system based on positioning a tracker by sensing a static magnetic field. The system includes a large permanent magnet that generates a magnetic field. The magnet used for actuation includes three box-shaped orthogonal coils and a soft iron core. The system also includes a sensor array board that includes sixty-four Hall effect sensors that measure magnetic fields in a direction perpendicular to the array.

[0017] Nicolae et al., "Evaluation of a Ferromagnetic Marker Technology for Intraoperative Localization of Nonpalpable Breast Lesions," American Journal of Roentgenology, April 2019, pp. 727-733, describe a handheld probe that can detect the position and distance of a magnetic marker. The method for locating a magnetic marker involves implanting a magnetic marker into a breast lesion and sensing a continuous magnetic field with a handheld probe.

[0018] Passive transponder-based methods are also used to determine the position and orientation of a positioning device. A passive transponder includes an embedded electromagnetic (EM) coil that operates at a radio frequency. The method includes recording the magnitude of the magnetic moment of the electromagnetic circuit and calculating the phase difference between the transmitted signal and the received signal. Willoughby et al., "Target localization and real-time tracking using the calypso 4d localization system in patients with localized prostate cancer" Int. J. Radiation Oncology Biol. Phys., 2006, Vol. 65, No. 2, pp. 528-534, and Hekimian-Williams et al., "Accurate Localization of RFID Tags Using Phase Difference" IEEE RFID, 2010, pp. 89-96 disclose the use of passive transponders.

[0019] The mechanical resonant magnetic structure is called a magnetic field sensor. Japanese patent application No. JP2005201775 discloses a magnetic field sensor including a substrate on which a vibration plate is formed. The sensor also includes a ferromagnetic film on the vibration plate. JP2005201775 discloses a magnetic field sensor including an excitation device for exciting the vibration plate and a detection device for detecting a resonant frequency of the vibration plate, the resonant frequency of the vibration plate depending on an external magnetic field.

[0020] US Patent No. US 8,519,810 B2 discloses a system for magnetic proximity determination. The system includes a substrate and a contact supported by the substrate. A movable element including two distinguishing ends is attached to the substrate. A first permanent magnet is disposed near the first end of the movable element to generate a first magnetic attraction and a first torque on the movable element. A second movable magnet is disposed near the second end of the movable element to generate a second magnetic attraction and a second torque about the rotation axis.

[0021] European patent application No. EP 3 583 896 A1 discloses a method for tracking a marking device or positioning device. The marking device includes a rotationally oscillating magnetic object and a restoring torque unit, which forces the magnetic object to return to the equilibrium position if an external magnetic field has caused the magnetic object to rotate out of its equilibrium position. The disclosed method includes the step of generating a magnetic field, which causes the magnetic object to rotate and oscillate out of its equilibrium position. The rotational oscillation of the magnetic object generates an induction signal. The induction signal is sensed and thereby enables the position and orientation of the marking device to be determined.

[0022] European patent No. EP 2 378 305 B1 relates to a method and system for locating an object. The method of EP 2 378 305 B1 comprises: emitting a magnetic field using a uniaxial source located on one side of a magnetic device, thereby causing a magnetic field to be generated by the magnetic device. The method also comprises: measuring the magnetic field generated by the magnetic device. The emitted magnetic field is subtracted from the magnetic field generated by the magnetic device, and this enables the location of the object to be determined.

[0023] A method for determining the position and orientation of a medical device is disclosed in European patent No. EP 2 034 879 B1. The medical device comprises a positioning device having an antenna and a circuit connected to the antenna. The method of EP 2 034 879 B1 comprises: using a transmission unit to emit electromagnetic radiation, thereby causing the circuit of the positioning device to generate electromagnetic radiation. The receiving unit senses the generated electromagnetic radiation, and this enables the position and orientation of the medical device to be determined.

[0024] U.S. patent application No. US2020 / 0397510 Al describes a tracking system for tracking a marking device or a positioning device. The marking device includes a housing in which a magnetic object is arranged. When an external magnetic field or electromagnetic excitation acts on the magnetic object, the magnetic object oscillates around its axis of rotation. A method for tracking a marking device is also described in US2020 / 0397510Al. The method includes: generating a magnetic or electromagnetic excitation field for inducing mechanical oscillations of the magnetic object, converting the magnetic or electromagnetic field generated by the induced mechanical oscillations of the magnetic object into an electrical response signal, and determining the position of the marking device based on the electrical response signal.

[0025] U.S. Patent Application No. US2022 / 0257138 Al describes a tracking system for tracking the position of a marking device for a medical procedure on a patient's body. The marking device includes a sensing unit, which includes a magnetic object that provides a permanent magnetic moment. The magnetic object is attached to one end of an attachment portion such as a filament, and the other end of the attachment portion is attached to a housing. The magnetic object can be rotated out of a balanced orientation by an external magnetic torque generated by an external magnetic field or electromagnetic field acting on the magnetic object. The rotation of the magnetic object occurs around a virtual rotation axis that passes through the magnetic object in the center, and the magnetic object is rotationally symmetrical relative to the virtual rotation axis. The sensing unit also includes a restoring torque unit. If the external magnetic field or electromagnetic field has caused the magnetic object to rotate out of its balanced orientation, the restoring torque unit provides a restoring torque to force the magnetic object back to the balanced orientation. The tracking system includes a plurality of coils configured to generate a magnetic excitation field or an electromagnetic excitation field for inducing mechanical oscillations of the magnetic object. The plurality of coils are also configured to convert the magnetic field or electromagnetic field generated by the induced mechanical oscillations of the magnetic object into a plurality of electrical response signals. The tracking system also includes a plurality of transceivers configured to be connected to the plurality of coils. The tracking system also includes a processor configured to determine a corresponding position of the marking device based on the one or more electrical response signals. Summary of the invention

[0026] This document discloses a Small Scale Magnetic Oscillation Localization (SMOL) method and device that is capable of wirelessly localizing, i.e. positioning, a tracker such as a millimeter-scale tracker. Using the method and device, the tracker can be positioned in all six degrees of freedom (6DoF) in a viscoelastic environment such as a biomaterial, over large distances and without the use of radiated signals or RF signals. The device is a mechanical resonant structure that utilizes a single and finite magnetic moment in the form of a magnet. The magnet is attached to a micro-cantilever and oscillates around a rotation axis perpendicular to the single and finite magnetic moment at a designed frequency to break the rotational symmetry of the magnet. The structure is excited by an excitation coil and the magnetic signal emitted after the excitation can be sensed by an external sensor unit, which can be evaluated for full six DOF positioning with sub-millimeter accuracy and very high angular accuracy using a single sub-millimeter-sized magnet.

[0027] The structure can also be excited by providing a linear mechanical motion (in the form of a longitudinal or transverse wave) in a direction substantially perpendicular to the long axis of the microcantilever and in the oscillation plane of the microcantilever. This motion excites the magnet on the microcantilever due to the relative motion between the housing and the magnet. The connection between the housing and the magnet is non-rigid, i.e., elastic, and has a finite length (corresponding to the cantilever length of the microcantilever), and the relative motion inputs kinetic energy into the microcantilever, which is converted into elastic (potential) energy of the microcantilever by the deflection of the microcantilever.

[0028] The microcantilever has a resonant frequency, and as would be expected, mechanical excitation of the microcantilever at this resonant frequency will result in an increase in the amplitude of the oscillations each time the housing moves. Since mechanical excitation does not require a magnetic field to excite the resonant structure, this type of excitation does not interfere with the magnetic signal generated by the oscillating magnetic moment. Unlike the prior art, some kind of torsional motion is not required to excite a pure torsional motion of the resonant structure of the device.

[0029] The use of magnets means that the device is compatible with common magnetic actuation schemes, allowing incremental robotic tracking. The SML device combines the frequency-encoded nature of EM devices with the miniaturized footprint of magnets. The alternating magnetic field generated by the oscillating micromagnet is measured at multiple locations and fitted to the magnetic field model by a weighted Levenberg-Marquardt optimization algorithm, allowing accurate determination of all three translational DoFs and three rotational DoFs of the device. The SMOL device can be easily integrated inside a spiral microrobot (millirobot), and the micromagnets can be used for both positioning and propulsion under different magnetic field excitations. The microrobot was tested in a biogel model that mimics human brain tissue and a real pig brain. The results show that full six DoF tracking of the microrobot is achieved with very high spatial resolution, with a spatial resolution of less than sub-millimeter for the three translational DoFs, less than sub-degree for the two rotational axes perpendicular to the cantilever, and about 4° for the cantilever axis. The SMOL approach requires simple instrumentation and exploits the unique frequency response of the device to maintain a high signal-to-noise ratio (SNR) in a magnetically noisy environment. Positioning small robots deep within the human body for practical clinical applications can be envisioned as a field application.

[0030] This document describes a method for determining the position and orientation of a positioning device such as a tracker. The positioning device has a magnet attached to an oscillating element located in the tracker. The magnet is excited using an external force or torque such as an excitation magnetic field or a mechanical wave, and this results in a composite oscillatory motion of the magnet, which produces its own changing magnetic field. The composite motion includes a translation and a rotation of the magnetic moment of the magnet. The composite oscillatory motion is a rotation of the magnet around an axis of rotation, and the axis of rotation is located at an offset distance relative to the center of the magnetic moment of the magnet. The inventors have found that, as emphasized above, the offset distance enables the magnet to be excited using a mechanical wave. At least one sensor is used to sense the magnetic field generated by the magnet, and the position and orientation of the positioning device can be calculated based on the sensing.

[0031] The mechanical waves may oscillate in the longitudinal direction and / or in the shear direction of the oscillatory element.

[0032] The axis of rotation and the magnetic moment vector from the magnet are non-parallel, and in one aspect, are substantially perpendicular to each other.

[0033] The oscillating element is located in a rigid or semi-rigid housing to protect the oscillating element from surrounding biological tissue.

[0034] To avoid saturation of the sensor, sensing is performed with the excitation magnetic field stopped.

[0035] The oscillating element includes a restoring force unit of at least one of a cantilever beam or a similar unit providing an elastic restoring force.

[0036] The actuation, sensing and determination of the position and orientation of the device may be repeated (continuously) or may be discontinuous.

[0037] The excitation frequency of the magnet is close to the resonant frequency of the oscillating element.

[0038] This method can be used to determine the local viscoelastic properties of a material.

[0039] Sensing the magnetic field generated by the magnet may then be used to determine the local viscoelastic properties of the material. The determined local viscoelastic properties of the material may further be used to determine the position and orientation of the positioning device.

[0040] Also taught in this document is a device for determining the position and orientation of a positioning device. The positioning device has a housing in which a magnet attached to an oscillating element is located. The device includes an excitation unit for exciting the magnet using one of an external force or torque, resulting in a composite oscillating motion of the magnet. The composite motion includes a rotation and translation of the magnetic moment of the magnet around an axis of rotation, which is located at an offset distance relative to the center of the magnetic moment of the magnet. The device also includes a data acquisition unit for sensing a magnetic field B generated by the oscillating magnet by using a sensor.

[0041] The magnet comprises a permanent magnet made of a magnetic material, preferably a ferromagnetic material.

[0042] The oscillatory element comprises a restoring force unit and in one aspect is a cantilever.

[0043] The device is used to locate a medical implant in an animal body or a human body, or to locate an anatomical structure, wherein the medical implant is selected from one or more of a catheter, a stent, a guide wire, an endoscope, a capsule endoscope, a drug delivery device or a small robot, and the anatomical structure is selected from one or more of a tumor, a blood vessel, a blood clot, a polyp, and a nerve. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] FIG. 1A shows an overview of the system in the case of magnetic excitation.

[0045] FIG. 1B shows an overview of the system in the case of mechanical excitation.

[0046] FIG. 2 shows a device with a cantilever in a rest position and in a deflected position.

[0047] FIG3A shows a schematic time series of F, θ and B.

[0048] FIG3B shows a real data time signal timeline of F, θ and B. ...

[0049] 4A to 4D show schematic diagrams summarizing four methods for determining the position and orientation of a device.

[0050] 5A to 5C show the results of sensing of the device within the housing.

[0051] FIG. 6 shows the device incorporated into an apparatus comprising interconnected components.

[0052] FIG. 7 shows a flow chart of data evaluation for determining the position and orientation of a device.

[0053] FIG. 8 shows a surface grid of the tracker's measured signal amplitudes in the x-direction.

[0054] FIG. 9A shows the positioning accuracy along the x-axis and the z-axis for translations of 50 mm and 25 mm along the respective axes of the tracker.

[0055] Figure 9B shows the angular accuracy of the rotation of the tracker around the intrinsic z-axis and y-axis. Figures 9A-9B show experimental and simulation results.

[0056] FIG. 10 shows a simulation of the absolute depth error for increasing depth under varying noise and magnet conditions.

[0057] FIG. 11 shows the signal-to-noise ratio of the B-field signal measured in the x-direction for different distances from the sensor.

[0058] FIG. 12 shows the maximum positioning depth at the resonant frequency of the device.

[0059] FIG. 13 shows a view of the housing of the device.

[0060] FIG14 shows the integration of a tracker into a microrobot as a potential implementation.

[0061] Figure 15 shows the positional and angular errors of the device integrated into a microrobot.

[0062] FIG. 16 shows an embodiment where a tracker inside a microrobot is inserted into the gray matter in the cerebrum of a pig brain.

[0063] FIG. 17 shows an image of a tracker inside a microrobot being inserted into brain tissue positioned using ultrasound.

[0064] FIG. 18 shows the results of the amplitude difference of the magnetic field for rotation of the tracker about the z-axis.

[0065] FIG. 19 shows a Maxwell diagram of a tracker in a viscoelastic medium.

[0066] FIG. 20 shows the damping coefficient of the magnetic signal of the device inside gelatin.

[0067] FIG. 21 shows the damping coefficient of the magnetic signal of the device inside animal tissue in vitro.

[0068] FIG. 22 shows an example of the shape of the cavity of the device.

[0069] 23 shows a flow chart for determining the position and orientation of a device. DETAILED DESCRIPTION

[0070] The present invention will now be described based on the accompanying drawings. It will be understood that the embodiments and aspects of the present invention described herein are examples only and do not limit the scope of protection of the claims in any way. The present invention is defined by the claims and their equivalents. It will be understood that the features of one aspect or embodiment of the present invention may be combined with the features of different aspects or aspects and / or embodiments of the present invention.

[0071] FIG. 1A shows an overview of a system for detecting a positioning device or tracker 10 in a (soft) biological tissue 20 using an excitation coil 30 supplied with current for generating an excitation magnetic field and a sensor unit 40 for measuring orthogonal components of time-varying magnetic fields Bx, By and Bz from the tracker 10. FIG. 1B shows an overview of a system for detecting a positioning device or tracker 10 in a (soft) biological tissue 20 using a mechanical excitation source 31 in physical contact through a transmission component 32 for generating mechanical waves and a sensor unit 40 for measuring orthogonal components of time-varying magnetic fields Bx, By and Bz from the tracker 10. As described above, the SMOL method is based on the principle of mechanical resonance of a cantilever structure, wherein an attached magnet 220 generates a finite magnetic moment m, as shown in FIG. 2. The tracker 10 comprises a housing 200 having a cavity 210. In a non-limiting example, the cavity 210 has a rectangular shape. The cantilever structure includes a cantilever 230 (or beam) with a magnet 220 disposed at a first end 235 of the cantilever 230 .

[0072] The magnet 220 is formed of a permanent magnet such as a ferromagnet and serves as a transmitter of mechanical force from the excitation force F to the cantilever 230 and as a transmitter of a varying magnetic field for sensing. In the following description, the magnetic flux density B of the varying magnetic field will be referred to as the B field or magnetic field, and the orientation description will be given as an extrinsic Euler rotation sequence z–x–y from the original orientation (0°, 0°, 0°) of the cantilever 230 in the rest position (solid outline) shown in FIG.

[0073] FIG. 22 shows another example of the shape of the cavity 210. The inventors have found that optimizing the shape of the cavity 210 enables the deflection angle θ of the magnet 220 to be larger. A larger deflection angle θ results in a stronger signal of the magnetic field B, thereby resulting in more accurate positioning of the device 10. In a non-limiting example, it was confirmed by simulation that by increasing the deflection angle from 10° to 20°, the positioning depth defined for a positioning error <1 mm increased by 20%. Since the positioning depth depends directly on the positioning error, by increasing the deflection angle, a higher accuracy at the same distance is obtained. Beyond a deflection angle of 30°, the percentage increase in positioning depth by increasing the deflection angle is greatly reduced.

[0074] For the same internal volume of the cavity 210, the shape of the cavity 210 as shown in FIG22 enables a larger deflection angle θ of the magnet 220 compared to the rectangular shape of the cavity 210 as shown in FIG2 . The optimized shape of the cavity 210 depends on the size and deformation of the cantilever 230, the size and shape of the magnet 220, the movement path 240 of the magnet 220, and the application field. Certain shapes of the cavity 210 are advantageous over other shapes.

[0075] It is recognized that the "optimized" shape of the cavity 210 should be wider so that the magnet 220 has more freedom for rotation and translation within the cavity. However, there is a trade-off between the size of the housing 200 and the strength of the signal. This trade-off must be recognized and depends on the needs of the application. Tracking of tools outside the human body (such as a scalpel) does not require a fairly small tracker 10. A larger tracker 10 with an optimized shape of the cavity 210 can be used. A smaller tracker 210 is advantageous for minimally invasive applications in vivo for tracking tools from outside the body. However, a smaller tracker has the cost of lower signal strength. The shape of the cavity 210 is designed based on the movement path 240 of the magnet 220 on the cantilever 230 (for example, by optical recording). The movement path 240 is estimated by a physical model, for example, by beam theory or by physical assumptions.

[0076] The magnetic field originating from the magnetic moment m of 220 is approximated by the ideal dipole model:

[0077]

[0078] It describes the changing magnetic field B at position r relative to the dipole center 225 =<Bx,By,Bz> components of , and describe m as the magnetic moment vector. is the normalized vector r, I is the identity matrix, and μ0 is the magnetic permeability of free space. With respect to a point in space (in this case the sensor 40), the distance to the dipole center 225 of an arbitrarily oriented cantilever 230 can be described by:

[0079]

[0080] in, is the vector between the sensor 40 and the center of rotation 237 of the cantilever 230, and is the vector between the center of rotation 237 and the dipole center 225 . The fixed position of the cantilever 230 is constant, and the vector depends on the current position of the magnet 220 at time t. When the magnet 220 moves together with the cantilever 230, a circular path of the magnet 220 with radius l0 can be assumed, and the 2D polar coordinates in the xz plane result in:

[0081]

[0082] in, is the length between the dipole center 225 and the rotation center 237, and R q is the 3D quaternion rotation matrix. The time-dependent equation 1 is completed with the static magnetic moment pointing in the positive x direction:

[0083]

[0084] Matrix R y describes the rotation of angle θ around the y-axis in a right-handed coordinate system, B r is the remanent field of the magnet, and V is the magnetic volume. Therefore, the time-dependent oscillating dipole field breaks the rotational symmetry of the static dipole about its magnetic moment axis by rotating about the vertical axis (as expressed by Equations 3 and 4), resulting in Equation 1 for the corresponding position r and the rotation matrix R q Therefore, all six degrees of freedom of the tracker 10 can be determined.

[0085] In the external magnetic field B ext Under the assumption that the magnetic moment m of the magnet 220 is perpendicular, a torque τ is applied to the magnet 220, which forces the magnetic moment m of the magnet 220 to be aligned with B ext alignment:

[0086] τ=m×B ext (5)

[0087] The torque τ is transmitted to the cantilever 230, which results in a restoring torque (bending moment) and an angular deflection θ. Due to the physical boundaries of the available oscillation volume within the cavity 210, the cantilever 230 with the magnet 220 is limited to a maximum angle θ max .

[0088] FIG3A shows a schematic time sequence of magnetic excitation and measurement at a single point for a single sensor 40. The measurement can be divided into an excitation phase (S100) and an evaluation phase (S110). In the first phase, the coil current I 线圈 The excitation coil 30 generates an excitation magnetic field and provides the energy input of the system, which drives the cantilever 230 at the resonant frequency of the cantilever 230, gradually increasing the deflection angle θ. Since the magnitude of the excitation magnetic field F exceeds the measurement range of the sensor 40, the sensor 40 is periodically saturated. During the second stage, the excitation magnetic field F is at time t off The cantilever 230 is closed (S105), and the energy stored in the cantilever 230 is released in an underdamped oscillatory motion, as shown in the second row of FIG. 3A. The position of the magnet 220 moves in space, as shown in FIG. 2 (dashed outline), and is described by equations 2 to 4. The movement of the magnet 220 generates the emission of a changing magnetic field according to equation 1.

[0089] The oscillation of the tracker 10 will now be described using the example in FIG. 3B . It should be understood that the values ​​are not limiting of the present invention and are merely used to illustrate the present invention. The cantilever 230 shown in FIG. 2 was magnetically excited by 10 square wave pulses in the excitation coil 30 at its resonant frequency of 187 Hz and recorded with a high-speed camera. The magnetic signal B in the x-direction for one of the sensors 40 is x (i.e., the x-component of the changing magnetic field of the magnet 220 oscillating on the beam) and the current I in the excitation coil 线圈 The measurement was performed for 0.3 seconds. In FIG3B , I 线圈 The value of the angle deflection θ and the magnetic signal B x At the beginning of the measurement, the external magnetic excitation field F leads to saturation of the magnetometer in the sensor 40, for which the saturation field reaches ±3.5 μT. A direct increase in θ can be seen, which is visually assessed by image analysis at 5000 frames per second. The excitation is at time t off After coming to a stop at θ, an exponential decay of θ can be observed, which can be mathematically described as a damped resonator with frequency f and damping coefficient η:

[0090] θ(t)=θ max sin(2πft)exp(-ηt) (6)

[0091] Similarly, the magnetic signal in direction i and position j can be described in terms of amplitude A, phase shift φ, and offset C as:

[0092] Bi,j(t)=Asin(2πft+φ)exp(-ηt)+C (7)

[0093] The offset C is a constant value that does not change and depends on many factors including the geometry of the system. The approximation in equation 7 is in the vector The length of the vector is much larger than The length of ) and the value of the B-field component does not change sign (since this results in double-frequency distortion in the magnetic signal).

[0094] 4A to 4D show schematic diagrams outlining four methods for determining the position H and orientation T of the tracker 10. All four methods include three main steps: exciting the magnet 220 using an external force or torque F in an excitation step S100, which results in a compound oscillatory motion of the magnet 220; sensing the changing magnetic field B generated by the magnet 220 in step 110; and deriving the position H and orientation T of the tracker in step 120.

[0095] The excitation of the magnet 220 in the excitation step S100 may be continuous, which means that the magnet 220 oscillates continuously, and at a certain moment, the magnetic field B is sensed (S110), and H and T are determined, as shown in FIG4A. As shown in FIG4B, the sensing in the sensing step S110 of B may be repeated during the continuous excitation in the excitation step S100, so that H and T can be repeatedly determined in the determination step S120. After H and T are determined in the determination step S120, the sensing in the step S110 of B may also be repeated.

[0096] The excitation step S100 may be discontinuous, which means that the excitation is stopped in step S105 and the composite oscillation of the magnet 220 decays over time. The magnetic field B is sensed in the sensing step S110, and H and T are determined, as shown in FIG4C. Since the excitation is stopped in step S105, the excitation step S100 is repeated after the sensing step S110 or after the determination step S120 for determining the position H and orientation T of the tracker 10, as shown in FIG4D.

[0097] After the continuous excitation (FIG. 4B) or the discontinuous excitation (FIG. 4D) in the excitation step S100, the sensing step S110 and the determining step S120 of the position H and orientation T of the tracker 10 are repeated so that the position H and orientation T of the tracker 10 over time can be determined. The discontinuous excitation step S100 and the following steps S105, S110 and S120 can be performed, for example, at periodic time steps or when needed.

[0098] 5A to 5C show the results of the sensing step S110 for the exemplary tracker 10 inside the housing 200. The magnetic signal B in the soft gelatin and hard gelatin agarose gels was recorded within 60 ms. FIG. 5A shows the magnetic signal B in FIG. 5A and FIG. 5B in the time domain and FIG. 5C in the frequency domain under the excitation (t shifted =0) after measuring the Bx component of the changing magnetic field B.

[0099] A small buffer of 3 ms was applied between the end of the excitation and the start of the evaluation as the excitation coil cools down. It can be seen that the raw signal exhibits low frequency noise, which can also be seen in the discrete Fourier transform (DFT) in Figure 5C. A high pass filter at the (higher) resonance frequency was applied, as shown in the filtered signal.

[0100] For this signal, Levenberg-Marquardt algorithm can be used to fit equation 7 to extract the characteristics of damped sinusoids (Fig. 5A and Fig. 5B, solid line). Due to damping behavior, the peak in DFT (Fig. 5C) appears wide, and the frequency resolution with 17Hz is very low, which makes the analysis of spectrum inaccurate. Fig. 5C also shows a 10s record of the noise magnetic environment in which all tests are performed. The strongest noise amplitude with up to 56nT is measured at 16.7Hz, 28Hz and 50Hz. The prominent frequency above 100Hz is about 2.5nT, which results in the limitation of positioning distance.

[0101] The tracker 10 may be incorporated into an apparatus 5 comprising interconnected parts as shown in Fig. 6. Here, for demonstration purposes, excitation using a magnetic excitation field is presented. Iterative device control and data processing are performed in MATLAB.

[0102] The sensing unit 40 includes three fluxgate sensors arranged orthogonally to the custom printed element and attached to the 2D positioning stage 45 by a 75 cm long rod to reduce the magnetic influence from the motor driving the positioning stage. The sensor 40 is moved to the position of the grid pattern in the xy plane. At each position, the estimated resonant frequency f res The predefined excitation signal at is sent to the current amplifier 35 and is also related to the current I 线圈 are sent together to the excitation coil 30. The alternating current (AC) induced into the excitation coil 30 generates an AC magnetic field, which can excite (S100) the mechanical resonance structure of the tracker 10 through the excitation force F as described above.

[0103] An exemplary signal evaluation process S120 is shown in FIG7 . It will be appreciated that the sensor signal recorded by the sensor 40 includes the excitation signal from the excitation coil 30 and therefore, initially, the evaluable signal is separated at a cut-off time. The cut-off time depends on the behavior of the excitation coil 30 and the individual configurations of the sensor 40. The calculation has a dependence on f exct The moving average of the window length of , which is used as a low-pass filter S121. The moving average is subtracted from the original signal B to obtain a high-pass signal, which includes the resonant frequency signal of the cantilever 230.

[0104] The Levenberg-Marquardt algorithm is deployed to fit Equation 7 to the signal to obtain the relevant free parameters of Equation 7 (S122). The signal amplitude obtained in step S122 can be further filtered in step S123 using parameters such as frequency, damping coefficient, or a determined coefficient. The threshold value of the physically unreasonable value in step S123 from step S122 can be, for example, a defined fixed value.

[0105] Throughout the process of S121 to S123, the acquired amplitude A (exemplarily shown in the x direction in the surface grid of FIG. 8 ) is used as input to the final positioning step S124. The above mathematical model M with a fixed cantilever length l0 of the cantilever 230 and a constant magnetic moment m (t=0) of the magnet 220 is used for a weighted Levenberg-Marquardt algorithm with the following cost function and weighting matrix W,

[0106]

[0107] in, is the optimized amplitude matrix of the magnetic signal at sensor position j calculated by the following equation,

[0108]

[0109] Where p is a vector of optimization parameters including position x, y, z, orientation given as quaternions q0, q1, q2, q3 and deflection angle θ. The parameters are randomized within a physically reasonable range and the optimization algorithm is repeated a fixed number of times to avoid outliers. After automatically selecting the best fitting parameters p, the position H and orientation T of the tracker 10 are obtained.

[0110] To demonstrate the positioning accuracy, both real experiments and simulations using a model M were conducted. Since it is difficult to establish a visual ground truth with respect to the measurement plane with an accuracy of less than 1 mm, differential measurements were performed.

[0111] FIG. 9A shows the positioning accuracy along the corresponding axes for a translation of 50 mm and 25 mm along the x-axis and z-axis. Along the x-axis, the positioning value perfectly matches the reference truth value over the entire 50 mm range (which is half of the total 100 mm x 100 mm scan plane), with an average accuracy of 0.6 mm ± 0.6 mm, and the maximum difference from the reference truth is 0.6 mm at the edge of the scan area. Since the scan area is symmetrical along the x-axis and y-axis, respectively, the errors in the -x, -y, +y directions are expected to be similar to +x. For the z-axis, the average accuracy is 0.7 mm ± 0.9 mm at z distances between 50 mm and 75 mm. Here, it can be noted that the accuracy decreases at greater distances because the magnetic field decays on the cube of the distance according to equation 1. Less than 65 mm distance, the accuracy is 0.5 mm ± 0.6 mm. Overall, the translation accuracy in all directions is significantly less than 1 mm, revealing the high accuracy of the SMOL method.

[0112] Fig. 9B shows the angular accuracy for the rotation around the intrinsic z-axis and y-axis (Fig. 2) respectively. In order to determine the angular deviation, the axis perpendicular to the axis of rotation is used as a reference, and the standard deviation is calculated using circular statistics. For the rotation around the cantilever axis, i.e. the z-axis (Fig. 2), the accuracy reaches 3.4 ° ± 3.7 °, and for the rotation around the y-axis, the accuracy is significantly better, wherein, 0.7 ° ± 0.8 °. Due to the orthogonality of the axis of rotation, similar accuracy can be expected for the rotation around the magnetic moment axis (x-axis). In general, compared with the other two axes perpendicular to the cantilever, the cantilever axis shows more changes, but all rotation positioning accuracy is significantly less than 5 °.

[0113] The simulation results are also shown in Figures 9A and 9B and match very well with the experimental results for all accuracy measurements. It reveals that the numerical model clearly represents the important features of the SMOL approach, since the numerical model takes into account magnetic noise in all directions. The agreement between simulation and experiment validates the numerical model, and thus the latter provides a valuable method to predict and optimize the performance of the tracker 10 with reduced size and increased measurement distance.

[0114] To gain insight into the performance of the SMOL method under different magnetic noise conditions, the absolute depth error z is simulated for increasing depth z under different noise and magnet conditions. err. As shown in Figure 10, the reference curve (black) represents a system with a noise factor (NF) and a magnetic moment factor (MF) both equal to 1, which means that the noise and magnetic moment used for the simulation are the same as those in the experimental setup. The effect of halving the noise (NF=0.5, MF=1) or halving the magnetic moment (NF=1, MF=0.5) is shown. It is observed in all curves that the positioning error remains at a very low (sub-millimeter) level at close distances, but increases sharply above a certain threshold. The maximum positioning distance is defined as the distance at which the positioning error first reaches 0.5mm (dashed horizontal line). The simulation results reveal that a tracker with half the magnetic moment can be accurately positioned up to a distance of 65mm, and that attenuating the magnetic noise by half can increase the distance to 90mm. In a magnetically shielded room (considering only the electronic noise of the magnetic sensor), a maximum detection distance of 110mm can theoretically be achieved. Overall, operating in a magnetically shielded or low-noise environment and using an even more sensitive magnetometer (40) can significantly increase the localization depth to over 100 mm, making the SMOL approach applicable to real clinical localization tasks, such as small robots deep within the human body.

[0115] The signal-to-noise ratio (SNR) of the B-field signal measured in the x-direction is presented in FIG11 for different distances z from the sensor. Since a high-pass filter S121 is applied to the damped sinusoidal signal, pure noise is treated similarly. Without removing frequencies less than 270 Hz (which is the resonant frequency of the tracker), the standard deviation of the noise reaches 20.9 nT, and with filtering, the standard deviation of the noise drops to 1.7 nT. 1.7 nT is used for evaluation, and the amplitude A is the highest measured amplitude after filtering. As shown in FIG11 , the SNR in the simulation is greater than 170 at a distance of 45 mm, and 25 at a distance of 80 mm, and the trend matches the model of the magnetic field decaying with the cube of the distance very well. The good fit with the experimental data again indicates the correct modeling of the physical process in the simulation.

[0116] Thus, the simulation reflects the real system with high accuracy, and in other words, the real system behaves ideally enough to be simulated numerically, and further characterization of the tracker 10 is performed numerically.

[0117] The frequency scalability of the SMOL approach is presented in FIG12 . The maximum localization distance (black) using a cutoff threshold of 0.5 mm localization error (dashed horizontal line in FIG10 ) was simulated for frequencies ranging from 100 Hz to 1 kHz using the recorded noise ( FIG5C ). It can be observed that the localization depth increases significantly by increasing the frequency. For example, for the tracker 10 at 100 Hz, the maximum localization distance is about 60 mm, and for the device at 800 Hz, the distance almost doubles to 120 mm. The main reason is the magnetic noise (from the environment and the sensing electronics) AN (grey) has an overall decreasing amplitude over frequency. It is noteworthy that there are strong noise amplitudes (shown as grey squares) at specific frequencies such as 250 Hz, 350 Hz and 450 Hz. Strong noise at these frequencies seriously hinders the positioning distance (black squares). Therefore, the optimal operating frequency for the SMOL method should be selected where the environmental and sensor inherent noise is minimal.

[0118] The increase in resonance frequency will not only lead to an increase in the maximum positioning distance, but also enable the tracker 10 to be further reduced in size. Using the two-dimensional geometric model of the spatially constrained cantilever 230 ( FIG. 2 ), a 1 mm 3 The result is shown as the black star in Figure 12. It has a total volume of 0.4mm 3 (1mm x 0.8mm x 0.5mm), a maximum deflection angle of θ = 17°, and a cantilever 230 length of 0.5mm. To obtain a resonant frequency of 800Hz for such a device, a steel cantilever with a thickness of approximately 5μm and a width of 1mm is required. Applying MEMS manufacturing techniques, it is feasible to construct such a device, which will achieve sub-millimeter accuracy, full 6DoF positioning at distances 100 times the size of the tracker. Therefore, the SMOL approach can open up unprecedented possibilities for the positioning and tracking of sub-millimeter implants deep in the human body, including small robots.

[0119] The method described in this document uses magnets 220, which can also be used for magnetic actuation of small robots. During actuation, a magnetic torque (Equation 5) around the cantilever axis is applied to the micromagnet 220, and the cantilever 230 is able to transmit the torque to the housing 200, which causes the rotation of the tracker 10.

[0120] In one embodiment of the proposed method and apparatus, as shown in FIG13 , the housing 200 may have a spiral or screw-like shape 201 on the surface to couple rotation to translation and thus propel in the soft viscoelastic material. Special care is taken in the robot R design to avoid damaging the thin cantilever 230. If the magnet 220 is free to rotate without angular constraints, the strong magnetic torque will keep twisting the cantilever 230 and exceed the strength limit of the cantilever material, which results in permanent plastic deformation and fracture of the beam 230. Geometric constraints inside the housing 200 (see FIG13 ) are added to transmit torque to the housing 200 by direct contact.

[0121] In one embodiment, the tracker 10 is integrated into a milli-robot R moving on a path P as shown in FIG. 14 . The actuation of the screw-shaped robot R is performed using a rotating permanent part with two rotation axes. In the case of forward propulsion, the actuation axis must be aligned with the cantilever axis. In order to turn the robot R, it is necessary to rotate the actuation magnet around the steering axis. Since simultaneous actuation and positioning are currently not possible with the SMOL method, the measurements (HT1 to HT9) are performed incrementally, which means that the container is transferred between the actuation setting and the positioning setting.

[0122] A detailed analysis shows that the in-plane position error (x, y in FIG15 ) obtained at a distance of 40-50 mm from the sensor is an average of 0.2 mm ± 0.1 mm compared to the visual reference truth. The z position is stable near an average of 50.3 mm ± 0.6 mm. The total average error of the angular measurements of the in-plane angle ψ is 4.7° ± 3.6°, with an average standard deviation of 1.5° for all measurement points. These results demonstrate the possibility of precise positioning using the proposed method; in addition, they demonstrate the possibility of using the same magnetic moment m on a miniaturized robot R for both actuation and positioning purposes. In one embodiment, the tracker 10 or robot R can be inserted into biological tissue, such as the brain, which is known to be one of the softest tissues in the human body. Strong mechanical damping behavior is expected to hinder mechanical oscillators in brain tissue, which creates additional challenges for obtaining a continuous oscillation signal of the tracker 10 for precise positioning.

[0123] Therefore, brain tissue was chosen as a realistic and rigorous testing environment for the proposed method. Figure 16 shows the results of the proposed method working in an isolated pig brain. It shows half of a pig brain and the tracker 10 inside the robot R inserted into the gray matter in the brain. US imaging is used to obtain planar information of the location H of the tracker 10 relative to the rigid boundaries of the container.

[0124] As shown in Figure 17, due to multiple reflections and scattering of the US beam in the inhomogeneous brain tissue, the overall US imaging resolution and contrast are poor. The robot R (circled) is almost indistinguishable from the background noise at a distance of 40mm from the US probe. In contrast to US imaging, the SMOL method accurately detects the position H and orientation T of the robot R in the brain. As shown in Figure 6C, the positioning information H, T is superimposed with the US image, and a very good correlation is found between the two positioning methods. At a distance of 4045mm z from the magnetic sensor, the standard deviation of 10 independent measurements is 0.9mm in the x direction and 0.7mm in the y direction. This reveals the high reproducibility of the proposed method in biological soft tissue. The white arrow indicates the detected orientation H of the main axis of the robot R, which is very well aligned with the estimated orientation by US imaging. See a displacement of about 3mm in the y direction. This systematic error may be caused by the deformation of the soft tissue under the pressure of the US probe, because the probe must be in close contact with the brain tissue through ultrasound gel during imaging. It indicates another important advantage of the proposed method over US imaging, namely, it is a wireless localization method that does not require any mechanical contact with biological tissues, which may be a crucial aspect in protecting fragile soft organs such as the brain in practical clinical applications.

[0125] The proposed method provides a completely wireless positioning technology that does not require physical contact of external devices 30 and 40 with soft tissue 20, which will benefit minimally invasive and robotic surgery, where direct contact of imaging probes with internal organs is generally not possible. The minimum incision required to insert the tracker 10 into the body is very small, and it can be easily introduced via a needle, catheter or endoscope. It has a small footprint and does not require an onboard power supply, which makes it easier to integrate with wireless medical devices such as capsule endoscopes and implants. The high SNR (Figure 11) and high accuracy over large distances (Figure 10) as well as its small size (Figure 12) exceed the possibilities of other wireless tracking methods such as those based on static permanent magnets. The tunable, unique frequency response of the tracker 10 helps to isolate it from DC and low-frequency magnetic noise (i.e., magnetic surgical tools).

[0126] In one embodiment, the unique frequency response of the tracker 10 enables identification of multiple trackers 10 in frequency space for multi-target 6DoF simultaneous localization.

[0127] The proposed method breaks the rotational symmetry of a static magnetic dipole by oscillating the magnetic moment about an axis perpendicular to the magnetic moment axis. A pure rotation of the magnetic moment, i.e. l0=0, means that the difference of the B field and the two peak deflections -θ and +θ produces a new dipole field that can be measured at the resonant frequency of the tracker 10 according to equations 1 to 4. This mathematical consideration means that only 5DoF can be determined, which is the same as the 5DoF of a static magnetic dipole.

[0128] To overcome this limitation, a translation is added to the rotation of the dipole moment, l0>0 (Figure 2), and the new dipole field can no longer be described as a 5DoF dipole, so the symmetry about the rotation axis of the dipole is broken. The difference between the two cases, represented by the solid line with the cantilever 230 and the case without the cantilever 230 represented by the dashed line, is shown in Figure 18. The tracker 10 is rotated about the z-axis and the amplitude difference of the oscillating magnetic field in the millitesla range can only be detected when the cantilever 230 is present to offset the oscillating magnetic moment m (Figure 2), while in the absence of the cantilever 230, the amplitude difference is close to or equal to zero. The high asymmetry of the amplitude for all rotations between 0° and 180° reveals the amplitude encoding feature of 6DoF determination using the proposed method.

[0129] In the measurement, only the amplitude difference is considered as useful information instead of the absolute DC magnetic field, because the DC field is affected by high noise and is not robust enough to detect such a small device at a long distance.

[0130] Another way to establish 6DoF is to capture the dual frequency component of the oscillating B-field. Due to the high spatial nonlinearity of the dynamic B-field component of the magnetic dipole, the amplitude field of the oscillating dipole has zero crossings. If the sensor position is located near such a zero crossing, the B-field signal shows a component at twice the resonant frequency. However, these features can only be reliably measured when the B-field is closely scanned. In contrast, the proposed method including the cantilever 230 provides a unique and more convenient way to detect all 6DoF with far fewer magnetic sensors 40 and does not rely on such features.

[0131] Due to the use of a single excitation coil 30, not all orientations of the tracker 10 can be sufficiently excited to achieve a large deflection amplitude. These blind spots occur at orientations where the magnetic moment τ (Equation 5) applied to the cantilever 230 by the external excitation field F (Figure 3) is close to or equal to zero. This is the case when the external field is parallel to the magnetic moment axis. Between perpendicular and parallel and aligned, τ gradually decreases, so that the maximum deflection is not always achieved. In order to cover all orientations, a total of three excitation coils 30 arranged in orthogonality are required, and the direction of the superimposed B field should preferably be parallel to the previously detected orientation T of the cantilever 230. Omnimagnets may be suitable for this application.

[0132] The proposed system (Figure 6) is a 2D scanning system that covers 25 points within a square with a side length of 10 cm in the xy plane. Since the range of the fluxgate sensor 40 is about ±3.5μT, the sensor is easily saturated when a strong ferromagnetic object is close to the scanning area. The manual B-field compensation function embedded in the sensor 40 is only used once in the center of the scanning area to compensate for the external B-field. If the B-field gradient along the scanning plane is larger than the range, the process cannot pick up a signal. In the future, automatic DC magnetic field compensation can be performed at each location, or a static sensor array 40 can be used.

[0133] Since the tracker 10 is a mechanical system, it can change its characteristics over time and use. The material used for the cantilever 230 (C1095) has a very low chromium percentage and is particularly susceptible to corrosion. Oxidation can be expected to weaken the cantilever 230, as a decrease in the resonant frequency over time has been observed in many prototypes. However, all cantilevers 230 are sealed and rarely used devices show much less or no decrease in the resonant frequency over time. Other possible explanations could be that the fixed end of the cantilever has loosened due to glue deterioration, causing the beam l0 to lengthen or that the Young's modulus E of the cantilever has decreased due to dynamic fatigue.

[0134] In one example, the determination of the position H and orientation T of the device 10 in the determination step S120 is performed by performing Fourier analysis on the signal of the magnetic field B in step S200 to obtain the amplitude A of the magnetic field B in the frequency domain in step S210. The position H and orientation T are determined according to the magnitude of the amplitude A of the magnetic field B between the sensors 40.

[0135] In another example, the determination of the position H and orientation T of the device 10 in the determination step S120 is performed by using a physical model of the oscillation of the magnet 220 in step S300. FIG. 23 shows that the determination step S120 includes a signal that directly evaluates the magnetic field B in the time domain in step S300. In step S310, the physical model uses the known value or calibrated value of the magnetic moment m of the magnet 220 required for step S300, the offset distance between the center of the magnet 220 and the center of rotation. Unlike the prior art, the magnet 220 does not rotate around its own axis, so the dipole center 225 is not the center of rotation of the magnet 220. The center of the magnet 220 is in most cases its center of mass. In step S300, the physical model also uses the maximum deflection angle θ, the signal damping ratio, the number and position j of the sensors 40. More physical parameters, such as air resistance, moment of inertia, elastic modulus of the beam, etc., can be added to refine the physical model.

[0136] Compared to Fourier analysis, the use of a physical model enables the necessary recording time of the signal required for the positioning device 10 to be reduced. This will now be explained. Determining the spectral components of the signal in the frequency domain requires a large number of periods, for example 10 or 40, in order to obtain a peak sharpness of the signal sufficient to accurately locate the positioning device 10. The physical model enables the necessary recording time of the signal to be reduced to an integer multiple of the half period N of the oscillation, and possibly also to a fractional multiple of the half period N of the oscillation. By using a physical model, the oscillating motion and the resulting recorded signal are well defined for any position T and any orientation T.

[0137] In step S300, the physical model is fitted to the time domain signal, thereby generating optimized parameters of the position H and orientation T. The time domain signal includes a half period N. An algorithm such as the least square method minimizes the error between the physical model of the signal and the recorded signal B in step S300. The minimum error is obtained for the optimized parameters, thereby obtaining the precise position T and orientation H of the positioning device 10. Since the random noise from the environment is averaged, the positioning accuracy of the positioning device 10 is further improved by increasing the number of half periods N.

[0138] In another example, the time domain signal is segmented into a desired integer number of half cycles N_seg. The desired integer number of half cycles depends on the required accuracy. Therefore, only a single excitation is sufficient to locate the positioning device 10 multiple times.

[0139] For example, a positioning device 10 with a resonance frequency of f=100 Hz can be positioned at a rate of twice the resonance frequency, i.e. 200 Hz, when each half cycle N is evaluated independently (N_seg=1). When two half cycles N are evaluated per segment, i.e. N_seg=2, the positioning rate can be 100 Hz. When four half cycles N are evaluated per segment, i.e. N_seg=4, the positioning rate can be 50 Hz. An increase in the number of half cycles N_seg results in a reduction in the maximum achievable positioning rate to 2*f / N_seg. Very high speeds of the positioning device 10, such as >200 mm / s, or very precise movement paths P are measured using the segmented method. The signal decays over time, so that the signal strength and positioning accuracy decrease until the positioning device 10 needs to be excited again. A continuous or weakly damped oscillation of the magnet 220 results in a continuous or weakly damped signal, and is therefore preferred over a discontinuous or highly damped signal to avoid re-excitation pauses during which the positioning device 10 cannot be positioned.

[0140] The positioning device 10 (i.e., tracker) can be positioned during the excitation if the magnetic field from the excitation coil does not saturate the sensor 40. The positioning device 10 (i.e., tracker) can be further positioned during the excitation if the magnetic field from the excitation coil at the sensor 40 is zero or very low.

[0141] Another method for localizing the locating device 10 is to mechanically actuate the locating device 10. Mechanical actuation does not disturb the sensor 40 and enables continuous localization, ie tracking, due to continuous actuation of the locating device 10 without pauses.

[0142] Example

[0143] Positioning system equipment. Iterative system control and data processing were performed in MATLAB (R2020b, MathWorks, USA). For signal transmission and analog signal conversion, a data acquisition board (USB-6343, NI, USA) with an input range of ±11 V and 16-bit resolution (corresponding to 0.33 mV resolution) was used. Weak magnetic fields were measured with three fluxgate sensors (Fluxmaster, StefanMayer Instruments, Germany), which were arranged orthogonally to a custom 3D-printed bracket. They are set up with manual offset compensation and have a sensitivity level of 1 V / μT, a range of approximately ±3.5 μT, a resolution of 0.1 nT, and an inherent noise of 20 pT Hz at 1 Hz. -1 / 2 . The sensor holder is attached to a 2D robotic positioning stage (M-414.2PD, 0.1 μm step size, PI, Germany) on a 75 cm long non-magnetic rod (polymethyl methacrylate) to reduce magnetic influences from the motor. Using this positioning stage, 25 points in a 5×5 point grid pattern in the xy plane are scanned. To excite the tracker 10, a custom electromagnetic coil 30 (0.56 mm diameter enameled copper wire, 150 turns on a 60 mm×50 mm×15 mm 3D printed mandrel) is built to generate a nearly uniform magnetic field above the coil 30 (1 mT at a distance of 30 mm). It is powered by a current amplifier 35 (A1110-05-E, HUBERT, Germany) with a gain of 1 V to 5 A. The current amplifier enables electrical components to be regulated by current rather than voltage, which is essential for fast and precise cooling of the electromagnetic coil 30. Between the end of the excitation phase S100 and the start of the evaluation phase S110 , a short buffer time of 3 ms is applied to avoid interference of the magnetic signal by coil cooling.

[0144] The noise data of the fluxgate sensor 30 in the shielded room used for simulation in this study was provided by the manufacturer (StefanMayer Instruments). For spatial and angular accuracy measurements, a manual linear stage with a resolution of 10 μm (PT1, ThorLabs, Germany) and a manual rotation stage with a resolution of 0.1° (XRR1, ThorLabs) were used to accurately translate and rotate the tracker 10, respectively. The translation along the x-axis was measured from 0 to 50 mm in steps of 10 mm. The translation along the $z$ axis was measured at a distance of 50 mm to 75 mm from the sensor origin. In the values ​​presented, positive z is defined as being further away from the sensor plane. The rotation around the system x-axis was measured from 0 to 90° in steps of 30°, and the rotation around the system y-axis was measured from -45° to 45° in steps of 15°. Each measurement was repeated 10 times independently. The mean and standard deviation were calculated and compared with the baseline true difference of the two corresponding positions. Statistical analysis was performed in MATLAB.

[0145] Due to the inaccuracies of manual manufacturing, each tracker 10 can have a unique frequency response even when using the same cantilever material, so the individual resonant frequencies must first be determined after manufacturing. Therefore, for each tracker 10, the amplitude filter parameters (S123) must be adaptive. Although a threshold of ±5\% of the excitation frequency is selected for the frequency filter, the damping coefficient threshold needs to be adjusted for each embedding material. The acceptable range for hydrogels used for precision measurements is set to 5s -1 Up to 30s -1 , and the acceptable range for tracking demonstrations is set to 30s -1 To 70s -1 These ranges were found to be optimal for the respective materials. Factors that directly influence the damping coefficient, such as proximity to the container wall or wetting of the surface of the tracker 10 from its environment 20, lead to the selection of larger margins.

[0146] To avoid such outliers, a boundary condition within the algorithm is employed that restricts the position H to the area below the sensing array within a volume of 10 cm × 10 cm × 10 cm. i is ±1, and the deflection angle θ is between 0° and 20°. The starting value is randomized within the above range, and the complete algorithm is repeated 10 times, from which the highest R 2 The values ​​are chosen to best fit. The choice of a large number of parameter limits makes the algorithm very robust to fluctuations, however, special attention must be paid to amplitude filtering to provide sufficient and correct information to the optimization algorithm.

[0147] After fitting the B-field signal (S121), another filtering step (S123) is applied to the signal with element A i,jThe main goal of the amplitude filter S123 is to detect physically unreasonable and strongly distorted results from the previous fitting process S121 and adjust the amplitude accordingly. This is crucial because amplitude distortion or outliers directly affect the efficiency and quality of the subsequent optimization S124. Here, three main filters are applied: frequency filter, damping coefficient filter and R 2 filter, from which the weight matrix W is derived. Outliers can be automatically detected by using a threshold around physically plausible values ​​(e.g., the excitation frequency). Since the damping coefficient depends on the embedding material of the tracker, the threshold must be adjusted accordingly. 2 , due to the redundancy from the physical frequency and damping filters, a larger cutoff value can be chosen. If any value lies outside the mentioned threshold, its corresponding amplitude A=0 and R 2 = 1, rather than removing it from the evaluation entirely. This step increases the amount of information passed to the subsequent optimization S124, since no detectable oscillations mean that the amplitude is very close to zero. The remaining values ​​within the threshold are simply passed to the amplitude matrix and R 2 matrix, and both matrices are used for final positioning S124.

[0148] The wireless tracker 10 includes two main parts: a spiral shell 200 and a mechanical resonant structure with attached micromagnets. The shell 200 is designed using computer-aided design (CAD) software (Inventor Professional 2021, Autodesk, USA) and printed using a stereolithography 3D printer (3L, Formlabs, USA) with a resolution of 50 μm and a translucent resin (Clear V4, Formlabs). Inside the shell 200, the cavity 210 is designed to allow attachment of the cantilever and sufficient space for bending. The oscillation frequency can be tuned by selecting the size and material of the cantilever 230 to achieve a frequency in the range of less than 50 Hz to 1000 Hz. In this work, a 3.5 mm x 0.5 mm x 30 μm strip (C1095 spring steel, Precision Brand, USA) was cut by laser (MPS Advanced, Coherent, USA) to form the cantilever 230, and two 1 mm x 0.5 mm (diameter x length) cylindrical NdFeB magnets 220 (N52, Guys Magnets, UK) with axial magnetization were attached to the end of the cantilever 230 using cyanoacrylate adhesive (Loctite 401, Henkel, Germany).

[0149] The total theoretical magnetic moment is 0.89mAm 2The cantilever 230 with the fixed magnet 220 is inserted into the housing cavity 210 and closed with a 3D printed cover. Overall, the dimensions of the spiral prototype tracker 10 are 3mm x 7mm (diameter x length).

[0150] The total theoretical magnetic moment is 0.89mAm 2 To avoid separation of the parts, cyanoacrylate adhesive was used. The cantilever 230 with the magnet 220 was manually inserted into the volume of 10 mm. 3 The cantilever 230 is placed in the cavity 210 and closed with a suitable print. Overall, the dimensions of the spiral prototype tracker are 3mm x 6.5mm. Many materials are suitable for the cantilever 230, such as spring steel, Nitinol or biaxial polyethylene terephthalate (PET). The resonant frequency increases with the increase of the elastic modulus of the material, however the thickness and width of the cantilever 230 are parameters to be considered.

[0151] Embedding material. In order to simulate the viscoelastic properties of biological tissues, as previously reported, a gelatin-agarose mixture was used as a tissue phantom in this study to simulate brain tissue. A hydrogel with 6wt.-% gelatin (Type A powder from pig skin, Sigma-Aldrich, Germany) and 3wt.-% agarose (Sigma-Aldrich) was used. The two components were stirred in double distilled water at 80°C for 30 minutes, placed in a plastic container and cooled to 22°C for at least 4 hours before use. A rectangular container with a size of 50mm x 60mm x 15mm and a cylindrical container with a size of 30mm x 90mm were used. In order to demonstrate the propulsion of the microrobot, a hydrogel with 3wt.-% gelatin and 0.2wt.-% agarose was used. All experiments were performed at room temperature (22°C).

[0152] Simulation. In order to simulate the B-field signal of the SMOL device after excitation, a damped resonator model with an initial angular deflection of θ = 12° was used. The corresponding differential equation of θ was solved using Simulink (MATLAB) and used as a time-varying input parameter of the oscillation. First, system dependent variables such as cantilever length, magnetic moment, position H and orientation T were defined, and the movement of the magnetic moment in space was calculated by equations 1 to 4. By calculating the time-dependent equation 1 according to the cantilever motion at the same position of the sensor 40 and adding the recorded noise (Figure 5C) to the signal B, an accurate representation of the real measurement is achieved. Since the magnetic noise is strongly dependent on the direction, three different noise signals (one signal for each direction) are applied to the corresponding B-field signal, and in addition, a random phase shift of the added noise is introduced to reflect any noise phase in the actual measurement. The analog-to-digital conversion is also simulated by subdividing the data into bit-related increments according to the DAQ characteristics. Further data evaluation and positioning optimization S120 are performed based on the actual measurement settings. The numerical simulation is implemented by custom code in MATLAB.

[0153] Mechanical excitation. As shown in FIG. 1B , the tracker 10 can also be excited by a mechanical force F, which is transmitted from the actuator 31 through the connection 32 to the embedded material 20 of the tracker 10. If the actuator 31 and the connection 32 are non-magnetic, the sensor 40 can record (S110) the magnetic signal B during the excitation S100, as shown in FIGS. 4A and 4B , without the need for additional stops (S105 in FIGS. 4C and 4D ). This enables the position H and orientation T of the tracker 10 to be determined more frequently.

[0154] Simultaneous excitation and positioning. Simultaneous excitation and positioning can be performed in cases where the excitation field does not interfere with the sensor 40.

[0155] The first method and the second method enable simultaneous excitation and positioning of the magnetic excitation field.

[0156] The first method uses a precisely known predefined excitation field. Assuming that there is no sensor saturation to produce a residual signal, the value of the predefined excitation field can be digitally or analog subtracted from the signal data of the sensor 40. The residual signal is the signal of the tracking device 10. This first method means that the excitation can be performed continuously and positioning can be performed when desired during the excitation.

[0157] The second method uses a second excitation unit. The second excitation unit generates an opposite magnetic field at each sensor 40 in the sensing array. The magnetic field generated from the excitation at each sensor 40 is canceled, resulting in no valid signal during the excitation. For example, the result of no valid signal can be achieved by mirroring the excitation coils with opposite polarity at opposite sides of the sensor array.

[0158] In addition to the second method, the first method can also be performed to reduce stray fields from small differences in mirrored excitation units. Since the excitation unit and the sensing unit must operate simultaneously, the first and second methods are premised on the independence of the excitation unit and the sensing unit.

[0159] Simultaneous excitation and positioning can be performed without the mechanical excitation unit creating a magnetic field for generating the mechanical field.The mechanical wave is able to excite the positioning device 10, ie the tracker.Simultaneous sensing and positioning can be performed at any time during the excitation.

[0160] Multiple device tracking. The device 10 operates at a resonant frequency that is defined and tunable by, for example, the size and material of the cantilever 230. The unique frequency response of the device 10 is used to distinguish and locate a large number of devices 10. The excitation S100, sensing S110, and determination S120 of the position H and orientation T of the device 10 can be performed simultaneously or sequentially. Multiple devices 10 in the device 10 can be used to track the relative motion of the devices 10, for example, to track the shape or deformation of a medical device or soft robot.

[0161] Fluxgate sensor array. The magnetic field B is sensed S110 using a large number of sensors 40 such as in a fluxgate magnetometer array to obtain more spatial information about the magnetic field B from sensing S110. The individual sensors 40 in the sensor array are spatially arranged in at least one dimension, preferably in two dimensions, and the array measures the magnetic field B in at least one direction, preferably in two orthogonal directions, and more preferably in three orthogonal directions.

[0162] Tumor positioning. The 3D position and shape of the tumor can be determined and reconstructed in 3D using medical imaging such as MRI and computed tomography CT. One or more of the tracking devices 10 are injected into the tissue under the guidance of ultrasound imaging. The tracking device 10 can be placed inside or outside the tumor, preferably on the boundary of the tumor. The position H and orientation T of the device 10 are imaged by non-magnetic medical imaging such as CT, and the spatial relative position and orientation of the tumor relative to the tracker are calculated based on these non-magnetic medical images. In the case where large-scale medical imaging is not possible, such as in an operating room, the tracker is positioned using the method described in this document, and the real-time position, orientation and shape of the tumor are calculated based on the positioning information of the device 10. Such information is displayed as an overlay image on the patient's body for the surgical scene, for example, via a screen, a projector or a pair of augmented reality glasses. The method can basically accurately locate the real-time position of the tumor without considering soft tissue deformation, so the method provides an accurate method for removing the tumor by surgery. The embedded device 10 is removed from the body after surgery together with the tumor. The method is generally also capable of tracking other important anatomical structures, such as blood vessels, blood clots, polyps, and nerves. These procedures are not limited to tumor surgery, but are also applicable to other medical procedures that require positioning, such as radiotherapy, targeted chemotherapy, selective embolization, etc.

[0163] Actuation system. For the actuation of micro robot R, an external rotating magnetic field is used. A cubic NdFeB magnet (side length 50.8mm, N40, Supermagnete, Germany) is mechanically fixed to a stepper motor (23HS30-2804S, Stepperonline, the United States), wherein the magnetic axis is perpendicular to the rotation axis of the motor. The assembly is placed on a rotating table (GFV5G50, Orientalmotor, Japan) to manipulate the rotation axis of the magnet in a 2D plane. The propulsion of micro robot R is limited to planar motion in the gel between the PMMA plate and the bottom of the container, wherein the gap is 6mm, and the propulsion path is predefined in the gel. The speed of 0.25Hz and the direction of the rotating magnetic field are controlled by an Arduino board (Ardunio Uno Rev3 SMD, Arduino), and the direction of the rotation axis is manually manipulated. In order to locate H, T, the propulsion is paused 8 times. At each pause, the sample box (wherein the robot R is statically embedded therein) is removed from the actuating device and placed in the positioning device. Afterwards, propulsion continued in the actuator. LED light sources were used for illumination, and a camera system (Canon EOS RP RF 24-105mm F4 with RF35mm F1.8 lens, 25fps, Canon, Japan) was used to image propulsion from a bird's eye view. The eight videos were linked and analyzed by custom code (MATLAB) to identify the robot center point and orientation in each frame (HT1 to HT9 in Figure 14) and plot the trajectory to overlay on the original video.

[0164] Complementary ultrasound imaging.Porcine brains were obtained from local butchers, transported on ice and stored in a refrigerator at 4°C. All experiments were completed within 12 hours after the animals were killed. The samples were hydrated with phosphate buffered saline solution (PBS, Sigma-Aldrich) and placed in a container of 60mm x 50mm x25mm for measurement at room temperature. For US imaging, a handheld US machine (iQ+, Butterfly Network, the United States) set to "MSK soft tissue" at a frequency of 1 to 10MHz was used, wherein the thermal index (TIS) of the soft tissue was 0.01 and the mechanical index (MI) was 0.28. The US probe was set to contact with the pig brain using US contact gel (Aquasonic 100, Parker Laboratories, the United States).

[0165] Mechanical property testing of viscoelastic media (such as biological soft tissue) is crucial for understanding and characterizing complex, multi-composite soft materials. In medicine, elastic properties are checked by palpation, which is the process of measuring the elastic response of tissue by direct contact. Such mechanical testing is performed by quasi-static or dynamic indentation testing using external loads, rheological measurements or mechanical wave propagation. Then, the results from such tests are used to simulate or estimate the material behavior of viscoelastic tissue. However, ex vivo testing may not represent the surface structure (e.g., skin) of physiological conditions and materials in vivo, which usually present strongly different properties from bulk materials. As another example, the brain is surrounded by a thin protective layer (piatine), which has a high elastic modulus compared to the brain bulk material. This difference can affect the bulk material test under external force, and will not produce real bulk properties.

[0166] A more general approach for bulk material properties is obtained from the combination of mechanical wave propagation and imaging. One such approach for mechanical sensing in biological tissue is magnetic resonance elastography (MRE), which can directly image elastic properties by evaluating the propagation of mechanical waves. However, very large and complex magnetic MR machines are required, which makes them unsuitable for long-term measurements and monitoring of elastic development. Mechanically resonant structures have been proposed for material sensing, such as magnetic MEMS devices for pressure sensing and tethered piezoelectrically driven cantilevers for viscoelastic characterization.

[0167] In order to wirelessly determine S115 the local viscoelastic properties of the soft biomaterial, a positioning device 10 can be used. The positioning device 10 can be directly embedded in the embedding material 20. Through its mechanical resonance frequency and the damping response of the positioning device 10, the material properties can be wirelessly determined (in step S115) without the need for any expensive equipment. The positioning device (10) can be implemented by minimally invasive surgery and can be used for long-term monitoring of changes in the mechanical properties of soft biomaterials.

[0168] Artificial hydrogels made of gelatin were prepared to simulate biological soft tissues and verify the function of the positioning device 10. 2wt.-\% to 4wt.-\% gelatin hydrogel (Type A from pig skin, Sigma-Aldrich) was prepared by stirring gelatin powder in distilled water at 80°C for 30 minutes. The mixture was poured into a 60mm x 50mm container and cooled to room temperature for at least 12 hours before use. Dehydration was prevented by covering the container with a lid. Ex vivo tissue specimens, i.e. turkey breast, pig liver and brain, were obtained from a local butcher and tested within 12 hours after the animals were killed. During the room temperature test, the samples were hydrated with phosphate buffered saline solution (PBS, Sigma-Aldrich) and placed in a 60mm x 50mm container for measurement.

[0169] The positioning device 10 includes an elastic spring element 230 with a spring constant of k1, whose internal damping is η1. The spring element 230 is coupled to two masses: m1 is a magnet 220 attached to a free end 235 of the spring element 230, and m2 is an effective mass consisting of a housing 200 and an embedding material 20. The embedding material 20 can be a viscoelastic material. In one example, the embedding material 20 can be modeled as a Maxwell or Kelvin-Voigt linear model and is shown in FIG19 with a dashed line.

[0170] Two 1 mm x 0.5 mm cylindrical N52 NdFeB magnets (glued to a steel cantilever with a thickness of 20 μm, a width of 200 μm, and a length of 2.5 mm, all within a 3D printed housing 200) were used at a resonant frequency f res =90.33Hz and f res = 100.73 Hz The two positioning devices 10 are manually assembled. For soft material measurements such as biomaterials, the device 10 is embedded into the sample 20 at a distance of at least 10 mm from any hard boundaries.

[0171] The rigid boundary reference is measured by fixing the positioning device 10 in a housing rigidly attached to the frame. Under the assumption of an ideal damped mass-spring system with quasi-infinite mass m2 (see FIG19 ), the spring constant k1 can be calculated by:

[0172]

[0173] Where f = f res , and wherein m1 is the mass of the magnet 220. η1=η r is the damping coefficient with rigid boundary conditions measured according to the decaying magnetic field (Equation 1). Where m1 = (7.9 ± 0.1) x 10 -6 kg, f res,1 =(90.33±0.04)Hz and η r =(4.2±0.1)s -1 , k1 becomes (2.54±0.03)Nm -1 The spring constant can also be determined from material and dimensional considerations using the formula for a cantilever:

[0174]

[0175] Among them, E is Young's modulus and the area moment of inertia is (w width, h height) and the cantilever length is L. This leads to the estimated spring constant k * 1.2 to 2.54Nm -1The error tolerance is due to the uncertainty of production. k1 is located between k * The assumption of a simple mass-spring system is verified within the estimated range of .

[0176] As mentioned, the internal damping η1 of the positioning device 10 can be obtained by Equation 7. This value can be compared with a system with m2 and a soft coupling of the viscoelastic environment 20, as demonstrated in Figure 20 for three concentrations of gelatin hydrogel. r is the lower limit of possible damping, so the total damping of the system can be expressed as the sum of the rigidity and viscoelastic contributions η = η r +η v By inserting the device (10) into gelatin and with decreasing gelatin content, η increases significantly. This phenomenon is expected since the gelatin matrix stiffens with gelatin content due to physical bonding of molecular entanglements. The literature reports that the stiffness of gelatin increases with its concentration, which is consistent with the current observations on the damping coefficient determined by the device (10).

[0177] In addition, the damping behavior of various ex vivo tissues was measured and is presented in Figure 21. The apparatus 10 used for these experiments included a spring constant of k1 = (3.17 ± 0.04) Nm -1 The (9.2±0.9)s for the rigid boundary was determined. -1 Compared with (24.2±1.6)s for pig brain -1 η increases significantly between turkey breast, pig liver, and pig brain, matching well with the decrease in stiffness of these biological tissues. While the stiffness between the muscle fibers in turkey breast and brain tissue reported in the literature varies by two orders of magnitude, η only varies by a factor of roughly about 1.7. This is an indication of a nonlinear dependence between the damping coefficient and the material stiffness.

[0178] Reference numerals

[0179] 5. Installation

[0180] 10 Positioning device / tracker

[0181] 20 Soft tissue / embedding material

[0182] 30 Magnetic excitation coil

[0183] 31 Mechanical excitation source

[0184] 32 Connectors

[0185] 35 Current Amplifier

[0186] 40 Sensors

[0187] 45 Positioning stage

[0188] 50 Data acquisition and calculation unit

[0189] 200 Shell

[0190] 210 cavity

[0191] 220 Magnet

[0192] 225 Dipole Center

[0193] 230 Oscillating element / cantilever

[0194] 235 First End

[0195] 237 Rotation axis

[0196] 240 Movement Path

[0197] Reference symbols

[0198] F Excitation Field

[0199] Θ Deflection angle

[0200] B Magnetic Field

[0201] H 10 position

[0202] T10 Orientation

[0203] R includes 10 robots

[0204] Actuation pathway of PR

Claims

1. A method for determining a position (H) and an orientation (T) of a positioning device (10) having a magnet (220) attached to an oscillating element (230), the method comprising: - exciting (S100) the magnet (220) using one of an external force or torque (F) to cause a composite oscillatory motion of the magnet (220), wherein the composite motion comprises a rotation and a translation of the magnetic moment of the magnet (220) about a rotation axis (237), and the rotation axis (237) is located at an offset distance relative to the center of the magnetic moment of the magnet (220); - using at least one sensor (26) to sense (S110) the magnetic field (B) generated by the magnet (220); and - Determining (S120) the position (H) and orientation (T) of the positioning device (10) based on the sensing (S110).

2. The method according to claim 1, wherein: The excitation (S100) using one of the external force or torque (F) is powered by one of an external magnetic excitation field or a mechanical excitation.

3. The method according to claim 2, wherein: The mechanical excitation is one of a pulse and a wave oscillating in at least one of a longitudinal direction or a shear direction of the oscillating element (230).

4. A method according to any one of the preceding claims, wherein: The distance between the rotation axis (237) and the magnetic moment of the magnet (220) is greater than at least 5%, preferably 25%, more preferably 100% of the largest dimension of the magnet (220).

5. A method according to any one of the preceding claims, wherein: The rotation axis (237) is non-parallel to the magnetic moment vector originating from the magnet (220), and is preferably substantially perpendicular.

6. A method according to any one of the preceding claims, wherein: The oscillating element (230) is located in a rigid housing (200), more preferably in a sealed rigid housing (200) under vacuum.

7. A method according to any one of the preceding claims, wherein: At least one of the sensing (S110) or the determining (S120) of the position (H) and the orientation (T) of the positioning device (10) is performed when at least one of the excitations (S100) of the magnet (220) is stopped (S105) or is performed continuously during the excitation (S100) of the magnet (220).

8. A method according to any one of the preceding claims, wherein: The oscillating element (230) includes a restoring force unit including at least one of a cantilever beam or a similar unit providing an elastic restoring force.

9. A method according to any one of the preceding claims, wherein: The sensing (S110) and the determining (S120) of the position (H) and orientation (T) of the device (10) are repeated.

10. The method according to claim 6, wherein: The frequency of the excitation of the magnet (220) is approximately the resonance frequency of the oscillating element (230).

11. A method according to any one of the preceding claims, wherein: Determining (S120) the position (H) and orientation (T) of the positioning device (10) comprises using a physical model of the compound oscillatory motion in the time domain.

12. A method according to any one of the preceding claims, wherein: Sensing (S110) the magnetic field (B) generated by the magnet (220) is followed by determining (S115) the local viscoelastic properties of the material.

13. The method according to claim 11, further comprising: The determined local viscoelastic properties of the material are used to determine the position (H) and orientation (T) of the device (10).

14. A device (5) for determining the position (H) and orientation (T) of a positioning device (10), the positioning device (10) having a housing (200) in which a magnet (220) attached to an oscillating element (230) is located, the device comprising: - an excitation unit (30) for exciting (S100) the magnet (220) using one of an external force or a torque (F), resulting in a composite oscillatory motion of the magnet (220), wherein the composite motion comprises a rotation and a translation of the magnetic moment of the magnet (220) around a rotation axis (237), the rotation axis being located at an offset distance relative to the center of the magnetic moment of the magnet (220); - a positioning device (10) having a housing (200) inside which the magnet (220) is attached to the oscillating element (230); and - a data acquisition unit for sensing (S110) the magnetic field B generated by the magnet (220) using a sensor (40).

15. The device (5) according to claim 14, wherein: The magnet (220) comprises a permanent magnet made of a magnetic material, preferably a ferromagnetic material.

16. The device (5) according to claim 14 or 15, wherein: The oscillating element (230) comprises a restoring force unit, preferably a cantilever.

17. Use of the device (5) according to any one of claims 14 to 16 for locating a medical implant in an animal or human body, or for locating an anatomical structure, wherein the medical implant is selected from one or more of a catheter, a stent, a guidewire, an endoscope, a capsule endoscope, a drug delivery device or a small robot, and the anatomical structure is selected from one or more of a tumor, a blood vessel, a blood clot, a polyp or a nerve.

Images