Patent ID: 12257016

DETAILED DESCRIPTION OF AN EMBODIMENT OF THE INVENTION

In the following description of preferred embodiments of the invention, identical reference numerals refer to identical or similar components.

Example: Magnetic Field Generator with 12 Magnets

The magnetic field generator illustrated inFIGS.1to3comprises of three groups of permanent magnets1, and four parallel magnets1belong to each group. Each magnet1in the drawing is in a cylindrical or cubical shape, yet other shapes would also be possible, for example spherical or cuboid shapes. The permanent magnets1have closely matched magnetization and strength and a permanent magnetization direction. They are arranged to be rotated by electrical motors (not shown) around an axis that is perpendicular to the magnets1magnetic moment Mi. Combined, the magnets generate resulting a magnetic field2with field vector B at the centre of the magnetic field generator where the workspace3is located.

For many applications, it is beneficial to generate a homogeneous magnetic field2in a large workspace3with negligible magnetic gradient force. In the magnetic field generator of figured1to3, the magnets1are arranged equidistantly to their next neighbours and in a circle around a hub that is located in centre of the workspace3, so as to minimize spatial and temporal gradients of the resulting magnetic field2. Should the magnets1differ in their magnetization, then in principle it is possible to compensate differences in the physical properties by an arrangement of the magnets1where these no all longer have the same distance from the hub or are no longer arranged equidistantly from their next neighbours.

Advantageously, in the arrangement ofFIGS.1to3, only three independent angular inputs (labeled as α, β, γ inFIGS.1and2), are needed to change the direction of the field vector B to point in an arbitrary direction in three-dimensional space while also allowing for the adjustment of the B field flux density. The flux density can be zero, but not larger than a maximum achievable flux density specific to the respective orientation of the vector B. Although there are in total 12 magnets (3 groups times 4 magnets per group) in the magnetic field generator shown inFIGS.1to3, only three independent rotational inputs are required, thus only three motors are needed for the setup.

In each group, there are at least 2 magnets (arranged on opposing sides of the workspace); and there can be more than four magnets1, as more magnets1result in a higher flux density over a larger workspace3. The mechanical driving mechanism (not shown) of the magnets1does not require the direct connection to a particular magnet1, and can include a belt drive, a gear driven or other means of actuation.

As the magnets1are placed on the edges of a cube, the workspace3can be accessed from many directions. Only one rotational degree of freedom is required for each magnet1, and there is no translational motion of the magnets1. This design feature allows changes of the magnetic field2to be realized; and it also enables long-term accessibility to the workspace2. Shown as hollow big arrows inFIGS.1and2, the workspace3can be accessed from the four sides between the magnets1, and also from the top and bottom. This is beneficial, for example in the clinical application as shown inFIGS.4and5. A patient11can lie on a bed sliding into the magnetic field generator via patient access16; and anaesthetic tubes, intravenous (IV) injections and electrical sensors12can stay connected to the patient11during the operation. Moreover, medical imaging modalities (x-ray, computer tomography (CT), ultrasound, optical, etc) are also allowed from the top or side imaging access13.

Possible applications of the invention include but are not limited to: (1) driving a propeller or robot to swim or drill through biological fluids or tissues as for example disclosed in the European Patent Applications 17 166 356 and 17 187 924; (2) steering an optical fibre or an electric wire to cut through biological tissues; (3) steering an endoscope or catheter in a body lumen; (3) driving a wireless miniaturized actuator; (4) driving magnetic micro- or nano-particles under the microscope, for biological study or for delivery, eg into a cell, or for a microrheology study; and (5) magnetically steering an electron beams.

Example: Actuation of a Medical Device in a Human Body

An exemplary application of the disclosed invention is to actuate and steer and control a medical device inside the human body by the generated magnetic field. Two embodiments are shown inFIG.4andFIG.5, to actuate an untethered medical device and a tethered medical instrument respectively. A tethered medical device has a physical material connection leading to the outside of the workspace, such as cable; an untethered medical device does not have such connection.

InFIG.4, an untethered medical device15is actuated by the magnetic field2in the workspace3. As the device15has a finite magnetic moment (eg due to a permanent magnet is attached to the device), it tends to align with the external magnetic field2direction. The magnetic field2from the magnetic field generator can be used to exert a torque on the medical device15and is actuated in this way. The device15can have a suitable shape, eg that of a helical propeller, to enable its translational motion during rotation. The device15can have multiple segments that have multiple magnetic moments so that the shape of the device is changed under the actuation of the magnetic field2. For example, the medical device can be a gripper or a stent that opens and closes, a valve that opens and closes, or a pump that moves periodically.

InFIG.5, a tethered flexible medical instrument15is steered by the magnetic field2in the workspace3. A part of the patient's11body (in the example ofFIG.5the head, for neurosurgery) is placed in the magnetic field generator through one of the open spaces defined as access16. A surgical tool15, for instance, can be applied through the workspace via another access14. As the tip of the tool15is equipped with a permanent magnetic moment, which here is assumed to point along the long axis of the instrument15(eg due to a permanent magnet encapsulated at the tip), the tip can be made to align with the external magnetic field2direction and the orientation of the instrument15tip is controlled in this way. Alternately, the flexible instrument15steered with the disclosed method can be an endoscope, a catheter, an optical fibre, a bundle of optical fibres, a tube, a wire, a gripper or any other suitable instrument.

The invention can be used to steer an active device to cut through biological tissues, eg an optical fibre that transmits laser light (for example pulsed laser light) to cut through biological tissue.

The part of the human or animal body placed in the magnetic field generator can be a head, brain, eye, arm, leg, knee, hand, foot, or any other desired part of the body (whole or in part). The position of the patient11relative to the magnetic field generator can be adjusted. The monitoring of the device or instrument15in the human body is accomplished by a suitable medical imaging modality. The positional information of the device or the tip of the instrument15is can be used as an input signal in a feedback control loop to drive the field generator, and the relative position of the patient11and the field generator can be adjusted to keep the device15or the tip of the instrument15well inside the workspace3, for example near its centre. In another case, the workspace3of the field generator is larger than the required movement range of the device15, so the position of the patient11is fixed relative to the field generator.

The device or instrument15can be actuated or steered in solid or liquid biological tissue, eg brain, liver, prostate, muscle, skin, eye or in an organ, or in a body lumen, such as urinary tract, kidney, urinary bladder, eye, heart, stomach, lung, blood vessel, or any other suitable biological tissue.

The device may also be steered by means of the magnetic field generator or the method according to the invention while an additional external force is provided to a tethered medical device. In this embodiment the magnetic field generator provides the direction control while the force required to penetrate tissue or other biological material is provided by other means.

There are several advantages of the magnetic field generator and the method according to the invention: a) it is a potentially wireless approach, thus it allows more dexterity of the medical device15; b) the workspace3is large enough to incorporate the human body or a part of the human body; c) a high magnetic flux density is realized, thus it results in larger actuation force or torque on the device15; and d) the accesses16to the workspace3allows the positioning of the patient11, the connection and inclusion of other medical instruments, e.g. IV tubes12, anesthesia tubes12, sensors12, and the application of medical imaging instrument13and surgical tools14, eg scalpel, scissors, needle.

Analytical Theory for Generating a Superimposed Magnetic Field

With the invention, it is possible to generate a controlled magnetic field2in both the field strength and the direction in the workspace3. In order to explain the theory behind the invention, first a situation is discussed in which one group of magnets1creates resulting magnetic field2with a fixed strength and continuously changing direction. Then, a situation is explained where one group of magnets1creates a resulting magnetic field2of fixed direction with oscillating strength. Finally, a resulting magnetic field2with arbitrary orientation and flux density is discussed.

Spatially Homogeneous Resulting Field that Rotates

Four magnets1in one group are shown as an example in this embodiment to control the in-plane resulting magnetic field2. The magnets1have the same magnitude of their magnetic moment, and they are distributed equidistantly from their next neighbours and at identical distances from hub of the group. A spatially homogenous field2in the workspace that rotates around the x axis is described by the following equations:
By=B0cos αB(1.1)
Bz=B0sin αB(1.2)
where Byand Bzare the component of the magnetic field2in y and z direction, respectively, and αBis the angle between the magnetic field2and the y axis as illustrated inFIG.3.

Each permanent magnet1is a cylindrical or disk-shaped magnet1that has a magnetic dipole in the diametric direction, and rotates around its cylindrical axis (which is along x, and which is perpendicular to the dipole moment), as shown inFIG.3. The magnetization vectors Miare oriented by an angle αiin the yz-plane. The magnetic field2vector B resulting from the superposition of the magnetic fields generated by the four dipoles at point p is given by:

B⁡(p)=∑i=14μ0⁢❘"\[LeftBracketingBar]"Mi❘"\[RightBracketingBar]"4⁢π⁢❘"\[LeftBracketingBar]"ri❘"\[RightBracketingBar]"3⁢(3⁢r^i⁢rˆiT-I)⁢M^i(2)
where μ0=4π×10−7T·m·A−1is the permeability of free space, I is the 3×3 identity matrix, riis the vector from the magnet1i to point p,is the unity vector in the direction of ri. A maximum combined field strength (ie flux density) in the yz-plane at the hub of the group is found for the orientation:
α1=α4=α0(3)
α2=α3=α0+π  (4)
where α0is defined as shown inFIG.3and is the initial angle for the magnets2according to the initial angle of the magnet field αB0:

α0=π2-αB⁢0(5)

It follows that when the magnetic moments of the magnets1are aligned pairwise in the diagonal position, ie the pairs M1& M4, and M2& M3, respectively, but they are opposed to each other (180° phase difference) between the two pairs, then a maximum resulting field strength is obtained. This state is taken to be the initial state, and from this state, the magnets1are mechanically rotated with the same angular velocity clockwise αB=αB0−ωt, so that their magnetic fields rotate with the same angular velocity ω but counter-clockwise, and the rotation angle is φ=ωt:
α1=α0+φ  (6)
α2=α0+π+φ  (7)
α3=α0+π+φ  (8)
α4=α0+φ  (9)

The measured resulting magnetic field2follows the theoretical prediction. As shown inFIG.6, the components in the y and the z directions oscillate with a phase difference of π/2, thus the combined field is constant in strength and rotates around the x axis. The maximal field Bmaxthat can be achieved by the set-up, where the coercive field strength of each spherical magnet with a diameter of 30 mm is approximately 955 kA/m, is also measured as a function of the distance between the magnets, as shown inFIG.7. The measurement fits the simulation very well, and the maximal strength for the current set-up exceeds 500 G in the current set-up.

Oscillating Resulting Field Along a Given Axis

The oscillating resulting magnetic field2has a fixed oscillation axis (direction) defined as αB, which is the angle to the y axis, and a field strength oscillates, which is given by:
|B|=Bmaxcos φ  (10)
where Bmaxis the maximal field strength (ie flux density) that could be achieved by the superposition of the four magnetic dipoles, and φ=ωt is the oscillating angle, and w is the angular velocity.

The geometry of the set-up and the initial conditions are the same as in Equations (3)-(5). The difference is that two pairs of magnets1rotate in opposite directions. Specifically, as illustrated inFIG.3, M1and M2rotate clockwise with an angular velocity of −ω, and M3and M4rotate counter-clockwise with an angular velocity of ω. The oscillating angle is φ=ωt, so the rotational angles of the four magnets1are given by:
α1=α0−φ  (11)
α2=α0+π−φ  (12)
α3=α0+π+φ  (13)
α4=α0+φ  (14)

With this approach, two outputs, ie the magnitude and the direction of the resulting magnetic field2at the hub of the group of magnets1, are fully controlled with two independent inputs α0and φ.

The simulation results of the magnetic flux density are shown inFIG.8. In this embodiment, a resulting magnetic field2oscillating in the z direction (αB=90°) is shown as an example. Simulations also show that the resulting magnetic field2increases non-linearly from a maximum of about 374 G at a distance of 120 mm, to a maximum of about 485 G at a distance of 110 mm, to a maximum of about 645 G at 100 mm. This is achieved with the same magnets2, all having a relatively small diameter of 30 mm. It clearly demonstrates the advantage of the permanent magnet1set-up over electromagnetic ones, as the field can easily achieve 3 to 6 times the strength of a common electromagnet, without any special cooling requirement or the need for expensive power amplifier systems. The resulting magnetic field2at the hub was measured by a gaussmeter and plotted inFIG.9. The experimental results fit the simulations very well.

Resulting Field with Arbitrary Orientation and Flux Density

The magnetic field generator disclosed here can also generate a magnetic field2vector B pointing in any arbitrary direction within the three-dimensional space enclosed by the magnets1and the magnitude of the resulting magnetic field2can also be controlled. It is The direction and the strength of the resulting magnetic field is fully controlled with only three independent angular control parameters for each group of magnets (labelled as α, β, γ inFIGS.1and2); at the same time, the flux density of the generated B field is tuned in the range from zero to the maximal achievable flux density.

The desired resulting magnetic field2in the workspace is:
B=B0ŵ=[Bx,By,Bz]T=B0[sin θwcos φw, sin θwsin φw, cos φw]T(15)
where ŵ is the unity vector in the direction of B, B0is the field strength (ie the flux density), and θw, φware the angles between the vector and the axes, as shown inFIG.10a. [⋅]Tis the transpose symbol.

The resulting magnetic field2is the sum of three magnetic vectors generated by each group of magnets1that are orthogonal to each other, thus:
B=Bxz+Byz+Bxy(16)
where Bxz, Bxz, Bxyare the in-plane magnetic field vector generated by each group of permanent magnets1. As inFIG.10b, the composed magnetic field B can be written in three components form:
B=[Bx,By,Bz]T=[Bxycos αxy+Bxzcos αxz,Byzcos αyz+Bxysin αxy,Bxzsin αxz+Byzsin αyz]T(17)
where Bxy, Bxz, Byzare the field strengths generated by only one group of magnets1in the xy-, xz- and yz-planes, respectively, and α . . . are the angles between the in-plane vector and the axes, as shown inFIG.10b.

In some embodiments, magnets1with the same size, the same magnetic moment and the same distances from the hub of their group are used, then the field strength in each directions are equal and the equation (16) is simplified with Bxy=Bxz=Byz=B1. Equating equations (15) and (17) results in the following equation:

B1[cos⁢αx⁢y+cos⁢αx⁢zcos⁢αy⁢z+sin⁢αx⁢ysin⁢αx⁢z+sin⁢αy⁢z]=B0[sin⁢θw⁢cos⁢φwsin⁢θw⁢sin⁢φwcos⁢φw](18)

The right side of equation (17) defined the required composed magnetic field with three parameters B0, θw, φw, and solving equation (18) will lead to the three unknown parameters αxy, αxz, αyzon the left side of the equation. From the instrument controlling point of view, three input parameters of the angles in each direction αxy, αxz, αyzresults in full control of three output parameters B0, θw, φw, which are the magnitude and the three-dimensional direction of the magnetic field vector. In some embodiments, the equation (18) is solved numerically in Matlab (R2017a, MathWorks).

In some embodiments, the groups of magnets are not orthogonal to each other, but the equation (16) is still valid. Decomposition of each magnetic field vector into the three axes will result in a new set of equations (17) and (18), but the general principle is the same as demonstrated herein, ie by controlling three input parameters of the angles α . . . in three different directions results in the full control of three output parameters B0, θw, φw, which are the magnitude and the 3D direction of the magnetic field vector.

With the solved angles in each direction α . . . , the angle of each magnet1in the group can be calculated using the following method. Considering the cross section of each group, eg with four permanent magnets1(n=4) in one group is illustrated inFIG.11. In this embodiment, each magnet1rotates about an axis (the x axis in this case) that is orthogonal to its magnetic moment with the same angular velocity ω. The rotation angle of the ith magnet βifollows the following relationship:
βi. . . =2γi−α . . . ,i==1,2,3,4  (19)
where . . . should be substitute with xy, xz, or yz that stands for the directions, γiis the angle between the line of magnet centre to workspace3centre and one axis (the y axis in the current embodiment).

The equation (19) is always valid, if the number of magnets1in each group is larger than or equal to two (n≥2), regardless the number of magnets1is an odd or even number. One embodiment with five magnets, which are 30 mm in side lengths and whose centre points are arranged on a circle of diameter 70 mm, is also shown as an example inFIG.12. Using equation (19), the angle of each magnet is calculated, and the design is verified by the finite element simulation of the magnetic field (Comsol multiphysics 5.2a, Comsol). InFIG.12b, a sequence of images show the simulation results in a step of 90°, that the resulting magnetic field2is temporally and spatially homogeneous in the workspace3, and the field direction rotates counter-clockwise as the five magnets1are positioned at the right angles according to equation (19) and rotate clockwise.

In another embodiment, it is required to generate a rotating resulting magnetic field2that is spatially and temporally homogeneous in the field strength, and the field direction rotates around a defined axis in 3D. An illustrated inFIG.13, the rotational axis is defined by the unity vector û:
û=[ux,uy,uz]T=[sin ϑucos φu, sin ϑusin φu, cos φu]T(20)
The rotational magnetic field vector is a function of time:
B(t)=R(t)B0=B0R(t){circumflex over (ν)}  (21)

where {circumflex over (v)} is the unity vector in the direction of the magnetic field B(t), and with a given initial value, {circumflex over (v)} can be solved by the following equation:
û·{circumflex over (ν)}=0  (22)

R(t) is the rotational matrix around the axis û by an angle δ:

R⁡(t)=[cos⁢δ+ux2(1-cos⁢δ)ux⁢uy(1-cos⁢δ)-uz⁢sin⁢δux⁢uz(1-cos⁢δ)+uy⁢sin⁢δux⁢uy(1-cos⁢δ)+uz⁢sin⁢δcos⁢δ+uy2(1-cos⁢δ)uy⁢uz(1-cos⁢δ)-ux⁢sin⁢δuz⁢ux(1-cos⁢δ)-uy⁢sin⁢δuz⁢uy(1-cos⁢δ)+ux⁢sin⁢δcos⁢δ+uz2(1-cos⁢δ)](23)
where δ=ωut=2πft, in which ωuis the angular velocity in the unit of rad/s, f is the rotational frequency in the unit of Hz, and t is time in the unit of second.

Generating a Three-Dimensional Magnetic Field with One Group of Magnets on Rotational Stages

One group of four magnets1is able to achieve an in-plane rotational magnetic field (as shown above inFIG.3). To realize the three-dimensional steering of the rotational axis of the field, the magnets are mounted to a 2 DoF rotational stage (shown as the rings inFIG.14). The stage rotates the whole setup (relative to the patient) in two directions, β and γ. The disadvantages of the embodiment are: 1) The access to the workspace is only limited to one direction, ie along the γ axis is permanent; however, access from other directions, eg along the β axis is blocked due to the rotation of the whole device; 2) The connections to drive the magnets1are cumbersome and expensive due to the rotation of the whole device; 3) The rotation of the whole device requires much higher power and is more dangerous to the patient11or the operator.

Example: Generating a Three-Dimensional Magnetic Field with Six Magnets that Each can Rotate in Two Directions

As shown inFIG.15, spherical permanent magnets1are arranged in three groups, and two magnets1in each group. The magnets1of each group simultaneously rotate with 2 DoF. It is also possible to achieve the full control of both the direction and the magnitude of the magnetic vector. Each magnet1(magnetic moment) can rotate around two orthogonal axes (two of the three axes, shown as α, β and γ).

Example: Experimental Methods of the Magnetic Generator

The magnetic set-up consists of four spherical magnets1with 30 mm diameter (K-30-C, neodymium N40, Supermagnete). They were held in spherical cavities in a custom-made coupler to connect to the motors. The orientation of the magnets1was maintained due to the large friction induced by the clamping force. Four stepper motors (1.8°/step, stall torque 0.15 N·m, SH3537-12U40, Sanyo Denki, not shown) were used with two individual driver boards (US1D200P10, 2.0 A, 16-division, Sanyo Denki, not shown) to drive the rotations in two directions, respectively. The power was supplied by a DC power supply (HM7042-5, HAMEG). The initial orientations α0of the four magnets1were adjusted manually, then they were rotated with the same absolute speed, controlled by a square wave signal generated from a function generator (33220A, Agilent, not shown). The motors were air cooled with four fans (not shown), as heat was generated, especially when the motors were held in a fixed static position against the magnetic torque.

The diagonal centre-to-centre distances of the magnets1were set at 120 mm. Changing the distance between the magnets1will change the maximal magnetic field strength. Decreasing the distance will result in a larger field, however, it also requires larger driving torque by the motor, which then exceeds the stall torque of this motor for particular orientations of the magnets1.

A digital gaussmeter (HGM09s, MAGSYS) was used to measure the resulting magnetic field2at the centre of the magnetic field generator in both the x and z directions, respectively. The field2was changed in steps of 22.5° (200 pulses) and the results are plotted as markers inFIG.7. The measurements were repeated for three times. At the same position, the magnitudes were reproducible within ±0.5 G, so the error bars are not plotted in the figure.

The magnetic field strength and direction were also simulated in Comsol 5.2a (Comsol Multiphysics). A three-dimensional simulation was carried out in a volume of 300 mm-side cube using a magnetic insulation boundary condition. Four spherical magnets1with 30 mm diameter were placed with a diagonal centra-centre distance of 120 mm, as shown inFIG.3a. The relative permeability of air and the four magnets1are set as 1 and 4000, respectively. The magnetization strength of each magnet was set to be 955 kA/m, and each orientation was calculated according to Equations 6 to 9. A parametric sweep was carried out for αB=0°, 15°, 30°, 45°, 90°, and β=0°˜360° in 10° steps. The magnetic flux density is shown by the grayscale, and the direction of the field is shown as arrows inFIG.6.

Example: Multiple Magnets in One Group

In each group, there are at least two magnets1(arranged on opposing sides of the workspace); and there can be more than four magnets1, as more magnets result in a higher flux density over a larger workspace3. The mechanical driving mechanism (not shown) of the magnets1does not require the direct connection to a particular magnet1, and can include a belt drive, a gear drive or any other suitable means of actuation.

Each group of magnets1has plane and a hub and the magnets1are equidistantly in a circle. The hubs of the groups coincide with each other, and with the centre of the workspace3. As shown inFIG.16, the central symmetric axis of each group is perpendicular to that of another group, but it is not necessary to be perpendicular to the axis of the workspace3(the coordinate system of the patient in this case). Three groups the orientations of which are orthogonal to each other achieve full control of the direction and strength of the resulting magnetic field2in the workspace3by the disclosed method in the patent.

In one embodiment, the setup with multiple magnets1can be extended to human-scale, as shown inFIG.16andFIG.17. In each group, there are 18 magnets1that are 100 mm in diameter and 200 mm in length. The inner diameter (gap) of each group is set to be 1000 mm, which fits a human through the opening space (access). The cuboid inFIGS.16and17represents the outer bounding box of a human, with a width of 500 mm, a thickness of 300 mm, and a length of 1700 mm. By finite element analysis of one group of 18 magnets with a coercive field strength of approximately 955 kA/m, the magnetic flux density is homogenous in the workspace and reaches approximately 448 Gauss.

Example: Powering a Linear Actuator with the Magnetic Field Generator

As one application of the oscillating magnetic field generated by the device, a linear actuator was powered wirelessly, as shown inFIG.18a. When the external field equals to zero, the soft structure stays at rest in its original shape (FIG.18b). When a magnetic field in the z direction is applied, magnetic torques are applied on the embedded small magnets, which result in the rotation of the soft linkages and compress the actuator (FIG.18a). The actuator with an original length l0=8.8 mm decreases to a minimal length of l=3.7 mm. When a magnetic field is applied in the opposite direction, it extends to l=10.5 mm. Thus an overall linear displacement of approximately 6.8 mm is realized by the actuator without external load, which is more than 70% of its original length. The displacement at compression (5.1 mm) is much larger than at elongation (1.7 mm), as the magnetic torque changes non-linearly with the orientation of the magnets, and it is maximal when the angle is 90° (close to the situation shown inFIG.19).

The load characteristics of the actuator was also tested. The maximal displacement is plotted as a function of the external load inFIG.20b. As the load increases, the displacement decreases non-linearly due to the variance in the orientation of the magnets. The output work of the actuator also drops dramatically as the displacement gets smaller. Further optimization of the structure and matching the soft material's elastic modulus with the load will enhance the performance of the actuator. The current miniature actuator can provide a maximal force of approximately 84 mN. It lifts more than 40 times of its own weight, while still achieving 10% displacement. It is also worthwhile to point out, as the soft structure is planar, it is fully compatible with traditional soft photolithography process, and thus it can be scaled down to the micrometre scale.

The features as described in the above description, claims and figures can be relevant individually or in any combination to realise the various embodiments of the invention.