Method for controlling a movement of a medical device in a magnetic field

Abstract

A method for controlling a movement of a medical device in a magnetic field, the medical device having a set of coils includes determining a torque that needs to be applied onto the medical device such that the medical device carries out the movement, determining a minimum current that needs to be supplied to each coil of the set of coils, respectively, to reach the determined torque by solving an optimization problem, and supplying the determined minimum current to each coil of the set of coils, respectively, such that the medical device carries out the movement.

Claims

1. A method for controlling a movement of a medical device in a magnetic field, the medical device comprising a set of coils, wherein the method comprises: determining a torque that needs to be applied onto the medical device such that the medical device carries out the movement, determining a minimum current that needs to be supplied to each coil of the set of coils, respectively, to reach the determined torque by solving an optimization problem, and supplying the determined minimum current to each coil of the set of coils, respectively, such that the medical device carries out the movement wherein the optimization problem is defined as follows: $I^{*}=\underset{I}{\arg \min }{.Math.{}_{\mathrm{coils}}-{}_{\mathrm{des}}.Math.}^2+.Math.I{.Math.}_R^2$ wherein: I represents a current supplied to each coil of the set of coils, respectively, .sub.coils represents a total torque generated by the set of coils when being supplied with the current I, .sub.des represents the torque that needs to be applied onto the medical device such that the medical device carries out the movement, and R represents a resistance of each coil of the set of coils represents a constant determined using a grid search to find a best fitting.

2. The method according to claim 1, wherein determining the torque comprises solving a further optimization problem to minimize the torque to be applied onto the medical device such that the medical device carries out the movement.

3. The method according to claim 1, wherein the medical device comprises a flexible, substantially rod shaped portion and the movement comprises a deformation of said rod shaped portion resulting in a movement of a tip of said rod shaped portion.

4. The method according to claim 3, wherein solving the further optimization problem comprises: determining the deformation of said rod shaped portion that is needed for the movement of the tip of said rod shaped portion from an actual location to a desired location such that a torque that is required for the deformation of said rod shaped portion is minimized, and determining the torque that needs to be applied onto the medical device such that the medical device carries out the movement to be equal to the torque that is required for the deformation of said rod shaped portion.

5. The method according to claim 4, wherein the deformation that is needed for the movement of the tip of said rod shaped portion from the actual location to the desired location is determined using a model.

6. The method according to claim 1, wherein the method comprises receiving user input with respect to the movement via a user interface.

7. The method according to claim 1, wherein the method comprises: determining an actual position of the medical device using medical imaging, and automated controlling of the movement based on the determined actual position.

8. The method according to claim 1, wherein the method comprises displaying, on a display device connected to the medical device, an actual position of the medical device and/or a position of the medical device after carrying out the movement.

9. The method according to claim 8, wherein the method comprises displaying the actual position of the medical device and/or the position of the medical device after carrying out the movement with respect to a tissue.

10. The method according to claim 1, wherein the magnetic field is produced by a medical imaging device.

11. The method according to claim 1, wherein the magnetic field is a static magnetic field.

12. The method according to claim 1, wherein the medical device comprises a catheter.

13. The method according to claim 12, wherein the catheter comprises: a tip, the set of coils surrounding the tip, and power wires arranged to supply the set of coils with electrical energy.

14. The method according to claim 13, wherein the set of coils comprises four side coils arranged around the tip such that a straight line standing orthogonal on a longitudinal direction of the tip crosses a center of the respective side coil.

15. The method according to claim 14, wherein: a first and a second one of the side coils are connected in series, a third and a fourth one of the side coils are connected in series, the first and the second one of the side coils are arranged on opposite sides of the tip, and the third and the fourth one of the side coils are arranged on opposite sides of the tip and in-between the first and the second one of the side coils.

16. The method according to claim 14, wherein the four side coils are arranged on the same circuit board.

17. The method according to claim 12, wherein a turn number of at least one of the four side coils is between 2 and 40.

18. The method according to a claim 12, wherein the set of coils comprises at least one axial coil arranged around the tip such that a straight line extending in parallel to the longitudinal direction of the tip crosses a center of the at least one axial coil.

19. The method according to claim 12, wherein at least one of the coils of the set of coils was manufactured using laser machining, laser lithography and/or manually wound.

20. The method according to a claim 12, wherein at least one of the coils of the set of coils has an Archimedean spiral coil design.

21. The method according to claim 12, wherein at least one of the coils of the set of coils has an in-plane design.

22. The method according to claim 1, wherein the medical device comprises an endoscope.

23. The method according to claim 22, wherein the endoscope comprises: a tip, the set of coils surrounding the tip, and power wires arranged to supply the set of coils with electrical energy.

24. The method according to claim 23, wherein the set of coils comprises four side coils arranged around the tip such that a straight line standing orthogonal on a longitudinal direction of the tip crosses a center of the respective side coil.

25. The method according to claim 24, wherein: a first and a second one of the side coils are connect in series, a third and a fourth one of the side coils are connect in series, the first and the second one of the side coils are arranged on opposite sides of the tip, and the third and the fourth one of the side coils are arranged on opposite sides of the tip and in-between the first and the second one of the side coils.

26. The method according to claim 24, wherein the four side coils are arranged on the same circuit board.

27. The method according to claim 23, wherein the endoscope comprises an end effector connected to the tip of the endoscope.

28. The method according to claim 27, wherein the end effector comprises a further set of coils for actuating the end effector.

29. The method according to claim 28, wherein the method comprises actuating the end effector by applying a current to the further set of coils.

30. The method according to claim 29, wherein the method comprises ablating and/or killing tissue using the Joule heating caused by the current supplied to the further set of coils for actuating the end effector.

31. The method according to claim 28, wherein: the end effector comprises a grasper with two jaws connected pivotably to each other, and the further set of coils comprises at least one side coil arranged at each one of the two jaws, respectively.

32. The method according to claim 31, wherein actuating the end effector comprises opening and/or closing the jaws of the grasper by applying the current to the further set of coils.

33. The method according to claim 22, wherein a turn number of at least one of the four side coils is between 2 and 40.

34. The method according to claim 22, wherein the set of coils comprises at least one axial coil arranged around the tip such that a straight line extending in parallel to the longitudinal direction of the tip crosses a center of the at least one axial coil.

35. The method according to claim 22, wherein at least one of the coils of the set of coils was manufactured using laser machining, laser lithography and/or manually wound.

36. The method according to claim 22, wherein at least one of the coils of the set of coils has an Archimedean spiral coil design.

37. The method according to claim 22, wherein at least one of the coils of the set of coils has an in-plane design.

38. The method according to claim 22, wherein the tip of the endoscope comprises: a camera, an illumination device, and/or an opening of an irrigation channel extending through the endoscope.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 shows schematically, in a perspective view a catheter in an initial position and four position being different from the initially position.

(2) FIG. 2 shows schematically side coils of the catheter of FIG. 1.

(3) FIG. 3 shows schematically a cross sectional view of a tip of the catheter of FIG. 1.

(4) FIG. 4 shows schematically, in a perspective view an endoscope.

(5) FIG. 5 shows schematically, in a top view a grasper of the endoscope of FIG. 4 in a closed state.

(6) FIG. 6 shows schematically, in a top view the grasper of the endoscope of FIG. 4 in an open state.

(7) FIG. 7 shows a flow diagram of a method for controlling a movement of a medical device in a magnetic field.

(8) FIG. 8 shows diagrams for illustrating power-optimized controller capabilities at various initial orientations and their corresponding Joule heating effects when coils are powered.

(9) FIG. 9 shows a flow diagram of a further method for controlling a movement of a medical device in a magnetic field.

DESCRIPTION OF EXEMPLARY EMBODIMENTS

(10) As required, detailed embodiments are disclosed herein; however, it is to be understood that the disclosed embodiments are merely exemplary of the invention that may be embodied in various forms. The figures are not necessarily to scale, and some features may be exaggerated to show details of particular components. Therefore, specific structural and functional details disclosed herein are not to be interpreted as limiting, but merely as a basis for the claims and as a representative basis for teaching one skilled in the art to variously employ the present invention.

(11) In the following a solution to the Lorentz force-induced heating concern without using active cooling or limiting microcoil activation times for steering of a medical device is described. This is accomplished using a heat-mitigated design and actuation strategy using the previously mentioned 44 C. as a heating threshold for safe navigation within the body (assuming no arterial flow; worst-case scenario).

(12) In FIG. 1 a catheter 1 is shown in a perspective view in five different states/positions. Furthermore a cartesian coordinate system is shown comprising a X-axis, a Y-axis and a Z-Axis, wherein an angle between these axes is 90, respectively. A magnetic field comprising a magnetic field vector B.sub.0 aligned in parallel to the X-axis is present.

(13) The catheter 1 comprises a rod-shaped portion 3 and a tip 2 arranged at a distal end of the rod-shaped portion 3, wherein a set of coils 4 is arranged at the tip 2.

(14) As can be gathered from FIG. 3, which is a cross sectional view of the cylindrical tip 2, the catheter 1 comprises a working channel 5 having a round cross section and extending from the tip 2 through the rod-shaped portion 3 such that devices, tissue etc. may be brought from outside a body in which the catheter 1 is located through the working channel 5 into the body and vice versa.

(15) As in FIG. 1, also in FIG. 3 a cartesian coordinate system is shown comprising a X-axis, a Y-axis and a Z-Axis, wherein an angle between these axes is 90, respectively. The position of the axes X, Y, Z in FIG. 3 corresponds to the initial/middle position of the catheter 1 in FIG. 1. Therefore, the X-axis is arranged in parallel to a longitudinal direction of the tip 2 and of the working channel 5.

(16) The set of coils 4 comprises two axial coils 6 having a round cross section and which are arranged around the working channel 5, wherein a center of these two axial coils 6 is located on the X-axis, i.e., windings of the axial coils 6 are wound around the X-axis. In other words, a straight line extending in parallel to the longitudinal direction of the tip 2 crosses the center of the two axial coils 6. Therefore, in the initial position of the catheter 1 shown in FIGS. 1 and 3, where the magnetic field vector B.sub.0 extends in parallel to the X-axis, no Lorenz force may be generated by the axial coils 6.

(17) The set of coils 4 comprises four side coils 7-10 arranged around the two axial coils 6 of tip 2 such that a straight line standing orthogonal on the longitudinal direction of the tip 2, i.e., a straight line arranged in the YZ-plane and standing orthogonal on the X-axis, crosses a center of the respective side coil 7-10. Therefore, in the initial position of the catheter 1 shown in FIGS. 1 and 3, where the magnetic field vector B.sub.0 extends in parallel to the X-axis, a Lorenz force may be generated by the side coils 7-10 when applying a current to them. To do so, the catheter 1 comprise power wires 13 arranged at an outer circumference of a isolation material 12 (which surrounds the side coils 7-10) of the tip 2 to supply the set of coils 4 with electrical energy.

(18) All side coils 7-10 are arranged on the same flexible circuit board 14 which is wrapped around the axial coils 6, wherein a polymide layer 11 is arranged between the side coils 7-10 and the axial coils 6 (see FIG. 3). As can be gathered from FIG. 2, the first and a second one of the side coils 7, 8 are connected in series and the third and the fourth one of the side coils 9, 10 are also connected in series. As can be gathered from 3, the first and the second one of the side coils 7, 8 are arranged on opposite sides of the tip 2 and also the third and the fourth one of the side coils 9, 10 are arranged on opposite sides of the tip 2, i.e., the first and the second side coil 7, 8 are arranged in-between the third and the fourth side coil 9, 10.

(19) The Lorentz force that is generated by the side coils 7-10 leads to a movement of the tip 2 of the catheter 1 substantially in the YZ-plane, as shown in FIG. 1. Depending on the direction/polarity of the current (indicated by +I and I in FIG. 1) supplied to the side coils 7-10, the tip 2 moves to the left or the right when current is supplied to the first and the second side coil 7, 8 and up or down when current is supplied to the third and the fourth side coil 9, 10. Of course these movements may be combined, e.g., moving the tip 2 simultaneously up and to the right. Therefore, with this quad coil design, four digress of freedom may be realized.

(20) When an angle of 90 is reached, i.e., when the rod-shaped portion 3 is bound to such an extent that the tip 2 magnetic field vector B.sub.0 and the center of side coils 7-10 are in parallel, no Lorentz force is generated by the side coils 7-10 and the axial coils 6 may be used to overcome this point.

(21) A turn number of the four side coils 7-10 may be between 2 and 40 (i.e, including 2 and 40) or between 4 and 30 (i.e, including 4 and 30), respectively. However, in the present case the turn number the four side coils 7-10 is 7 (seven), respectively. Together with the rectangular Archimedean spiral, in plane coil design of the side coils 7-10, which are manufactured using laser machining, a very small tip 2 diameter may be reached, e.g., around 1 mm.

(22) This will be explained in detail below with respect to one specific implementation of the disclosure which is described solely for explanatory purposes and is not intended to limit the scope of the disclosure, especially the claims, in any way.

(23) Lorentz-force actuators have proven to be effective for various robotic/medical applications due to their precision, high force output, and scalability for soft device integration. These actuators utilize external magnetic fields to generate a force directly controlled for robotic actuation. Therefore, Lorentz-force actuators can utilize the high external magnetic field such as generated in MRI environments to develop robotic devices.

(24) It has been demonstrated integrating such actuators to catheters through the use of copper coils for Lorentz force-based steering in blood vessels and the heart. In this approach, controlling microcoil current polarity directly translates to a tip deflection of the tip 2 in the respective direction (se FIG. 1). The generated magnetic moment, m, and corresponding torque, T, can be determined in terms of the number of coil loops, N, current, I, and area normal vector, A, of a coil loop, and magnetic field vector (e.g., within an MR scanner) (B.sub.0=(0, 0, B.sub.0)), where B.sub.0 is the (e.g., uniform, permanent, i.e., static) magnetic field (e.g., inside the MRI). This relation is represented as (Equation 1)
T=mB.sub.0=NI(AB.sub.0)
which can be used to govern axial coil torque for a Lorentz force-actuated catheter with equally-sized coil loops. In terms of saddle (side) coil implementation, microcoils can be integrated to the catheter tip for additional degrees of freedom (DoF). Design optimization of an (e.g., MRI-driven) catheter 1 using a four coil configuration allowed for maximizing the achievable workspace (e.g., within the heart) given certain constraints such as the number of coil sets and current inputs.

(25) However, maximizing the number of coil turns and area may not be feasible for navigating within narrow vasculature. In order to improve upon both existing design schemes, laser machining may be used in conjunction with the Archimedean spiral coil design to create an in-plane, quad-configuration, microcoil design shown in FIG. 2.

(26) The proposed design enables more compact and significantly smaller final catheter diameters, e.g., down to 1 mm, than previously proposed designs while achieving comparable steerability. In this approach, both saddle/side coil sets are integrated on the same circumferential plane without introducing additional layer thickness compared to the state of the art.

(27) The governing equations for a rectangular Archimedean spiral are given below for estimating the microcoil's magnetic moment. The approximate effective area of all coil loops 7-10 can be expressed as (Equation 2)

(28) $A_{\mathrm{total}}=\underset{i=0}{\overset{N-1}{.Math.}}\left(L_c-w-i\left(w+2t\right)\right)\left(W_c-w-i\left(w+2t\right)\right)$
and corresponding total wire length for estimating power consumption as (Equation 3)

(29) $L_{\mathrm{coil}}=\underset{i=0}{\overset{N-1}{.Math.}}2\left(W_c+L_c-2i\left(2t+w\right)-2w\right)$

(30) Inserting Equation (2) into Equation (1) yields the magnetic moment of a single saddle coil
m=IA.sub.total
Achieving higher bending angles for Lorentz force-based actuation implies maximizing the coil's magnetic moment. As shown in the above equations, tuning various parameters (i.e., coil turn number, current, catheter diameter) can influence the performance. Typically, a larger coil turn number implies better bending performance due to the increasing coil area. However, when power is constrained to the heating threshold (e.g., 0.5 W) to mitigate heating effects, an inverse relation exists between the magnetic moment and coil turn number. In other words, a lower coil turn number is ideal for mitigating heat but requires higher currents to generate such magnitudes of electromagnetic torque leading to undesirable heating within the power wires 13. However, using larger power wires 13 to mitigate heating increases flexural rigidity depending upon wire gauge and thus has undesirable effects on catheter steerability. Therefore, a microcoil turn number in the above description ranges, especially of approximately 7, may be used to maximize the magnetic moment while remaining within well-established current ratings for power wires 13 and an acceptable range of stiffness for (e.g., endovascular) catheters.

(31) In the following an endoscope 15, here a neuroendoscope, that makes use of the same quad coil design as the catheter 1 is described in detail with respect to FIG. 4. The above given description applies mutatis mutandis to the endoscope 15 and is thus not repeated. Also here a cartesian coordinate system is shown comprising a X-axis, a Y-axis a and a Z-Axis, wherein an angle between these axes is 90, respectively. A magnetic filed comprising a magnetic field vector B.sub.0 aligned in parallel to the X-axis is present.

(32) The endoscope 15 comprise a tip 16, a rod-shaped portion 151, a set of coils 17 surrounding the tip 16 which was already described above with respect to the set of coils 4 surrounding the tip 2 of the catheter 1 and (not shown) power wires arranged to supply the set of coils 17 with electrical energy in the same manner as the above described power wires 13 of the catheter 1. The tip 16 of the endoscope 15 comprises a camera 18, an illumination device 19, optionally comprising an LED, and an opening 20 of an irrigation channel extending through the endoscope 15.

(33) The endoscope 15 comprises an end effector 21, here a grasper, connected to the tip 16 of the endoscope 15 The end effector is Lorentz force-actuated. Therefore, the grasper 21 comprises a further set of coils 22 for actuating jaws 23 of the grasper 21.

(34) This is shown in detail in FIGS. 5 and 6. The two jaws 23 (only one is shown in FIGS. 5 and 6) are connected pivotably via a pivot joint 24 to each other. The further set of coils 22 comprises a side coil arranged at each one of the two jaws 23 such that by applying a current to the side coils of the further set of coils 22 the jaws 23 may be open and or closed by turning them around the pivot about joint 24 (FIG. 5 shows the closed and FIG. 6 the open state).

(35) In the following a method for controlling a movement of the above described medical devices, i.e, the endoscope 15 and the catheter 2, in a magnetic field is described in detail. A flow chart of the method is shown in FIG. 7. The method is beneficial since Joule heating may remain a concern even with the above described design of the medical devices and therefore optimizing microcoil (saddle/axial) power distribution may impact the performance of the medical device 1, 15.

(36) Both medical devices 2, 15 have in common that they comprise a flexible substantially rod-shaped portion 3, 151. The movement of the tip 2, 16 comprises a deformation of said rod-shaped portion 3, 151 resulting in a movement of the tip 2, 16 of said rod-shaped portion 3, 151. Therefore, the principles described below may be applied to both, the catheter 2 and the endoscope 15.

(37) In a first step S1 of the method a torque that needs to be applied onto the medical device 1, 15 such that the tip 2, 16 of the medical device 1, 15 carries out the movement is determined.

(38) Determining the torque may comprise solving a first optimization problem to minimize the torque to be applied onto the medical device 1, 15 such that the tip 2, 16 of the medical device 1, 15 carries out the movement.

(39) Solving the first optimization problem may comprise determining the deformation of said rod-shaped portion 3, 151 that is needed for the movement of the tip 2, 16 of said rod-shaped portion 3, 151 from an actual location to a desired location such that a torque that is required for the deformation of said rod-shaped portion 3, 151 is minimized. The torque that needs to be applied onto the medical device 1, 15 such that the medical device carries out the movement is then set to be equal to the torque that is required for the deformation of said rod-shaped portion 3, 151.

(40) The deformation that is needed for the movement of the tip 2, 16 of said rod-shaped portion 3, 151 from the actual location to the desired location may be determined using a model, optionally a Cosserat model, depicting the nonlinear dynamics of said rod-shaped portion 3, 151.

(41) This will be explained in detail below with respect to one specific implementation of the disclosure which is described solely for explanatory purposes and is not intended to limit the scope of the disclosure, especially the claims, in any way.

(42) Steerable catheters undergo large deformations/motions during surgical procedures. One method of modeling such motions commonly used to model elastic rods and continuum rods is the Cosserat rod theory. The Cosserat rod model integrates the traditional bending and twisting of Kirchhoff rods with additional stretching and shearing to capture full beam dynamics. The Cosserat model accurately depicts the nonlinear dynamics of elastic rods with different materials and geometries. The catheter 1 may be modeled as a cantilever beam undergoing an external torque and tip force. The state of the catheter may be described using a set of N discretized segments Y=[y.sub.0.sup.T, y.sub.1.sup.T, . . . , y.sub.N.sup.T].sub.N.sup.T. The discretized state vector for each segment i contains segment position (p.sub.iR.sup.3), orientation (R.sub.iSO(3)), extension force (nR.sup.3), and shear torque (mR.sup.3), which can be expressed in one vector y.sub.i=[p.sub.i, R.sub.i, n.sub.i, m.sub.i]. The rotation matrix is defined in the (e.g., MRI's) fixed coordinate frame, along with two additional coordinate frames L; control frame C representing the catheter free length starting position and tip frame T locating the start of the microcoils. Therefore, a system of nonlinear ordinary differential equations (ODEs) can be expressed as (Equations 5 to 8)
{dot over (P)}.sub.i=R.sub.iv.sub.i
{dot over (R)}.sub.i=R.sub.iu.sub.i
{dot over (n)}.sub.i=Ag
{dot over (m)}.sub.i={dot over (p)}.sub.in.sub.i
where v and u are tangent and curvature vectors defined as, v={circumflex over (z)}+K.sub.1R.sup.Tn and u=K.sub.2R.sup.Tm m, where is the unit vector in local coordinate frame, K.sub.1=diag(GA,GA,EA) and K.sub.2=diag(EI.sub.A, EI.sub.A,GJ). G, A, E, I.sub.A, and J represent the shear modulus, cross-sectional area, elastic modulus, area moment of inertia, and polar moment of inertia, respectively. Catheter forward kinematics, Y=f (n.sub.0, m.sub.0), can be calculated through numerical integration using fourth order RungeKutta algorithm, given the catheter's initial conditions: R.sub.0=R.sub.C, p.sub.0=p.sub.C, n.sub.0=n.sub.C, m.sub.0=m.sub.C. Although the forward kinematic model in an initial value problem form is useful for simulating catheter motion given a base wrench, an inverse kinematic model is needed to determine the minimum catheter torque for reaching desired orientations. An inverse kinematic model in a boundary value problem (BVP) form may be formulated with the following boundary conditions: R.sub.0=R.sub.C, p.sub.0=p.sub.C, n.sub.=0, m.sub.=.sub.des and R.sub.=R.sub.des. Here, n.sub. and m.sub. are expressed as the magnetic wrench at the tip 2 of the catheter 1. Due to the negligible magnetic gradient pulling force acting on the catheter tip in comparison to the magnitude of a distributed Lorentz force, it is assumed there is only torque at the tip 2. Therefore, the inverse kinematic for desired tip torque (.sub.des=IK(R.sub.des)) is calculated by solving the following optimization problem for tip torque (Equation 9)

(43) $\underset{Y}{\arg \min }{.Math.R_{,\mathrm{des}}{R}_{}.Math.}_2^2+{.Math.{}_{\mathrm{des}}.Math.}_2^2$$s.t.Y=f\left(n_0,m_0\right)$
where the box minus (: SO(3)SO(3).fwdarw..sup.3) is the rotation difference operator based on the matrix logarithm defined in Lie algebra. Tip torque is .sub.des=m.sub.N. Optimization is solved in real-time using the iterative LevenbergMarquardt method implemented in C++, where catheter forward kinematics is used as the shooting function. It is important to note that the error may be essential for the stability of the solution for near singular values, and the quadratic on tip torque regularizes the cost function to eliminate inverse kinematic solutions with loops. The above given description applies mutatis mutandis to the endoscope.

(44) In a second step S2 of the method a minimum current that needs to be supplied to each coil 6, 7-10 of the set of coils 4, 17, to reach the determined torque (_des) by solving a second optimization problem is determined, respectively.

(45) This will be explained in detail below with respect to one specific implementation of the disclosure which is described solely for explanatory purposes and is not intended to limit the scope of the disclosure, especially the claims, in any way.

(46) Microcoil-based heat generation can be reduced by optimally distributing current to the side and axial coils 6, 7-10. The tip orientation controller therefore comprises a two-stage optimization scheme: 1) inverse kinematics to determine torque using Equation (9), and 2) saddle/axial coil current distribution. A power-optimized current distribution problem is formulated as a non-linear quadratic optimization (Equations 10 and 11)

(47) $I^{*}=\underset{I}{\arg \min }{.Math.{}_{\mathrm{coils}}-{}_{\mathrm{des}}.Math.}^2+.Math.I{.Math.}_R^2$$s.t.{}_{\mathrm{coils}}={}_{\mathrm{side},1}+{}_{\mathrm{side},2}+{}_{\mathrm{axial}}$
where I=[I.sub.side,1, I.sub.side,2, I.sub.axial] represents the saddle/sie and axial coil currents, and .sub.coil represents the total torque generated by a saddle and axial coilset 6, 7-10, respectively. The first term of the costfunction is for consistency between desired tip torque and total coil torque, and second term is the coil power consumption cost, where R=diag(R.sub.side,1, R.sub.side,2, R.sub.axial] is the resistance of the coils. Due to the difference in magnitude between torque error and induced currents, an a constant is incorporated (determined using a grid search to find the best fitting; 110.sup.6). This optimization is also solved using the LevenbergMarquardt method. A comparison between actuating coils using equally-distributed power versus the optimal approach is shown in FIG. 8. In FIG. 8A-i) defines the initial angle between the catheter tip 2 and B.sub.0 field vector, , and final tip orientation, , upon excitation. A,B) represent when the quad-configuration microcoil (QCM) begins aligned with and perpendicular to the B.sub.0 field, respectively. Power was compared between both actuation schemes in (A-i) and (B-i): equally distributed (E.D.) power and optimized current distribution between coils. Conserved power using the optimal approach is equal to the area between the two curves. (A-ii) and (B-ii) show the current distribution using both actuation schemes. (A-iii) and (B-iii) show total power conserved using the power-optimized controller. The current distribution optimization minimizes power consumption and Joule heating effects by prioritizing the axial coils 6 when achieving angles between 90 and 160 (FIG. 8A-ii), resulting in an increase in the conserved power. Beyond 160, the side coils 7-10 generate more torque resulting in current reprioritization and thus a loss in the conserved power. This phenomenon is also observed when =90 (FIG. 8B-ii); between 20 and 50, the axial coils 6 are prioritized. Angles less than 20 cause current redistribution toward the side coils 7-10 as the catheter aligns parallel to the B.sub.0 field vector. Due to the differences in coil resistance between the saddle/side and axial coils 6, 7-10, significant power changes can be observed (FIG. 8A-iii, B-iii). FIG. 8A-iii demonstrates 3 mW of conserved power for smaller angles and as much as 50 mW for larger angles when the catheter 1 begins aligned with the B.sub.0 field vector. FIG. 8B-iii indicates a conserved power magnitude of 10 mW when =90 and the catheter 1 aligns parallel to the B.sub.0 field vector. 25% conserved power regardless of initial orientation may be demonstrated. Such power conservation improves overall catheter safety during steering at low rotation angles, and increases the catheter workspace up to 10 at higher angles. The above given description applies mutatis mutandis to the endoscope 15.

(48) In a third step S3 of the method the determined minimum current (I_side1, I_side2, I_axial) is supplied to each coil of the set of coils 6, 7-10, respectively, such that the tip 2, 16 of the medical device 2, 15 carries out the movement.

(49) The third step S3 may comprise, in case the medical device is the endoscope 15, actuating the end effector 21 thereof by supplying a current to the further set of coils 22. In case the end effector 21 comprises the grasper, actuating the end effector 21 may comprise opening and/or closing the jaws 23 of the grasper 21 by applying the current to the further set of coils 22. The opening may be a movement where the jaws of the grasper are moved away from each other by turning them around the pivot joint 24 and the closing may be a movement where the jaws 23 of the grasper are moved towards each other by turning them around the pivot joint 24. The method may comprise ablating and/or killing tissue, optionally comprising tumor cells, such as cancerous brain tumor cells, using the Joule heating caused by the current supplied to the further set of coils 22 for actuating the end effector 21, optionally for opening and closing the jaws 23 of the grasper.

(50) The Joule heating caused by actuating the grasper may be used in the third step S3 of the method for cauterization. More specifically, the cauterization comprises actuating the end effector by applying a current to the further set of coils 22, and ablating and/or killing tissue, optionally comprising tumor cells, using the Joule heating caused by the current supplied to the set of coils for actuating the end effector.

(51) This will be explained in detail below with respect to one specific implementation of the disclosure which is described solely for explanatory purposes and is not intended to limit the scope of the disclosure, especially the claims, in any way.

(52) With the proposed design of the MM-driven endoscope 15 described above, leveraging the high (3-7 T), external magnetic field of an MR scanner for heat-mitigated steering within the ventricular system of the brain becomes possible. The Lorentz force-based grasper may be used for diseased tissue manipulation and ablation, i.e., cauterization. Feasibility studies show the neuroendoscope 15 can be steered precisely within the lateral ventricle to locate a tumor using both MRI and endoscopic guidance. Results also indicate grasping forces as high as 31 mN are possible and power inputs as low as 0.69 mW can cause cancerous tissue ablation.

(53) In FIG. 9 a flowchart for a flow diagram of a further method for controlling the movement of the medical device 1, 15 in a static magnetic field produced by a medical imaging device, here a magnetic resonance imaging device. The method comprises the above described steps S1-S3. The method further comprises in an initial step S0 receiving user input with respect to the movement via a user interface, optionally comprising a joystick. The user interface may be connected to the medical device 1, 15. The method further comprises a fourth step S4 carried out simultaneously to the steps S0-S4, wherein this step S4 comprises determining an actual position of the medical device 1, 15, optionally the tip 2, 16 thereof, using medical imaging, here the MRI, continuously and displaying the determined position of the medical device continuously on a display device with respect to a tissue, optionally of a human being or an animal, in which the medical device 1, 15 is located. The display device may be connected to the medical imaging device.