Abstract
A method where a propeller is set into locomotion relative to a medium at least partially surrounding the propeller. An actuator induces a rotation of the propeller relative to the medium and about a rotational axis of the propeller, and the propeller converts its rotational movement into locomotion relative to the medium. The aspect ratio of at least one cross-section of the propeller is three or more. Also a helical or modifiedly helical propeller for converting rotational movement of the propeller into locomotion of the propeller relative to a medium at least partially surrounding the propeller, where the aspect ratio of at least one cross section of the propeller is three or more. And a method of producing a propeller, including the step of providing a plate extending along the helical axis, where the aspect ratio of at least one cross section of the plate is three or more.
Claims
1. A helical or modifiedly helical propeller for converting rotational movement of the propeller into locomotion of the propeller relative to a medium which at least partially surrounds the propeller, wherein the aspect ratio of at least one cross section of the propeller, which cross section is a cross section related to the propeller's helical axis, is 3 or more, and on at least one cross section which is perpendicular to the helical axis of the propeller, the axis passes through the propeller, and wherein the propeller is at least partly magnetized or further comprises a component materially connected with the propeller, which component is magnetized.
2. The propeller of claim 1, wherein the largest radius of any cross section of the propeller that is perpendicular to the propeller's rotational axis is 5 mm or less.
3. The propeller of claim 1, wherein the smallest radius of any cross section of the propeller that is perpendicular to the propeller's rotational axis is 300 μm or less.
Description
BRIEF DESCRIPTION OF THE FIGURES
(1) The invention is illustrated in greater detail with the aid of schematic drawings:
(2) FIG. 1(a) is a perspective view of an embodiment of the propeller according to the invention in perspective view;
(3) FIG. 1(b) is a cross sectional view of the propeller of FIG. 1(a)
(4) FIG. 2 is a light microscope image of a propeller according to the invention to which a magnet is attached and which is embedded in soft tissue;
(5) FIG. 3 shows two light microscope images of the propeller of FIG. 2 penetrating a Matrigel®, the bottom image taken 18 seconds after the top image;
(6) FIGS. 4(a) to (d) schematically compare the cross-sectional shapes of a propeller according to the invention as shown in FIG. 4(a) with those of prior art propellers as shown in FIGS. 4(b) to 4(d);
(7) FIG. 5 is a schematic cross-sectional representation of a propeller according to the invention with medium co-rotating with the propeller;
(8) FIG. 6(a) shows a frame from a video of the propeller in a viscoelastic medium with tracer particles embedded in the medium to visualize the deformation of the medium;
(9) FIG. 6(b) indicates the trajectory of one tracer particle over the period of many rotations of the propeller; the large normalized deformation provides large axial propulsion force;
(10) FIG. 7 illustrates in a cross-sectional view a propeller according to the invention rotating in a viscoelastic medium and the effectively deformed area of the medium induced by the rotation of the propeller is labelled with hatch;
(11) FIG. 8 illustrates in a cross-sectional view a prior art propeller design rotating in a viscoelastic medium and the effectively deformed area of the medium induced by the rotation of the propeller is labelled with hatch;
(12) FIG. 9 illustrates in a cross-sectional view another prior art propeller design rotating in a viscoelastic medium and the effectively deformed area of the medium induced by the rotation of the propeller is labelled with hatch;
(13) FIG. 10 is a force diagram of a short part on the edge of a propeller according to the invention;
(14) FIG. 11 shows two light microscope images of the propeller of FIG. 2 penetrating porcine brain tissue, the bottom image taken 300 seconds after the top image;
(15) FIG. 12 illustrates the method of producing a propeller according to the invention;
(16) FIG. 13 illustrates another method of producing a propeller according to the invention; and
(17) FIG. 14 is a perspective view of two propellers according to the invention with forward tapers at both ends.
DETAILED DESCRIPTION OF THE INVENTION
(18) Propeller Moving in a Tissue Model
(19) It is an achievable advantage of the propeller 1 according to the invention that it can efficiently self-propel through a viscoelastic medium, for example a biological tissue. In FIG. 2, a propeller 1 according to the invention is shown that is fully embedded in a gel medium 2 of Matrigel®, a hydrogel that is used as a tissue model for the validation of the propeller. Matrigel®, available from Gibco®, Life Technologies® is the trade name for a gelatinous protein mixture secreted by mouse sarcoma cells. It resembles the complex extracellular matrix (ECM) found in many tissues, and it is widely accepted as an in vitro model for cell 3D culture, tumour cell metastasis studies and cancer drug screening. Here, Matrigel® serves as a gel medium 2 model for connective tissues for the propeller 1 to penetrate. The Matrigel® solution was used as received, thawed on ice and gelled in an incubator under 37° C. for 1 hour.
(20) The propeller 1 was inserted into the gel medium 2 by means of tweezers. A magnetic field with a homogeneous magnitude (adjustable from 50 to 1000 Gauss) and a continuous rotating direction (frequency in the range of 1 to 100 Hz (hertz) was applied, and the field was rotated with a speed of 10 Hz. One end of the propeller 1 a cylindrical magnet 3 of a neodymium, iron and boron (NdFeB) material, 200 μm (micrometres) in diameter and 400 μm in length and magnetized in the diameter direction is attached in a torque-proof fashion. The magnet has a permanent magnetic moment and rotates together with the external rotating magnetic field. Due to the special shape design of the propeller, it couples the rotation to translational motion (forward or backward propulsion) and achieves net displacement in the gel medium 2 or biological tissues.
(21) As can be best seen in FIG. 1(a), the propeller 1 has a chiral, more precisely a helical shape. It is left-handed but of course a right-handed design would be suitable likewise. The axis of rotation 4 and the helical axis coincide in the propeller of FIG. 1. The direction of locomotion v is indicated as a rightwards arrow v. The direction of rotation is indicated as a semi-circular arrow ω. As can be seen in the cross-sectional view in FIG. 1(b), the aspect ratio of any cross-section 5 of the propeller 1 perpendicularly to the helical axis is considerably larger than 5. The aspect ratio is obtained by dividing the largest radius 6 of the cross section by the smallest radius 7 of the cross section 5. The radii 6, 7 extend from the point 8 where the rotational axis 4 perpendicularly pierces the cross section 5 to a point of the circumference 9 of the cross section.
(22) From the images in FIG. 3 it can be seen how the propeller 1 propagates through the Matrigel® gel medium 2. The bottom image was taken 18 seconds after the top image. The dotted line indicates the initial position of the magnet 3. A speed of approximately 45 μm/s (micrometres per second) along the helical axis of the propeller was observed at the rotational frequency of 10 Hz. By choosing the rotational direction of clockwise or counter-clockwise, the propeller 1 can move either forward or backward.
(23) In FIGS. 4(a) to (d) schematically the cross-sectional shape of a propeller 1 according to the invention is compared with cross-sectional shapes of propellers known from the afore-mentioned publications by L Zhang, J J Abbott, L X Dong, B E Kratochvil, D Bell, and B J Nelson, FIG. 4(b), A Ghosh and P Fischer, FIG. 4(c) and T Qiu, J Gibbs, D Schamel, A Mark, U Choudhury, and P Fischer, FIG. 4(d). In the top row, 3D views are provided while in the bottom row the cross-sectional shapes are shown. It can be seen that the cross section 5 of the propeller of the present invention has a considerably larger aspect ratio than the cross sections 5′ of the prior art propellers 1′ based on their radii 6′ and 7′.
(24) Moreover, as the propeller 1 rotates in and moves through the viscoelastic medium 2, parts 10 the medium 2 may attach to the surface of the propeller 1 and rotate together with it. This is schematically shown in FIG. 5. In the example of FIG. 5 the aspect ratio of the cross section of the rotating body that comprises the propeller 1 and the parts 10 of the medium 2 that rotate with the propeller 1 is still larger than 3. The aspect ratio in this case is obtained by dividing the largest radius 11 of the cross section of the rotating body by the smallest radius 12 of the cross section of the rotating body. The radii 11, 12 extend from the point 8 where the rotational axis 4 perpendicularly pierces the cross section to a point of the circumference 9 of the cross section of the rotating body.
(25) Propulsion Mechanism of the Propeller
(26) The inventor believe, without prejudice, that the propeller 1 according to the invention when used in viscoelastic media exploits a new propulsion mechanism, which is different from the mechanism for propulsion in viscous fluids as has been published before. FIGS. 6(a) and 6(b) show results of a Particle Imaging Velocimetry (PIV) experiment. In the experiment, fluorescent polystyrene beads (FluoSpheres®, Life Technologies), 15 μm in diameter, were used as tracer particles and mixed in the Matrigel® gel medium 2 to show the movement, in particular the deformation, of the gel medium 2. The beam of a green laser with a wavelength of 532 nm (nanometres) was expanded by a cylindrical lens to a laser sheet and directed on a thin sheet of the Matrigel® gel medium 2. The motion of the propeller 1 and the tracer particles was recorded by a microscope with a long pass filter (OD4-550 nm, Edmund Optics) and a video camera. The position of the tracer particles were analysed by a customized script in Matlab (R2014b, Mathworks), and circled in every frame of the video. The circles can be seen in both FIG. 6(a) and the enlarged FIG. 6(b). In FIG. 6(b) the trajectory of one tracer particle 13 is indicated. The particle 13 follows a closed, essentially elliptical trajectory 14 over a period of many rotations of the propeller 1. A normalised deformation can be calculated as the quotient of radial displacement d and the distance r from the rotational axis.
(27) The experiment suggests that the movement (deformation) of the viscoelastic medium 2 is clearly different from the flow around a propeller in a viscous fluid. In a fluid, the particles rotate together with the propeller for a full rotation, and the difference of fluidic dynamic drag in the two perpendicular directions at low Reynolds number results in a forward propulsion force, which was explained in the literature. However, a different motion trajectory of the particles was observed with the propeller 1 disclosed here, suggesting that the new design of the propeller 1 enables a new propulsion mechanism in the viscoelastic media, which has not been reported before.
(28) The relaxation time of the viscoelastic solids, which include most biological tissues, are often on the order of minutes, whereas the propeller typically rotates at a frequency of 1 to 10 Hz. As, accordingly, the cycle time (0.1 to 1 s) of the propeller's 1 rotation is much shorter than the relaxation time, only the elastic response of the gel needs to be considered. As an example, shown in the FIG. 7, the cross-section 5 of the propeller 1 is modelled as a rectangular solid that rotates in an initially rectangular hole 15 of the medium 2. Note that in FIG. 7(b) the medium 2 is not flowing but is deformed as the propeller 1 rotates. Large deformation (strain) of the medium 2 is induced by the rotation of the propeller 1. The effectively deformed volume of the medium 2 around the propeller 1 is dramatically larger than in prior art propeller designs (as shown exemplarily in FIG. 8 where the corresponding elements are a propeller 1′ in the form of a screw reported in prior art; and FIG. 9 where the corresponding elements are a propeller 1′ in the form of a conventional screw. The medium 2′, the gap 15′ and the effective deformed area in hatch are also shown in the figures). The medium 2 is considered elastic, ie a spring where the recoil force is positively correlated to the deformation. Therefore, larger deformation of the medium 2 requires more torque for rotation, and exerts larger forward propulsion force. Both of these two phenomena were observed in the experiment.
(29) For further illustration, in FIG. 10 the force diagram of a small section of the propeller 1 (left-handed, the front edge of the propeller rotates upwards in order to move to the right) is shown. The direction of rotation is indicated as an upwards arrow v. It is clear from the force diagram that there is a propelling force component F_p pointing towards the right. Similarly to the situation shown in FIG. 7, the larger the deformation, the larger is the forward propulsion force. Therefore, the proposed propulsion mechanism of the propeller 1 according to the present invention can be summarized in the following three aspects: First, the rotation of the propeller 1 induces large deformation of the gel medium 2. More specifically, large aspect ratio on the cross section 5 of the propeller 1 induces large deformation of the gel medium 2, which leads to large forward propulsion force F_p. Second, the pressure on the tip 16 of the propeller 1 should be higher than the tensile strength of the gel medium 2 in order to break it. It requires an area of the tip 16 as small as possible, for example, a sharp tip 16 is preferable. Moreover, the newly cut area (crack) 15 of the medium 2 due to the forward motion of the tip 16 of the propeller also has a high aspect ratio, such as a rectangular shape, shown as the white area in FIG. 7(a), which again allows the large deformation of the medium 12 when the propeller 1 rotates. It is different from the traditional propeller's 1′ design that the crack 15′ is almost circular, see FIG. 9(a), and the deformation of the medium 2′ induced by the traditional propeller 1′ is small. Third, after the possible attachment of the medium 2 around the propeller 1 such as FIG. 5, it should still fulfil the two conditions above. This criterion ensures a continuous movement of the propeller 1 in the tissue.
(30) The traditional propeller 1′ designs with a hollow opening in the middle, such as the published designs shown in FIG. 4(b) and FIG. 4(c), do not propel efficiently in viscoelastic media. The reason lies in that the opening is filled with the viscoelastic medium during rotation of the propeller, and when considering the medium rotating together with the propeller, the overall structure does not have a high aspect ratio on any cross-section, as shown in FIG. 8(b). In other words, a plug of the gel changes the traditional propeller shape into an almost cylindrical shape, inducing very limited deformation of the media around it, thus the traditional propellers can only rotate at the same position in the viscoelastic medium and no net displacement can be achieved. The present invention in a preferred embodiment clearly differs from the prior art designs in that on at least one cross section, preferably all the cross sections, which are perpendicular to the helical axis of the propeller, the axis passes through the propeller. Or in other words, on at least one cross-section, preferably all the cross-sections, the rotational centre is inside of the propeller.
(31) For some particular kinds of viscoelastic media, such as a yield-stress fluid, the propeller can break (or liquefy) part of the medium due to the shear stress induced by the rotation of the propeller. And the transportation of the broken (or liquefied) parts of the medium to the backwards can also result in the forward propulsion of the propeller.
(32) Preferably, the rotational speed that leads to highest propulsion speed should be used to actuate the propeller 1. This value, which depends on both the geometry of the propeller 1 and the rheology of the medium, can be determined experimentally by sweeping the frequency and measuring the propulsion speed. It has been found that the optimal frequency in a viscoelastic medium 2 of the propeller 1 disclosed here can be much lower than the step-out frequency. When the frequency is increased above the optimal value, the propeller 1 continues to rotate, but the propulsion speed dramatically decreases until it reaches zero. On the contrary, in viscous fluids at low Reynolds number, the optimal frequency of a propeller 1 is very close to the step-out frequency, and the propulsion speed increases linearly with the driving frequency before it reaches step-out. This observation too, suggests that the present propeller 1 enables a new propulsion mechanism in viscoelastic media.
(33) Propeller Moving in a Brain Sample
(34) The light microscope photos in FIG. 11 show a propeller 1 according to the invention that penetrates a porcine brain tissue to demonstrate its capability to move through real biological soft tissues. Fresh porcine brain was stored on ice and received from a local slaughterhouse. A volume of about 25×25×8 mm.sup.3 (cubic millimetres) of the brain was dissected, and the propeller 1 was inserted by tweezers. As the tissue was relatively thin, and bright white light back illumination was used, the movement of the propeller was observed inside the brain tissue. The dotted line indicates the initial position of the propeller 1. An average propulsion speed of approximately 35 μm/s was measured at a rotational frequency of about 1 Hz. Due to the shape of the propeller 1, the rotation of propeller 1 can be actuated with limited magnetic torque. In the experiment, a magnetic field with a magnitude of 100 to 300 G was sufficient to drive the propeller 1 through the brain tissue sample. This field is applicable with common magnetic field generators, such as electric coils or permanent magnets setup as discussed in more detail further below.
(35) Fabrication of the Propeller
(36) A method of producing the propeller 1 according to the invention is illustrated in FIG. 12. The propeller 1 was made of copper with a mechanical machining approach. A copper wire, 50 μm in diameter, was mechanically rolled into a flat plate 17 with a width of 255 μm and a thickness of 13 μm. As shown in FIG. 12, the plate 17 was mounted between two concentric clamps 18, 19 which can be rotated relative to each other. By rotating one 18 of the clamps while leaving the other 19 stationary, the plate 17 was twisted into a chiral structure. During twisting, a normal force occurs on the axial direction v, thus the distance between the two clamps 18, 19 was adjusted accordingly. Sensors can be used to measure the force and torque during this process, and the distance and angular position of the clamp can be controlled by motors with a computer. The pitch dimension and chirality of the propeller can be controlled in this way. The long twisted plate 17 was subsequently cut into individual propellers 1 with a desired length of 2 mm. Finally, a miniaturized magnet, 200 μm in diameter and 400 μm in length, was attached to one tip of the propeller 1.
(37) The cutting procedure can be done by machining, laser etching, (focused) ion etching, or chemical etching. The mask for etching can be fabricated by photolithography on the two sides of the plate before the twisting process. In this way, a mass production process of the propeller can be achieved.
(38) Another method of producing the propeller 1 according to the invention is illustrated in FIG. 13. A structure of the propeller 1 is first obtained, for example in copper material by the method described above or by 3D printing (FIG. 13(a)); then, the structure is moulded into a second material, such as a soft polymer, eg PDMS (FIG. 13(b)); the first structure is removed from the negative mould 20, for example by rotating the propeller 1 in the right direction and it propels out of the mould 20, or by expanding the soft polymer mould 20 (FIG. 13(c)); liquid polymer material or mixture is injected into the negative mould 20 (FIG. 13(d)), for example a mixture of epoxy resin and ferromagnetic particles (mean diameter 40 μm), the polymer is cured at room temperature in the presence of an external magnetic field as illustrated by the arrow in the FIG. 13(d); finally, the propeller 1 is obtained by releasing it from the negative mould 20, either by breaking the mould 20, or by rotating the propeller 1 in the right direction and it propels out of the mould 20 (FIG. 13(e)). The propeller 1 have the right magnetic moment M (as indicated by arrow in (FIG. 13(f)), as the magnetic particles in the structure are aligned in the right direction when the external magnetic field B is applied. Drugs can be incorporated in polymer mixture in the moulding step above, or be absorbed to the propeller materials after releasing in the last step above.
(39) FIG. 14 illustrates how the two tips 16 of the propeller 1 can be cut or etched or moulded into designed shape, preferably a sharp tip. This way, the pressure at the tip 16 can be increased by decreasing the contact area; also, the shear rate in the medium 2 in front of the propeller can be increased. As many biological media are shear-thinning, a larger shear rate also helps the forward propulsion of the propeller. In this case, the sharp tip of the propeller is preferably at the edge of the propeller tip 16 and far from the rotational axis.
(40) Actuation of the Propeller
(41) A suitable setup for inducing rotation into the propeller by means of a rotating magnetic field is for example known from the afore-mentioned publication by T Qiu, J Gibbs, D Schamel, A Mark, U Choudhury, and P Fischer. The relevant parts of this document are incorporated into the present disclosure by reference.
(42) The field can be spatially homogeneous or with a magnetic gradient in space, but preferably the pulling force acting on the propeller generated by the magnetic gradient is in the same direction as the direction of the self-propelling force of the propeller 1. The magnetic field can be generated with electric coils. For example, three pairs of Helmholtz coil can achieve the motion control of the propeller in three dimensional space by changing the phase and magnitude of the current in different coils. The magnetic field can also be generated with the rotation of permanent magnet(s), which can be several magnets specially arranged in space or only one magnet keeping a required distance away from the propeller. To control the propulsion trajectory with the permanent magnets setup, the rotational axis of the setup should be changed.
(43) For the realisation of the invention in its various embodiments, the features disclosed in the present description, claims and drawings can be of relevance individually as well as in any combination.
