Helical magnetic robots driven by an external magnetic field have been extensively studied for robotic endovascular intervention to treat occlusive vascular disease. Most previous researchers have utilized cone-shaped head helical magnetic robots (CHMRs) with helical blades for thrombus drilling. However, the CHMR may become stuck in the thrombus or drilling performance may be significantly reduced after the cone-shape head enters the thrombus. We propose a sawtooth head helical magnetic robot (SHMR) to improve drilling performance. Furthermore, the pitch length of the SHMR was optimized experimentally. Finally, improved drilling performance of the SHMR compared to CHMR was verified by in vitro drilling experiments with a pseudo thrombus containing 0.8 wt. %, 1.0 wt. %, and 1.2 wt. % agar.

Occlusive vascular disease (OVD) such as stroke in the brain, myocardial infarction in the heart, and peripheral artery disease in the leg occurs when a blood vessel becomes narrowed or blocked due to accumulated blood clots and lipids and is a major cause of human death in modern society.1 A medical doctor can perform an endovascular intervention in which catheters and guidewires are inside of a patient body but actuated outside of the patient body to approach a target lesion and deliver drugs and a balloon or a stent based on X-ray images. In order to improve the limitations of precise manipulation of catheters and exposure of surgical staff to X-ray radiation in the conventional endovascular intervention, many researchers have investigated both magnetic robots containing a permanent magnet and an electromagnetic navigation system (eMNS) that can remotely control the motion of the magnetic robot for navigation, thrombus drilling, and drug delivery.2–4 Helical magnetic robots inspired by the screw mechanism have been widely studied for their simple structure and flexibility within the vasculature.5–9 

The helical magnetic robot is driven by an external magnetic field to drill holes for thrombus removal using its rotational motion. The power delivered to the helical magnetic robot is determined by the external magnetic flux density and the rotating frequency for the given permanent magnet of the helical robot. The shape of the helical magnetic robot’s drill bit is another important factor affecting drilling performance because it determines how effectively the magnetic power is utilized.9 In previous studies of thrombus removal by helical magnetic robots, many investigators used a cone-shaped head drill geometry.8,10–14 Alternatively, many researchers have used a sharp tip for helical magnetic robot drill geometry. However, helical magnetic robots with this geometry have some drilling limitations. For example, in blood vessels, there is a risk that helical magnetic robots with sharp coned heads will puncture the blood vessels. Moreover, in our usual drilling experiments, we found that the CHMR is prone to embed in the thrombus and become jammed due to the insufficient magnetic torque of the helical magnetic robot.

To solve the potential problems of the CHMR while drilling a thrombus, we propose a sawtooth head helical magnetic robot (SHMR) that uses rubbing and crushing actions for thrombus removal. Also, to enhance the propulsive force of the SHMR at constant length and diameter, its pitch was optimized experimentally. Moreover, the thrombus drilling performance of CHMR and SHMR was compared through in vitro experiments with a pseudo thrombus made of agar with 0.8 wt. %, 1.0 wt. %, and 1.2 wt. %.

The helical magnetic robot with a built-in permanent magnet uses magnetic torque Tm generated by a rotating magnetic field (RMF) and magnetic force Fm generated by a magnetic gradient to obtain angular velocity ω and propulsive velocity v along the propulsive direction as follows:

(1)

where coefficients a, b, and c are determined by the geometric parameters of the helical magnetic robot and the fluid viscosity according to Lighthill’s resistive force theory.15,ξv and ξω are translational and rotational drag coefficients of the helical magnetic robot head, respectively.16 Since magnetic torque is more efficient than magnetic force when a magnetic field is used to drive the helical magnetic robot,17 only the magnetic torque is used in this study. After neglecting Fm, the propulsive efficiency of the helical magnetic robot v/ω can be obtained as follows:

(2)

Equation (2) shows that the helical magnetic robot with different geometries has different propulsive velocities under the same rotation speed of RMF.

The helical magnetic robot consists of a body and a head. As shown in Fig. 1(a), the bodies of SHMR and CHMR use the same double helical thread for optimal propulsive efficiency.10 A radially magnetized cylindrical NdFeB is embedded inside the body and can be rotated by the RMF. As shown in Figs. 1(a) and 1(b), the conventional head of CHMR is cone-shaped, and the head angles α of the CHMR in this study are 60 and 120 degrees. The SHMR proposed in this study uses a head with a sawtooth structure at a 120-degree head angle.

FIG. 1.

(a) Geometries of CHMR (60°, 120°) and SHMR with a pitch length of 10 mm. (b) Side views of the heads of CHMR and SHMR.

FIG. 1.

(a) Geometries of CHMR (60°, 120°) and SHMR with a pitch length of 10 mm. (b) Side views of the heads of CHMR and SHMR.

Close modal

In rotational drilling of the thrombus by the helical magnetic robot, CHMR and SHMR differ in their drilling mechanisms due to the difference in head geometry. With the same propulsive force originating from the body, the CHMR with a relatively low drag coefficient due to its cone-shaped head presents a screwing approach for drilling the thrombus. On the other hand, the SHMR which has a large contact area with the thrombus utilizes a grinding approach due to a relatively large drag coefficient. During drilling, the load torque Tload is determined by the thrombus resistance torque Tclot and the fluid drag torque Tdrag. After the head of the magnetic robot enters the thrombus, the applied magnetic torque should be equal to or greater than the thrombus resistance torque Tclot for effective drilling. Thus, the required power for thrombus removal can be expressed as

(3)

where θ is the rotational angle of the magnetic robot. As shown in Fig. 1(b), the red triangle representing the contact area of the robot with the thrombus is then the head’s surface area entering the thrombus. Figure 1(b) shows that the CHMR with a head angle of 120 degrees has a three times larger contact area with the thrombus than the CHMR with a head angle of 60 degrees for a given drilling depth δ. Since the SHMR with a 120-degree head has an additional sawtooth structure, it has a larger contact area with the thrombus than the CHMR with a head angle of 120 degrees for a given drilling depth in three dimensions. Since Tclot is proportional to the contact area of the thrombus, the SHMR further increases the magnetic torque delivered to the thrombus.

(4)

Equation (4) is valid below the step-out frequency where the magnetic torque is greater than the load torque (TmMaxTload>0). This was verified in the experimental section.

The magnetic torque applied by the RMF to the helical magnetic robot is as follows:

(5)

where m is the magnetic moment of the magnet, and Brot is the magnetic flux density of the RMF. The RMF can be expressed as follows:

(6)

Where f, N, and U are the rotating frequency of the RMF, the unit vector of the rotation axis, and the unit vector perpendicular to N, respectively.11 

The proposed CHMR and SHMR are made of photocurable dental resin for biocompatibility and were manufactured with a 3D printer using Digital Light Processing (DLP), as shown in Fig. 2(a). The CHMR with a 60-degree head, CHMR with a 120-degree head and SHMR have the same diameter of 4 mm and the same body length of 6 mm, but their total lengths are 9.46 mm, 7.15 and 7.34 mm, respectively, due to their different head geometries. Radially magnetized cylindrical NdFeB magnets (N55 grade NdFeB) with a length of 5 mm and a radius of 1 mm are embedded inside the CHMR and SHMR. The eMNS used in this study consists of two pairs of saddle coils that produce uniform magnetic fields along the y- and z-axes.18 

FIG. 2.

(a) Prototyped CHMR (60°, 120°) and SHMR with a pitch length of 10 mm. (b) Mean velocity of the SHMR with different pitch length in a glass tube filled with 40% glycerol under the RMF.

FIG. 2.

(a) Prototyped CHMR (60°, 120°) and SHMR with a pitch length of 10 mm. (b) Mean velocity of the SHMR with different pitch length in a glass tube filled with 40% glycerol under the RMF.

Close modal

The SHMR proposed in this study has a slower propulsive velocity than the CHMR because the sawtooth head geometry has an additional sawtooth area. Moreover, when removing a thrombus by rubbing and crushing, it is necessary that the propulsive force in the length direction should be optimized to invade the thrombus better. In this study, the optimal pitch length of the SHMR was selected experimentally. As shown in Fig. 2(b), the mean velocity of the SHMR according to pitch length was investigated in a glass tube with a diameter of 5 mm filled with 40% glycerol under the application of 1 mT RMF. The navigation experiment was repeated three times. The maximum magnetic torque applied to the SHMR was 0.0186 mN m from Eq. (5). The SHMR with a pitch of 10 mm had the greatest propulsive velocity.

As the RMF frequency increases, the fluid drag to the SHMR also increases. When the fluid drag is greater than the maximum magnetic torque, the SHMR will not be able to rotate synchronously with the RMF. The frequency at this point is called the step-out frequency. From the experimental results, the step-out frequency of the SHMR with pitch length of 9 mm and 10 mm was higher than that of SMHR with pitch length of 11 mm and 12 mm.

To verify the improved drilling performance of the SHMR compared to the CHMR, the drilling performance of the SHMR and CHMR with a pitch length of 10 mm was investigated in in vitro experiments of a 10 mm pseudo-thrombus under a magnetic field density of 5 mT and a rotating frequency of 155 Hz. This is illustrated in Fig. 3(a). The concentration ratio of agar was controlled to express blockage stiffness.19 Each set of experiments was repeated three times. The maximum magnetic torque applied to the SHMR was 0.0986 mN m from Eq. (5). Neither the CHMR nor the SHMR had a step-out at the beginning of drilling. Figure 3(a) shows that the CHMR with a 60-degree head angle and a 120-degree head angle and the SHMR with a 120-degree head angle completed the drilling of the thrombus with 1 wt. % agar after 70, 55 and 13 s, respectively. Figure 3(b) shows that the drilling performance of the SHMR was much better than that of the CHMRs, and that the drilling performance of both gradually decreased with increasing agar concentration. At agar concentrations of 0.8 wt. % and 1.0 wt. %, the average drilling rates of SHMR were 1.12 mm/s and 0.73 mm/s, respectively. However, the average drilling rates of CHMR with a 60-degree head were only 0.46 mm/s and 0.13 mm/s, respectively. Meanwhile, the CHMR with a 120-degree head has more contact area with the thrombus than the CHMR with a 60-degree head. Therefore, the average drilling rate of CHMR with a 120-degree head was 0.7 mm/s, and 0.19 mm/s, respectively. At the highest agar concentration of 1.2 wt. %, the CHMR with a 60-degree head could not drill the agar, but SHMR still had an average drilling rate of 0.22 mm/s.. And the CHMR with a 120-degree head also could drill the agar with an average drilling rate of 0.056 mm/s.

FIG. 3.

(a) Drilling experiments of CHMR (60°, 120°), and SHMR with 1 wt. % agar. (b) Average drilling rates of the SHMR and CHMR (60°, 120°) for pseudo-thrombus (10 mm) prepared with different agar concentration ratios.

FIG. 3.

(a) Drilling experiments of CHMR (60°, 120°), and SHMR with 1 wt. % agar. (b) Average drilling rates of the SHMR and CHMR (60°, 120°) for pseudo-thrombus (10 mm) prepared with different agar concentration ratios.

Close modal

This paper proposes a helical magnetic robot with a sawtooth head to improve drilling performance. When drilling a thrombus, the SHMR head has a larger contact area with the thrombus at the same drilling depth in comparison with the CHMR with a 60-degree head or a 120-degree head. The SHMR removes more thrombus than the CHMR when the maximum magnetic torque is greater than the resistance torque. In order to maximize the propulsive power of the SHMR, navigation experiments were conducted using the proposed SHMR with different pitch lengths, and the fastest propulsive velocity of the SHMR was achieved at a pitch length of 10 mm. Finally, drilling experiments with pseudo-thrombus containing different agar concentrations showed that the SHMR had better drilling performance than the CHMR. This research will contribute to the improvement of drilling performance for robotic endovascular intervention.

This research was supported by a grant of the Korea Health Technology R&D Project through the Korea Health Industry Development Institute (KHIDI), funded by the Ministry of Health & Welfare, Republic of Korea (grant number: HI19C1055).

The authors have no conflicts to disclose.

J. Sa: Data curation (equal); Formal analysis (lead); Investigation (lead); Methodology (equal); Validation (equal); Visualization (lead); Writing – original draft (lead). J. Kwon: Data curation (equal); Formal analysis (supporting); Investigation (supporting); Methodology (equal); Validation (equal); Visualization (supporting); Writing – original draft (supporting). G. Jang: Funding acquisition (lead); Project administration (lead); Supervision (lead); Writing – review & editing (lead).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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