# Performance Evaluation of a Magnetically Driven Microrobot for Targeted Drug Delivery

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## Abstract

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## 1. Introduction

## 2. Electromagnetic System Configuration of Targeted Drug Delivery Microrobot

_{x}= 293.4 mm, R

_{y}= 211.4 mm, R

_{z}= 157.4 mm, N

_{x}= 216, N

_{y}= 174, N

_{z}= 126, respectively. The magnetic induction intensity range after current is applied is 0–30 Gs.

## 3. Targeted Drug Delivery Microrobot

#### 3.1. Motion Mechanism of Targeted Drug Delivery Microrobot

#### 3.2. Dynamic Model

_{c}and axial velocity v

_{a}of the targeted drug delivery microrobot during rotation are decomposed along the spiral direction and perpendicular to the spiral direction, respectively, to form the velocity W along the spiral direction and the velocity V perpendicular to the spiral direction [23]. θ

_{r}is the spiral rise angle of the helix, a is the pitch, b is the thread width, h is the thread height, c is the gap between the top of the thread and the inner wall of the intestinal tract, and μ is the fluid viscosity. Then, W and V can be obtained from u

_{c}and v

_{a}:

_{0}and c

_{0}are undetermined coefficients, which are determined as h and c in the A

_{1}and A

_{2}regions. P

_{1}and P

_{2}are obtained by bringing the parameters of the A

_{1}and A

_{2}regions into Equation (3).

_{r}= b/(a + b), γ

_{r}= h/c.

_{p}and the resistance F

_{r}when the targeted drug delivery microrobot moves is expressed as:

#### 3.3. Quantitative Targeted Delivery Model

**n**is the normal vector of the rotating magnetic field plane; α, β and γ are the included angles between

**n**and the X axis, Y axis and Z axis, respectively, and

**n**can be expressed as (cosα, cosβ, cosγ). The current driving method of the targeted drug delivery microrobot in the three-axis Helmholtz coil can be as follows [24]:

_{x}= (cosβ/cosα·cosγ), tanφ

_{y}= (cosα/cosβ·cosγ), I

_{x}, I

_{y}and I

_{z}are the amplitude of the input currents of the three coils, respectively, I

_{0}is the current amplitude, and ω is the angular frequency of the current.

**n**to

**n**, and the rotation angle is θ, which is the angle between the vectors

_{1}**n**and

**n**, so the percentage of drug delivery bin η can be expressed as:

_{1}_{1}is the long radius of the cam structure and L

_{b}is the length of the drug bin. The targeted drug delivery microrobot can accurately control the percentage of drug delivery bin by controlling the radial rotation angle of the permanent magnet. The relationship between the rotation angle of the permanent magnet consolidated cam structure of the targeted drug delivery microrobot and the percentage of the drug delivery bin is shown in Figure 5. According to the structural parameters of the targeted drug delivery microrobot, it can be obtained that the drug delivery starts when the permanent magnet rotates to 41°. When the permanent magnet rotates to 90°, the percentage of the drug delivery bin is 100% and all drugs can be released. The type and quantity of drugs can be determined according to the condition of the lesion, and the targeted drug delivery microrobot can be controlled to move to any position in the human intestine through the external magnetic field to achieve an accurate targeted drug delivery function.

## 4. Analysis of Drug Delivery Process of Targeted Drug Delivery Microrobot

#### 4.1. Model of Drug Delivery

_{rb}, the propulsive force F

_{pb}of the cam pushing the drug bin and the resistance F

_{reb}of the fluid when the drug bin goes out, and their relationship can be expressed as:

_{pb}of the cam pushing the drug bin and the resistance F

_{reb}of the fluid when the drug bin goes out can be expressed as:

_{m}is the magnetic torque, ρ is the density of the fluid, S is the maximum cross-sectional area perpendicular to the fluid flow, v

_{b}is the speed of the drug bin of the targeted delivery microrobot, and C

_{re}is the resistance coefficient.

#### 4.2. Electromagnetic Analysis

_{m}produced by magnetic field can be given as:

_{v}is the angle between the rotating magnetic field vector and the magnetic moment vector of the NdFeB permanent magnet.

#### 4.3. Hydrodynamics Analysis of Targeted Drug Delivery Process

## 5. Experimental Results

#### 5.1. Motion Characteristics of Microrobot

#### 5.2. Drug Delivery Conditions of Microrobot

#### 5.3. Microrobot Performs Drug Delivery Task

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 4.**(

**a**) Dynamic model of targeted drug delivery microrobot. (

**b**) Magnetic vector analysis model.

**Figure 5.**The relationship between percentage of drug delivery bin and the rotation angle of the permanent magnet in the targeted drug delivery microrobot.

**Figure 10.**Relationship between the pushing and recovery speed of drug bin and the resistance of the targeted drug delivery microrobot.

**Figure 13.**Relationship between rotational frequency and moving speed of targeted drug delivery microrobot.

**Figure 14.**Relationship between the drug delivery region of targeted drug delivery microrobot and the current and frequency of the external magnetic field.

**Figure 16.**Displacement of targeted drug delivery microrobot during targeted drug application tasks.

Microrobot | Parameter |
---|---|

Diameter of microrobot (mm) | 9.5 |

Length of microrobot (mm) | 24 |

Weight of microrobot (g) | 4.0 |

Thickness of spiral structure (mm) | 2 |

Pitch of spiral structure (mm) | 6.6 |

Height of spiral structure (mm) | 1 |

Material of body | Photosensitive resin |

Size of permanent magnet (mm × mm × mm) | 6 × 3 × 4 |

Weight of permanent magnet (g) | 1.0 |

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**MDPI and ACS Style**

Cai, Z.; Fu, Q.; Zhang, S.; Fan, C.; Zhang, X.; Guo, J.; Guo, S.
Performance Evaluation of a Magnetically Driven Microrobot for Targeted Drug Delivery. *Micromachines* **2021**, *12*, 1210.
https://doi.org/10.3390/mi12101210

**AMA Style**

Cai Z, Fu Q, Zhang S, Fan C, Zhang X, Guo J, Guo S.
Performance Evaluation of a Magnetically Driven Microrobot for Targeted Drug Delivery. *Micromachines*. 2021; 12(10):1210.
https://doi.org/10.3390/mi12101210

**Chicago/Turabian Style**

Cai, Zhuocong, Qiang Fu, Songyuan Zhang, Chunliu Fan, Xi Zhang, Jian Guo, and Shuxiang Guo.
2021. "Performance Evaluation of a Magnetically Driven Microrobot for Targeted Drug Delivery" *Micromachines* 12, no. 10: 1210.
https://doi.org/10.3390/mi12101210