Advances in Finite Element Analysis of External Field-Driven Micro/Nanorobots: A Review

to clinical feasibility. How to develop equipment and strategies that can be operated on a large scale in combination with clinical practice is a problem that still needs to be solved to achieve on-demand, accurate, and directional MNR movement. Finally

With the development of nanotechnology, micro/nanorobots (MNRs) have become promising medical tools given their advantages of unconstrained and precisely controlled navigation. However, given the complexity of MNRs' dynamic biological environments and the limitations of current experimental methods, it remains challenging to simulate the motion mechanism, functional implementation strategy, and adaptability of MNRs in dynamic environments. Finite element analysis (FEA) plays an important role in MNR research; thorough review of state-of-the-art research on MNRs. FEA is used to simulate MNRs motion mechanism, and theoretical models combined with experimental results are proposed to explain the motion mechanism. FEA can reduce the error rate of experiments. Combined with the simulation results, the optimal scheme is selected for experiments, and a reliable design strategy of MNRs is obtained. FEA has become a more effective method to obtain the optimal design of MNRs for in vivo applications. Therefore, herein, the design and driving mechanism of MNRs, the different solutions proposed for complex dynamic environments, and the use of FEA in the related research are introduced by this review. The current challenges and future research directions of FEA combined with external fielddriven MNRs are summarized.
In the past three decades of research, MNRs were mostly considered as a concept, and there is still a lot of work to be done for clinical application and large-scale use. The motion control of MNRs still faces two major problems: a low Reynolds environment [14] and molecular Brownian motion. [15] In this complex biological environment, MNRs must overcome viscous forces and blood-flow velocity to move autonomously. In addition, given the large gap between the size of MNRs and ordinary robots, the lack of related monitoring technology and equipment is still the bottleneck to realize the dynamic analysis of mechanical deformation of MNRs. As the size decreases, especially for MNRs for in vivo applications, the higher the requirements for their speed and displacement are. In this regard, researchers have developed a more mature type of finite element analysis (FEA). In the life sciences, FEA is often used to perform complex analytical calculations (e.g., protein folding or unfolding) since molecular dynamics technology does not develop as fast as finite-element technology. [16] Reviewing the research of MNRs, FEA has been used to predict the deformation of MNRs and analyze the coupling with the environment, which is of great help to the study of the motion mechanism of MNRs. In the study of MNRs, size and computational simulation also influence each other. The performance of MNRs of different sizes and shapes is also different, and the optimization design strategy using FEA is still an effective method.
This review mainly describes MNR strategies based on FEA simulations ( Figure 1). First, we discuss the applications of FEA in MNRs, and summarize the design of single MNRs and swarms composed of single MNRs. Second, we outline the research status of MNRs driven by external fields (magnetic field, ultrasound field, light field). Third, we introduce the low Reynolds number environment and Brownian motion, and highlight related studies of MNRs combining FEA to overcome both challenges. Finally, based on our conclusions, we discuss the current challenges in the field.

Finite Element Analysis
FEA is a numerical simulation method that is widely used in static, dynamic, and nonlinear problems. Finite element model refers to the model reconstruction of computer 3D models using finite element software. The given physical properties and boundary conditions, combined with computer graphics, are used to simulate the physical behavior of the object of study or the theoretical calculation of physical phenomena (e.g., force, heat, electromagnetism, fluid properties). Common FEA software includes ABAQUS, ANSYS, and COMSOL Multiphysics.
Computational fluid dynamics are important for solving and predicting the laws of motion and mechanism of MNRs. Using FEA to simulate the distribution of the blood-flow field under different disease states is a hotspot in current medical research. [17] It also has great potential for the application of MNRs in medicine. For example, in vascular environment simulation analysis, FEA can be used to predict the influence of wall pressure, blood-flow rate, and other parameters on MNR mechanical movement behavior. Wang et al. reported a strategy for diffusion transportation by MNRs to achieve thrombus clearance, simulating fluid velocity and fluid concentration in the "Y" tube and collateral vessels with or without MNR. [18] The simulation results were compared with an in vitro experiment using dye molecular diffusion to demonstrate the feasibility of the proposed magnetically driven MNRs. Induced changes in boundary conditions are a major challenge in precision medicine. [19] The shear rate of non-Newtonian fluid affects its viscosity, and blood, as a typical non-Newtonian fluid, is also affected by the shear rate. Non-Newtonian blood simulations require a longer calculation time to be stable, and require a finer boundary layer to analyze flow. Therefore, how to make FEA results closer to the actual situation is another problem area in the research. In the simulation process, the deformation of biological tissues (e.g., the intestine and blood vessels) is complex. The computational effort is large when solving Navier-Stokes equations with deformable mesh and moving boundaries. [20] In this regard, when the FEA is used to study the fluid flow, concentration, and other factors around the MNR, the biological tissue is removed to simplify the theoretical model to study its motion mechanism. Aubret proposed a microgear-structure MNR that was assembled by phototactic rotors along light gradients. [21] FEA simulated the concentration field around the rotor and the diffusion equation of externally modified particles to study the diffusiophoretic coupling mechanism. In contrast, the peanut-like MNRs reported by Lin et al. had two modes: swinging and rolling. [22] The swinging mode could achieve the action of climbing over obstacles, but the rolling mode could not. The author used the rotating machinery module in COMSOL Multiphysics to study the difference between the two motion modes, so as to further obtain the motion mechanism under the two modes. The difference between the two motion modes was due to the pressure difference at two ends of the peanut-like MNRs in the swing mode, while the pressure distribution at two ends of the peanut-like MNRs in the rolling mode was the same. Based on peanut-like MNRs, another study proposed that the size of the vortex of the swarm assembled under a rotating magnetic field is affected by the surface area of the MNR. [23] The velocity of a swarm composed of a different number of particles and the fluid interaction in the early stage of vortex formation was simulated. The experimental results supported the theory, demonstrating the existence of phase separation during vortex growth. Then, the discrete particle simulation method was used to simulate the vortex formation process of 40 particles, further demonstrating that the phenomenon was attributable to the coherent motion of the vortex.
In the design of single MNR and swarm, the purposes of FEA are different. For the design of single MNRs, because of differences in synthesis, the hydrodynamics and coupling relationship between the force and velocity of MNRs of the same shape may differ. Through the simulation of MNRs based on the Navier-Stokes equation, one study investigated changes in velocity and stress to evaluate performance and then calculate and determine the optimal shape. [24] Li et al. designed a micro-rocket robot driven by near-infrared (NIR) light ( Figure 2A). [25] The thermophoretic force generated by the temperature gradient between its head and tail pushed the micro-rocket robot forward. To demonstrate its high propulsion, he used FEA to simulate the temperature profiles of the micro-rod robot, micro-tube robot, and micro-rocket robot, respectively. The theoretical calculation results and the experimental results agreed that the micro-rocket robot was faster. For swarms, FEA can efficiently analyze the interaction mechanism and force between particles. Shakya et al. proposed swarms consisting of monodisperse disk-in-sphere droplets driven by an acoustic field. [26] Droplets were suspended in an acoustic field, and droplets attracted each other to form swarms when they approached another droplet. The phenomenon indicated that there were interaction forces between the droplets. The FEA method was used to simulate the forces and torques of one droplet to six droplets, and the local forces from the center to the edge of droplets drove the swarm motion. Liang used FEA to simulate O 2 concentration between particles to study diffusiophoretic repulsion. [27] Under the irradiation of UV light, the H 2 O 2 on the surface of TiO 2 particles decomposed and the resulting O 2 molecules accumulated between the particles. The resulting O 2 concentration gradient induced the particles to produce diffusiophoretic repulsion, so that the particles were pushed away from each other. To study the assembly principle of dynamically assembled swarms for functional implementation at the gas-liquid interface, Wang et al. performed simulations of fluid flow around the swarms ( Figure 2B). [28] He found that the Reynolds number led to differences between the theoretical model and the experimental results. Dynamic and stable self-assembling pattern swarms were formed by the interaction between magnetic force, capillary force, and hydrodynamic force. The simulation result showed the circulation flow of the fluid in the center of the swarm.
The external fields such as light field and magnetic field trigger and control the motion of MNRs. The strength of the external field is calculated theoretically using FEA method, so as to further study the motion mechanism of MNRs. Taking magnetic-driven MNRs as an example, FEA can theoretically calculate different magnetic-field parameters (e.g., magneticinduction intensity, magnetic flux density) and magnetic-field distribution. Using this approach, the magnetic force and magnetic moment can be obtained to elaborate and analyze the motion mechanism. The model can be optimized for calculation and then compared with experiments to further support the conclusion. Sun et al. proposed an MNR with sunflower pollen loaded with magnetic droplets. [29] Since the shape characteristics of urchin-like sunflower pollen, the swarms formed could eliminate the biofilm with their sharp edges driven by the magnetic field ( Figure 2C). To obtain a stronger magnetic field, he used a permanent magnet system to build and drive the swarms, and theoretically simulated the magnetic-field distribution and magnetic flux density. The rotating magnetic field provided by the permanent magnet enabled the MNRs to form circular swarms and achieve precise navigation in complex environments. Another study simulated the temperature around light-driven MNRs to investigate the relationship between the thermophoretic force generated by the asymmetric temperature gradient and its velocity. [30] Moreover, an ultrasonic-driven transformable metal gallium MNR was reported in a different study. Based on an analysis of the acoustic pressure gradient field using the acoustic pressure module of FEA, it was found that the driving force was the primary acoustic radiation force generated by the asymmetric structure, not the acoustic streaming force. [31] In the past research of MNRs, FEA has analyzed and explained the fluid environment, the design principle of MNRs, and the propulsion mechanism. It provides a more convenient way to evaluate the feasibility of MNR strategies. However, there are still differences between theoretical and experimental models, so how to reduce this difference is a challenge.

Single-MNR Design
Challenges facing the in vivo biological application of MNRs include drug-release functionality, biodegradability, and adaptability to dynamic environments. [7,32] Researchers have therefore investigated different MNR shapes to achieve superior performance, such as spherical, [31,33] array, [34] and helical [35][36][37] shapes. The structure and surface areas of differently shaped MNRs and their ability to manipulate and transport cargo during treatment can also vary greatly. In addition, different structures have different operability, assembly, and interaction with the internal environment (e.g., the intestine and blood vessels); thus, many functions can be achieved by designing structures. For example, Liu et al. reported a pH-sensing "Euler disk" structure adapted to the gut environment, intended to resist strong gastric acid and achieve movement in a narrow chamber. [38] Chen et al., meanwhile, proposed MNRs in the shape of thumbtacks and frisbees that could identify intestinal fluid and gastric fluid for the purpose of maintaining stability in gastric fluid and sustaining drug release in intestinal fluid. [39] The adaptability of those two shapes to the environment was examined using FEA to calculate the interaction with the fluid in the case of fast motion ( Figure 3A). Under the external magnetic field, the velocities of both MNRs were positively correlated with the frequency, and they continued to decrease after reaching the peak value. This result was consistent with the FEA simulation results, from which the optimal driving frequency of the MNRs could be obtained. To achieve more complex operations and dynamicenvironment adaptation, pH-responsive intelligent MNRs have been reported, and different preparation methods have been proposed to achieve the functions of these MNRs in the research and manufacturing processes. For the application of oral enteral drug delivery, for example, Chen et al. reported several shapes for intelligent hydrogel MNRs (referred to as CPMs) utilizing the droplet generator T-junction microfluidic (MF) device for manufacturing. [40] The devices had three flow modes: laminar flow phase, plug phase, and droplet phase. FEA was used to  [25] Copyright 2020, Springer Nature. (B) Reproduced with permission. [28] Copyright 2019, American Chemical Society. (C) Reproduced with permission. [29] Copyright 2022, Wiley-VCH GmbH.
www.advancedsciencenews.com www.advintellsyst.com calculate the fluid flow in the microchannel, and the formation of CPM was observed by comparing the experimental process with the simulation process. [40] The main purpose of FEA was to study the formation process of CPM, so as to explore the influence of the formation process on the shape and size of CPM. Inspired by nature, a number of bionic MNRs have been proposed based on biological motion mechanisms. For example, helical MNRs, based on the characteristics of the swimming of Escherichia coli, have attracted considerable research interest. [41] Helical-shaped MNRs can convert rotating motion into forward linear motion. This swimming mechanism can overcome the problem of low driving force in a low Reynolds environment. However, considering the limitations of the driving form, the deformation and function realization of MNRs have attracted more research attention. Developed in 2009, the first helical MNR consisted of a soft magnetic "head" and a helical "tail" that could be propelled by a low-intensity field. [42] Ghosh et al. also proposed a magnetic-driven helical swimmer with a width of 200-300 nm, which was also designed with a smaller-sized helical MNR. [43] The small size can achieve the limited size of the navigation requirements in vivo. To improve the ability to load drugs, Xin et al. designed conical hollow microhelices based on the good motion characteristics of the helical structure. [41] Compared with a solid microhelix, both the empty surface and the interior can be loaded with drugs, which expands the surface area of the loadable drug and enhances the loading capacity. Magnetically driven double-helix MNRs were also proposed that could label breast cancer cells and degrade into collagen, constituting various extracellular matrices, which is helpful for tissue remodeling. [44] Recently, Chen et al. proposed an Au-and Ni-modified magnetically driven helical MNR (C-HNR) for biosensing and photothermal cancer therapy. [45] The desired length of C-HNR can be obtained by ultrasonic crushing. FEA was used to simulate the process of entering the cell membrane, and the balance of the propulsion force and resistance of C-HNR was obtained, as well as the distribution of pressure and magnetic force on C-HNR, reflecting its ability to penetrate the cell membrane ( Figure 3B). Meanwhile, hydrogels have attracted attention because they can achieve the reversible deformation of MNRs on demand under environmental stimulation, especially in drug release and cell manipulation. Recently, environmentally adaptive MNRs with three shapes (fish, butterfly, and crab) were synthesized and designed using 4D printing technology. [46] At different pHs, the different expansion rates of hydrogels led to the opening and closing of "claws" to achieve grasping, transporting, and releasing actions for cancer treatment ( Figure 3C). FEA was used to predict the deformation of the "butterfly" and "crab" MNRs. The pH changes were used to induce the morphing of the MNRs. An MNR (ionic shapemorphing microrobotic end-effector (ISME)) that mimics the predation behavior of starfish was also reported, [47] using the pH response and ion displacement of hydrogels for behavioral on/off switching. ISMEs with hexagram, shuriken, and Triangulum shape designs were prepared using the electrodeposition method. Under heterogeneous electrodeposition, the ISME structure could achieve shape deformation under pH or ion stimulation, and current density was simulated to study ISME deformation. The adhesion of MNRs to organs plays a decisive role in achieving medical functions. Therefore, an octopus MNR with controllable adhesion was proposed to achieve strong adhesion to organs. [48] The convex structure interacted with liquid molecules on the surfaces of organs to generate cohesion and achieve strong adsorption. FEA simulation explained the adsorption principle of the sucker structure, and it was found that the adsorption force was proportional to the diameter of the protrusion.
When MNRs are applied in vivo, however, it is challenging to ensure their biodegradability and biocompatibility while also guaranteeing motion performance. Biological barriers in the body (e.g., the blood-brain barrier) will regard the MNR as an "invader," which will trigger an immune response aiming to remove the MNR. Moreover, if the MNR be recovered in time after performing tasks in the body, it can cause inflammation and other adverse reactions. The natural biological affinity of cells has inspired the design of MNRs, and on that basis, biological hybrid robots have been proposed (e.g., a swimmer combining MNR with bacteria [49] or cells). [50,51] Cellular MNRs mainly pack drugs and magnetic nanoparticles into cells (e.g., erythrocytes, [52] macrophages) by wrapping magnetic materials in cell membranes or through endocytosis. [53,54] Thus, an MNR using neutrophils and E. coli as a camouflage shell was proposed, [55] in which the E. coli biofilm could protect the drug from leaking and greatly improve phagocytosis efficiency. Another study reported a cell robot combining superparamagnetic iron oxide nanoparticles and macrophages. [53] Macrophage activation can produce anticancer substances to induce cancer cell apoptosis and stimulate immune response. A recent study that reported magnetic-powered Janus cell robots loaded with oncocytic adenovirus to treat bladder cancer also used numerical simulation to simulate the flow of the fluid environment to study the MNRs' motion performance. [56] The oncolytic adenovirus cell robot retained the inherent properties of the cancer-treating virus host system, was biocompatible, and did not cause harm to humans. The combination of cell robots and viruses can selectively kill tumor cells, which expanded the biological application range of cell robots. Spermatozoa have the ability to swim against a current (i.e., rheology), and the flagellar structure of spermatozoa can generate a great propulsion force in the process of swimming, which has also become an important aspect of biological MNRs. [57] Xu et al. designed a sperm MNR that could actively fight against blood flow and used its natural biocompatibility and high swimming ability for the investigation of biological MNRs ( Figure 3D). [50] Multiple sperm micromotors were induced to self-assembly into a train-like structure by a uniform magnetic field, and the magnetic-field changes during assembly were calculated and simulated. Pollen has a natural lumen structure that holds great potential for drug encapsulation and can communicate with cells through electrostatic forces. [12] Pollenbased MNRs hold promise for cancer therapy. A sea urchin shape based on sunflower pollen could penetrate cancer cells to achieve drug release, having a strong ability to penetrate cell membranes. One study used FEA to simulate the flow field between particles and then examined the collective behavior of the particles during the assembly process. [58] We discuss the design strategies of three types of MNRs combined with FEA: MNRs with different geometric shapes, bionic MNRs, and biological hybrid robots. These studies provide design methods that take into account biocompatibility, cargo carrying capacity, high propulsion, and other factors. Although there is still a long way to go for application in vivo, it sets the stage for the functional design of MNRs.

Design of Swarms
MNR individuals are limited to achieving certain complex tasks. The cooperative movement of swarms has great advantages in nature since a swarm can customize its shape by interacting with the complex environments to obtain the best propulsion strategy. There are nonlinear interactions between the individuals in swarms. Swarms are formed due to the synergy of external-field guidance and interparticle interactions. It is worth investigating how swarm complete tasks and the effect of individual interactions on their functions. For example, magnetically driven swarms can design collective behavior based on the interaction of magnetic fields. [59,60] The self-assembly behavior of living cells and the ordered movement of substances in disordered motion have inspired research on self-assembly. Self-assembly is a method of spontaneously assembling components into patterns and structures that is widely used in research. [61] Self-assembly is divided into two modes: static and dynamic. Static self-assembly remains stable once the structure is formed while dynamic self-assembly can enable individuals with a continuous energy supply to interact and thus achieve energy dissipation. [62] Dynamic selfassembly can provide an effective method for MNRs to form collective patterns and adapt to dynamic environments. The magnetic field has high permeability and maneuverability, and the force range generated by magnetic particle assembly under magnetic-field guidance is wide. Such properties make magnetic-field-guided dynamic self-assembly an effective strategy for swarm design. A study from 2018 reported a dynamically reconfigurable banded magnetic nanoparticle (ribbon-like paramagnetic nano-particle (RPN)). [63] Here, the reversible assembly of magnetic particles in Brownian motion induced by a composite magnetic field formed a banded RPN. Field strength and efflux were the main factors affecting the interaction force between particles ( Figure 4A). Flow-field simulations of swarms at different times and the response of free particles in the flow field have been computed numerically. The results showed that freely moving particles were attracted to the microgravity field but repelled from the top of the swarms. Therefore, the magnetic attraction and repulsive forces of the flow field maintained a dynamic balance between the RPN particles. On that basis, a dynamically balanced magnetic rotating particle chain was proposed. [28] The input and adjustment of magnetic-field-related parameters could change the interaction forces between swarms to customize their shape. The magnetic force, flow-field dynamics, and interparticle forces generated by the introduced magnetic field formed a dynamic balance, which ensured the stable work of the swarms. Since each particle was affected by the velocity field of the other particles, FEA analysis was used to further study the relationship between the flow field-induced flow and the interaction force between particles. It was found that the ring flow in the core of the swarm played a significant role. However, different shapes of MNR swarms have different advantages in different environments. For example, chain-like swarms can perform tasks in narrow channels to achieve motion in limited space. When a large-area operation is required, ribbon is preferable; however, vortex can be used for task operations requiring a high load capacity owing to high-density aggregation.
To achieve the conversion of more complex functions and multiple motion modes, the morphological transformation of MNRs needs greater flexibility and adaptability. A dynamic self-assembled MNR swarm is more functional and efficient than a single MNR. Swarms guide individuals to display rich collective behaviors (e.g., aggregation, dispersion) under the stimulation of external fields. As the environment changes, changing the external field can customize the collective behavior of the swarm to overcome the complex environment. Sun, for example, reported an "octopus arm" swarm using the spatiotemporally programming external magnetic field drive and ferrofluid droplet dynamic assembly for liquid-like and solid-like swarms. [64] Under the control of a high-frequency magnetic field, these two modes could achieve the reversible transformation of  [63] Copyright 2018, Springer Nature. (B) Reproduced with permission. [64] Copyright 2021, Wiley-VCH GmbH. (C) Reproduced with permission. [66] Copyright 2021, American Association for the Advancement of Science.
www.advancedsciencenews.com www.advintellsyst.com each other, showing the deformation behavior of the octopus arm ( Figure 4B). Mizuki et al., meanwhile, proposed a superhydrophobic nanomagnetite swarm. The design used the aerophilic and hydrophobic properties of fire ants to achieve the transformation of the two modes of "bivouacs" and "rafts" and then achieve the functions of transportation and obstacle avoidance. [65] However, when operating in vivo, real-time monitoring of behavior, distribution, and location of swarm is required. Thus, there are still many difficulties to overcome for the application of targeted drug therapy in living organisms. To address this challenge, Wang et al. reported a strategy for the dynamic assembly of magnetically driven MNR, applied to blood-related diseases (thrombolysis and tumor therapy) assisted by ultrasound Doppler imaging. [66] Reducing the influence of blood flow on swarms and strengthening the force between individuals is a challenge, considering the influence of blood flow in the blood vessel. Therefore, they assembled MNR swarms and navigated them at vessel boundaries to reduce the influence of blood flow. The FEA method was used to analyze the influence of the swarms on peripheral blood flow, and the movement trajectory of erythrocytes was simulated after the swarms approached. It can be concluded that hydrodynamic resistance and trapping force were the main influencing factors ( Figure 4C). The integration of ultrasonic feedback mechanisms and dynamic self-assembled swarms shows great prospects for medical imaging systems in targeted drug application. Inspired by swarm movements in nature, an energy-saving mechanism (master-slave configuration method) was used to strengthen individual connections to increase the control of swarms. This mechanism mainly divides the swarm into leader and follower. [67] The leader is responsible for implementing the main functions of the swarm while the follower is responsible for sensing and executing tasks. Compared with particleundifferentiated swarms, master-slave MNR swarms can respond to multiple modes and have more complex functions. Examples include the leader-follower-like swarms (L-TiO 2 / S-TiO 2 , L-TiO 2 /S-SiO 2 , L-SiO 2 /S-TiO 2 ) reported by Liang et al. [27] Under the action of the electric field, microparticles were guided to assemble into layered leader-follower-like swarms. Different functions were generated because of the different responses to light between leader and follower. In another study, Mou et al. proposed a chaser and flight strategy based on natural predation relationships (prey will change into more cohesive swarms to avoid predation and monitor risk-improving decisions to avoid predation). [68] Given the interaction between the repulsive force of the predator particle and the attractive force of the prey particle, the predator particle and prey particle showed interesting dynamic reconstruction and bending behavior after being activated.

External Field-Driven MNRs
Due to the microscale and unconstrained advantages of MNRs, they are able to reach hard-to-reach regions in the human body, and MNRs have great potential for biomedical applications. To achieve continuous, efficient, and accurate navigation, the choice of fuel power is particularly important in the design of MNRs. An external field drive has good time controllability, biocompatibility, environmental friendliness, and low cost, and it can effectively convert external field energy into mechanical energy. Since this type of power source is not bio-toxic, an external field drive has become the preferred power source. The external-field drive is mainly divided into 3 types: lightdriven MNRs, magnetic-driven MNRs, and ultrasonic-driven MNRs. Here, we review the current research on those types of MNRs, the potential and challenges of driving modes, and the analysis of motion obtained from the driving site combined with FEA.

Light-Driven MNRs
Light-driven MNRs have advantages for MNR control strategies because of their high spatiotemporal responsiveness and control application. [69] Light-driven MNRs are generally made of photoactive materials (e.g., photocatalytic materials), and under the irradiation of light, they will cause photochemical reactions, photothermal conversion, and other chemical reactions. [32,70] The propulsion force of light-driven MNRs is mainly generated by an induced asymmetric gradient field. Compared with selfdriven MNRs, light-driven MNRs need light energy to turn on and off and achieve controllable speed. Since light itself is a common renewable energy source, light energy has become an effective way for MNRs to obtain driving force.
TiO 2 is commonly used in the design of light-driven MNRs because of its high photocatalytic activity and refractive index. First proposed by Hong et al., TiO 2 MNRs (also called micromotors) have great advantages owing to their high biocompatibility compared with self-driven MNRs and other light-driven methods. [71] TiO 2 microtubules are also typically studied based on different applications. [72] Dong et al. proposed hemispheres coated with Au metal, composed of TiO 2 particles, to form asymmetric structures of TiO 2 -Au Janus micromotors. [73] TiO 2 -Au Janus micromotors could trigger the self-electrophoresis mechanism under the induction of ultraviolet light (UV light), which does not require additional fuel and can increase speed by enhancing light intensity. UV light is used as the driving source for light-driven MNRs. Recently, Kang et al. proposed a peanutlike Fe 2 O 3 colloid coated with polysiloxane bands. [74] It was placed in H 2 O 2 , and the end of Fe 2 O 3 was induced by UV light to catalyze the decomposition of H 2 O 2 , resulting in an asymmetric concentration gradient. The resulting concentration difference could create an attractive force that allows particles to assemble, according to the FEA ( Figure 5A). The assembled swarm also generated a propulsion force owing to the surrounding H 2 O 2 concentration gradient, which enabled it to complete precise movement. The two cases with and without the propulsive force were studied separately: the absence of the propulsive force was due to the fact that no concentration difference was generated and the swarm made Brownian motion. When there was propulsion force, the H 2 O 2 concentration at the top of the swarm was higher than that at the bottom, and the propulsion force generated by the concentration difference made the swarm move directionally. Similarly, a walnut hematite/Pt Janus MNR also performs UV light-induced self-assembly and selfelectrophoretic propulsion. [75] The walnut self-assembled microchains exhibited three motion modes (parallel, vertical, www.advancedsciencenews.com www.advintellsyst.com and rotation), and the difference in motion modes was attributable to particle orientation during self-assembly. To support this theory, calculation was simplified during FEA simulation; two miniature robots were used to simulate the concept of Pt reaction. Compared with UV light, NIR light has the highest light absorption in biological regions and is safer. The exploration of the motion mechanism of MNRs has also become an important area of research. The driving-force source of light-driven MNRs is the applied light field; thus, it has gradually become a trend to use FEA to explore light-field intensity to study the motion mechanism. Au-sputtered SiO 2 motors (also known as JMSNMs) proposed by Xuan et al. were subjected to NIR for self-electrophoretic propulsion. [76] The steady-state temperature distribution of JMSNMs irradiated by 3 W cm À2 NIR has been numerically analyzed. The influence of temperature on asymmetric JMSNMs was discussed and compared with the experimental temperature measurement, and then the driving force of thermophoresis was studied. [76] Another study reported a rocket-like MNR functionalized with an Au-modified nanoshell using NIR radiation to generate temperature gradients inside and outside the shell. [77] The asymmetric design of the rocket could produce a large thermophoretic force, which could ensure the continuous propulsion and remote control of the rocket. To explore the thermophoretic force generated by the photothermal effect, FEA was used to simulate the stable temperature distribution of the cross section of the rocket ( Figure 5B). The temperature rise in the lower part of the rocket was lower than that of its upper part, and the temperature rise of the inner part was higher than that of the outer part. As the water temperature around the rocket increased, so did buoyancy. This is because increased temperature produced nanobubbles inside the rocket, which reduced the influence of gravity on the rocket and achieved the purpose of speeding up. Based on the ease of processing and photothermal conversion of liquid gallium, and inspired by an ultrasonic-driven rod structure, another study reported a needlelike liquid gallium micro/nano-swimmer (LMGNS). [78] After NIR light irradiation at a fixed frequency,  [74] Copyright 2022, American Chemical Society. (B) Reproduced with permission. [77] Copyright 2016, Wiley-VCH GmbH. (C) Reproduced with permission. [78] Copyright 2021, Elsevier BV.
www.advancedsciencenews.com www.advintellsyst.com the fluorescence intensity of the water in which the LMGNS was located decreased. The temperature of the water around the LMGNS and the temperature of the LMGNS were theoretically calculated to study the effect of NIR intensity on the LMGNS ( Figure 5C). The temperature of water around the LMGNS was significantly higher than that at a distance, and there was a temperature gradient in the tail and tip of the LMGNS. The thermophoretic force generated by the temperature gradient could drive the LMGNS to move in a directional manner. Light-driven MNRs have the advantage of high biocompatibility and can effectively convert light energy into mechanical energy for controlled navigation and precise work in living organisms. However, owing to the low permeability of the light field, it can only be used for near-epidermal manipulation in biological applications, and it remains a challenge for treatment modalities that require high permeability, such as cancer therapy. Although the penetration depth can be increased by increasing the intensity of light, the safety of high-intensity light sources for organisms cannot be guaranteed. Thus, improving permeability without compromising biocompatibility remains a difficult problem that needs to be addressed. Whether FEA computational simulation can be used to study high-permeability light sources that meet biocompatibility also needs to be studied. FEA analyzes the light-intensity distribution, nonuniform concentration gradient, and other parameters of photo-driven MNRs to better understand the motion mode and principle of MNRs. In this regard, a finite-element model is ideal, and how to optimize it to be closer to the experimental situation remains a difficult research problem.

Ultrasonic-Driven MNRs
Ultrasonic-driven MNRs were first reported in 2012. [79] They have considerable prospects for biological applications because of their high biocompatibility (especially in the MHz range) and high permeability. In MNR research, ultrasound has also become an efficient power source. In particular, the strong propulsion provided by ultrasonic-driven MNRs swimming in fluid means that the high viscosity and ionic strength of fluid do not need to be considered. Considering this advantage, Kagan et al. proposed an ultrasonic-driven strategy namely, irradiating perfluorocarbon (PFC) emulsions in MNRs by ultrasound and utilizing the high-speed force generated by the evaporative expansion of PFC for propulsion. [79] This highlights the potential of ultrasonic waves driven by MNRs. [79] Acoustic radiation force plays a role in the ultrasonic driving mechanism and is divided into primary radiation force and secondary radiation force. The primary radiation force is the force exerted by the sound wave on the particles in the flow field; the secondary radiation force is the interaction force between the particles under the sound field, which can cause the particles to assemble and separate. The rodlike liquid metal gallium MNR proposed by Wang et al. is driven by the acoustic radiation force caused by the asymmetric structure, and the source of the acoustic radiation force is the battery at the bottom; the existence of the sound pressure gradient field could be demonstrated through computational simulation. [31] Since the force generated by the standing wave is greater than that of the traveling wave, research on ultrasonic driving mainly focuses on standing-wave driving. There have been various cases of ultrasonic-driven MNRs in recent years. The asymmetric distribution structure of designed MNRs is an effective way to achieve ultrasonic-driven "on/off" action. Studies have reported the action schemes of MNRs with nanowires, [80] nanorods, [81] nanotubes, [82] and erythrocyte motors [52] driven by ultrasound. Microbubbles are generated on the surface of the tubular structure to generate enough force to maintain propulsion. These have been used in various driving strategies, but the movement of tubular micromotors is affected by the rapid fluid disturbance caused by bubbles. To address this problem, Lu et al. proposed combining tubular swarms with ultrasound, which mediated and slowed down the force generated by bubble injection, and the tubular MNRs assembled under the effect of ultrasound to form a "dandelion swarm." [83] In the study, the cross sections of two observation areas were selected for the establishment of calculation models, and the acoustic pressure, acoustic streaming, and the track of oscillating bubbles near the micromotors in the two areas were simulated, respectively ( Figure 6A). As they can be seen from the simulation results, the oscillating bubble destroyed the electrostatic pressure condition and the acoustic pressure was largest near the bubble. Different pressures in the space area produced local acoustic streaming. Under the guidance of ultrasound, the micromotor moved toward the high-pressure area with the bubble. Bubbles fuse to form large bubbles to guide the formation of dandelion swarms, and swarms can achieve superspeed movement under the action of acoustic flow. Achieving on-demand precise control of MNR motion using ultrasound remains a major challenge. In that regard, Lu et al. proposed a human-computer interaction strategy. [84] Through audio source encoding position information, a particle with a positioning error of 10 μm could be accurately and quickly delivered to the desired location in one trip. The interface was integrated into an acoustic robot platform, which enabled MNRs to vibrate at different frequencies under the excitation of a piezoelectric transducer, resulting in a synthetic propulsive force to complete the drive. This acoustic drive could be used to control the speed and direction of moving particles and cells. Finite-element numerical simulations showed that acoustic oscillations around microscale linear structures could generate locally enhanced acoustic flow and provide sufficient propulsive force for particle transport in fluid environments ( Figure 6B). Such a human-computer interaction interface greatly improves the sustainability and repeatability of MNR operation. Recent studies have also proposed a strategy to control swarm behavior with hybrid acoustic electrodes, which have two functions: the electrolysis of water to produce microbubbles and modulating acoustic flow with/without microbubbles. [85] The oscillating bubbles generated by the acoustic electrode can guide the random movement of the micromotor, and another aggregation behavior of the micromotor will be achieved if there is no bubble and the sound flow is isolated. Based on perturbation theory, flow patterns with and without bubbles were calculated ( Figure 6C). The results showed that acoustic flow flowed out from the center in the presence of bubble; in the absence of bubble, the acoustic flow was uniformly distributed. The simulation results illustrated that the hybrid acoustic www.advancedsciencenews.com www.advintellsyst.com electrode could create different streaming profiles to control swarms, so the strategy was effective and feasible in controlling swarm behavior. However, the high efficiency requirement of ultrasonic-driven MNRs will lead to biological tissue damage. It is important, therefore, to select the appropriate ultrasound power for MNR driving.

Magnetic-Driven MNRs
Magnetic application is relatively mature in medicine. Magnetic fields can penetrate tissues with high efficiency and do not attenuate energy; thus, magnetic-driven MNRs show great promise for in vivo application. Such robots move by applying the  [83] Copyright 2020, Wiley-VCH GmbH. (B) Reproduced with permission. [84] Copyright 2019, American Chemical Society. (C) Reproduced with permission. [85] Copyright 2021, Wiley-VCH GmbH.
www.advancedsciencenews.com www.advintellsyst.com magnetic force and magnetic moment provided by an external magnetic field. The formulas for magnetic force and magnetic moment are as follows, [86] where V is the volume of the magnetic object, M is the magnetization of the object, and B is the magnetic-field strength of the applied magnetic field.
Under a uniform magnetic field, MNRs are not subject to magnetic force. The applied external magnetic field must vary in space or time to ensure the continuous advancement of MNRs in vivo. In obtaining a better motion performance for MNRs, the source of a magnetic field is also controllable. Rotating, oscillating, and gradient magnetic fields are all typical magnetic fields that change with time. We can design different magnetic-field-generating devices to apply different magnetic fields regulate MNR behavior. The magnetic-field information (e.g., magnetic-field strength) can be obtained using the FEA method. In 2014, one study reported a self-assembled magnetic response hydrogel [87] a magnetic setup of two permanent NdFeB magnets to be used as a drive-power source. FEA analysis was used to calculate the magnetic-field profile and flux density parameters generated by the device. The magnetic field near the central symmetry axis was found to be the smallest. Another study proposed a magnetic control device for a novel solid tumor treatment MNR system. [88] The device consisted of eight coils, each with an angle of 45°to the Z-axis. The device had a larger workspace for in vivo experiments and had five directions of freedom and force ( Figure 7A). FEA was used in the experiment to study and predict the trajectory of MNRs and calculate the magnetic field. The magnetic-field situation under different magnetic-field gradients was simulated, and the maximum output of the device was obtained; it was then compared with the measured magnetic field of the device in the actual situation to calibrate the magnetic field. Dong et al. designed a p-Fe 3 O 4 magnetic swarm [89] in which particles converge to form a stable circular swarm under the adjustment of rotation frequency and magnetic-field strength. Then, a rotating magnetic field was applied, which could cause the magnetic swarm to be directed to the target position. In that study, two magnetic systems (three-axis coil system and permanent magnet system) were used to verify the construction and driving ability of p-Fe 3 O 4 Figure 7. Magnetic-driven MNRs. A) Schematic diagram of the designed magnetic control device and simulation diagram of magnetic-field distribution. B) FEA simulation diagram of triaxial Helmholtz coil. A) Reproduced with permission. [88] Copyright 2019, American Chemical Society. B) Reproduced with permission. [18] Copyright 2021, Wiley-VCH GmbH.
www.advancedsciencenews.com www.advintellsyst.com magnetic swarms. The permanent magnet system was different from the three-axis coil system in that the rotating motor and movable chassis could provide speed and movement speed, and the magnetic-field strength could be adjusted according to the movable space and the distance of the spherical magnet. The permanent magnet was chosen for the subsequent experiment. Here, the magnetic flux density on the base surface of the workspace of the permanent magnet system was simulated using COMSOL Multiphysics. The magnetic flux density of the working plane could be known, and the magnetic-field intensity could be adjusted according to the distance between the activity space and the spherical magnet. Thus, the magnetic induction intensity could be adjusted more intuitively according to experimental needs. For achieving accurate control, a Helmholtz coil with threeaxis orthogonal superposition has the advantages of a simple structure and uniform magnetic field. It is often used as a magnetic-field generator for MNRs. Wang et al. treated thrombus with a magnetic field generated by a triaxial Helmholtz coil ( Figure 7B). [18] The simulation model of Helmholtz coil was established, and the magnetic field in one period was simulated. The results demonstrated the homogeneity of the magnetic field. Under the control of such a magnetic system, the rotating microrod loaded with the tissue plasminogen activator (TPA) drug could reach the blocked collateral vessels under the driving of the magnetic field. In this process, blood flow enhanced the diffusion efficiency of the TPA drug to achieve the goal of targeted therapy. Considering the limited operating space and flexibility of the coil, a C-shaped magnetic drive system was designed and experimentally verified in vivo. Combined with the FEA method, this strategy was shown to be an effective treatment for thrombolysis in vivo. The magnetic field could also be used to control parameters (e.g., frequency, amplitude) to design the shape of MNRs. More recently, a deformable magnetic slime was reported. [90] By adjusting the magnetic field, [90] the magnetic slime could be deformed into complex circles, hexagons, and rings. Experiments and simulations showed that the shape of magnetic slime was similar to that of the permanent magnet placed at the bottom. Since magnetic-field-driven MNR must select magnetic materials for synthesis, the selection of materials is limited. However, many magnetically driven MNRs have poor biocompatibility. Thus, how to ensure the safety of magnetic and biological applications remains a major research topic.

Low Reynolds Environment
In research on MNRs, whether in the context of in vitro or in vivo experiments, we cannot ignore the low Reynolds number environment. This is beneficial for force analysis and propulsion research on MNRs in fluid environments. The Reynolds number is less than 1 (i.e., low Reynolds number environment) for microand nanoscale objects. [14,91] In a low Reynolds number environment, the force of MNRs is not affected by the inertial force but is related to the viscous force. The Reynolds number is the ratio of inertial force to viscous force. Reynolds number is expressed by where a is the size of the object, η is the fluid viscosity, ρ is the density, v is the motion velocity, and υ is the kinematic viscosity. Viscous force is expressed by Equation (4) For the Navier-Stokes equations (N-S equations) used in fluid analysis, the formula where inertia is neglected is given by Equation (5) where ν is the velocity vector, P is pressure, and η is fluid viscosity. Computational fluid dynamics are generally used to solve the N-S equations. The N-S equations represent the conservation of mass and momentum in flow.
Compared with the swimming behavior of organisms such as humans and fish, MNRs are time reversible. This is like an object being driven by a driving force, but once the driving force is removed, the object will continue to move forward for some distance because of inertia. Time-reversible MNRs, however, will immediately stop moving when there is no driving force. The classical theory for explaining the reversibility of time is the scallop theorem: to overcome the symmetry of the deformation process in time, swimming can be achieved in a low Reynolds number environment. In a low Reynolds number environment, a single degree of freedom object cannot move back and forth; thus, at least two degrees of freedom should be added when designing MNRs. MNRs also need to overcome the influence of Brownian motion in the liquid environment, [92] requiring them to make a nonreciprocating motion. [93] To predict the motion of MNRs in this environment, FEA can be used to simulate their force distribution.
Helical MNRs convert rotational motion into forward motion and are classical structures that can swim at the low Reynolds number. [94] Helical MNRs' introductions can be found in Section 2.2. The streamlined design of MNRs can effectively reduce the flow resistance, which is an effective strategy to reduce the impact of the low Reynolds number environment. Yang et al. proposed a streamlined MNR for a dynamic low Reynolds number environment. [95] Driven by magnetic field, it could overcome the resistance of blood flow and make spiralrolling movement on the wall. The flow velocities and pressures of the cylindrical and streamlined MNRs in the pipeline were simulated using the FEA. The results suggested that the fluid resistance of the streamlined MNR was smaller than that of the cylindrical MNR. The flask is also a streamlined geometry. In another study, Yan et al. proposed MNRs with asymmetric, hollow, and flask shapes. [96] The asymmetric structure allowed H 2 O 2 to decompose, creating a gradient in hydrogen concentration inside and outside the cavity. The concentration gradient caused the MNR to move continuously and the magnetic field caused it to move in a directed direction.

Brownian Motion
In addition to the effect of high viscous force in low Reynolds number environments on MNR motion, we also consider Brownian motion. Tiny particles suspended in a liquid can exhibit irregular motion a phenomenon called Brownian motion. [97] For MNRs, the randomness caused by Brownian motion harms their directional control and precise targeting. The Brownian motion of MNRs inhibits their autonomous motion and makes the motion trajectory appear disordered.
In most practical systems, material transport has both convective and diffusive components. The physical meaning of the Peclet number is the ratio of the convective and diffusive rates. When the Pe number is large, the motion of the MNR is mainly affected by the propulsion force. Otherwise, when the Pe number is small, the motion of the MNR is mainly affected by Brownian motion. [98] This can be expressed as where U is the moving speed of the MNR, L is the size of the MNR, and D is Brownian diffusivity without propulsive force.
The external field provides a constant and stable energy that is conducive to the control of the MNR to overcome Brownian motion. FEA can be used to calculate Brownian motion, by assigning boundary conditions such as when calculating the initial concentration to have a very large finite value at the origin and 0 elsewhere. The initial concentration diffuses from the origin to the periphery, and diffusion can be modeled based on the particle method. [99] FEA based on the particle tracking method can be calculated for pure convective motion, pure diffusive motion, and motion between the two states. In studying the diffusion of MNRs or the diffusion efficiency of drugs after removing the external field, the solution of the diffusion equation is often used. [21] In the process of implementing the application strategy of MNRs, it is crucial to overcome the track randomization of Brownian motion to achieve accurate active motion. Wu et al. proposed the state-dependent coefficient robust two-stage Kalman filter (SDC-RTSKF) algorithm combining a SDC and RTSKF to study the dynamics model of magnetic Janus micromotors. [100] They adjusted the magnetic field to overcome the Brownian motion and provide the directionality of the motion, and realized the directional motion of the magnetic Janus micromotors. The dynamics model of the magnetic Janus micromotors was theoretically analyzed, and the theoretical results were combined with the experimental observations using SDC-RTSKF. The method was an effective way to achieve accurate control and trajectory prediction. The driving force provided by the external field could make the disordered moving particles assemble into swarms and realized unconstrained motion. It can be found in the introductions of swarm in Section 2.3. In the case of turning off the external field, swarms will disperse into particles and make disordered Brownian motion. Inspired by band-aid, Yue et al. proposed a magnetically driven wheel-like swarm. [101] Under magnetic actuation, particles assembled into wheel-like swarms. FEA modeled this process, and it was known that particles were attracted to each other before they formed wheel-like swarms. It can keep a stable structure of the wheel-like swarm even when the magnetic field was removed, so as to prevent the wheel-like swarm from dispersing into Brownian motion. The direction of the rotating magnetic field was reversed continuously in a period, and the wheel-like swarm shrunk under such a continuous magnetic field and formed a compact and stable geometric structure. This stable structure of wheel-like swarms can prevent intestinal fluid leakage, and has a broad prospect for the treatment of intestinal perforation.

Conclusion and Perspectives
Research on MNRs in the past two decades has revealed their great prospects for clinical use, such as targeted drug delivery, gene transport, and nanosurgery. First, because of the combined effects of the external field, fluid field, and other physical fields, current scientific means cannot effectively study the complex motion modes of external-field-driven MNRs. FEA provides a research method for studying the motion mode of externalfield-driven MNRs, analyzing their motion mechanisms using theoretical models and experiments in parallel. However, the experimental models are not completely consistent with the FEA models. Thus, reducing the differences between theory and experiments through optimization calculation is a research problem that urgently needs to be solved. FEA can quickly explore the experimental scheme by evaluating the process and results of the experiment through multiple simulations. It plays a significant role in promoting the development of MNRs.
Second, the design shape of MNR greatly affects its performance. This review summarizes many shapes of MNRs, but whether there is an optimal shape for different specific applications still needs to be explored. FEA can select the optimal shape of MNRs through a large number of assumptions. It can greatly reduce the time and cost of research. Many cases reviewed in this paper prove demonstrated its great prospects. However, when a single MNR faces an internal environment, its single functionalization cannot deal with the complex and changeable environment. In this regard, swarm design and behavior can provide a new solution. However, because of size constraints, the mechanism of individual interaction between swarms needs to be further studied and clarified. With regard to tracing, MNRs can be considered "invaders" of the human body, and biocompatibility needs to be considered in the design. After that step, the next one concerns selecting the MNR control and strategy for completing the task. Then, the degradation and recovery of MNRs pose difficult problems as well. [20,70,[102][103][104][105][106][107][108][109][110] Third, external-field-driven MNRs can ensure continuous and efficient directional propulsion motion with little damage to the human body. The use of FEA to simulate external field is useful for the study of propulsion principles when designing propulsion strategies. Multiple simulation results can assist in selecting the optimal external field control parameters and methods. The multi-field coupling between the external field and the flow field of the driving mechanism also needs to be clarified when we investigate its motion mechanism. Finite element simulations provide an intuitive perspective to study the effects of multi-field on the motion of MNRs. Over the past decade, although there has been increasing research on MNRs, there are still huge obstacles www.advancedsciencenews.com www.advintellsyst.com to clinical feasibility. How to develop equipment and strategies that can be operated on a large scale in combination with clinical practice is a problem that still needs to be solved to achieve on-demand, accurate, and directional MNR movement. Finally, we summarize low Reynolds number environments and Brownian motion and some related MNRs design strategies. These MNRs reduce the effects of low Reynolds number environment and Brownian motion through high propulsion mechanisms and shape designs. The FEA is used to show the advantage of these strategies. However, in vivo environments are more complex and variable, and research still faces many challenges.
In conclusion, FEA provides an effective research method for MNRs. In specific research, how to use FEA to construct the design scheme of MNRs is the effort that researchers need to make. There are still many deficiencies in MNR research, MNRs have great potential for future application in the medical field. It is believed that in the near future, scientists will have mature MNR treatment strategies that can be applied in clinical programs.