Patent Publication Number: US-11657940-B1

Title: Methods and apparatus for microagent control

Description:
FIELD OF THE INVENTION 
     The present invention relates to microagent control, and more particularly to controlling of migration of a microagent, or a swarm of microagents. 
     BACKGROUND 
     Microagents, such as microparticles, microrobots, etc. are useful in many industrial applications. For example, precision targeted therapy is a modern medical treatment that can precisely locate a lesion in a human body and deliver drugs or therapeutic cells to interact with it. The used drugs or cells can identify specific genes, proteins, and environmental characteristics (pH values, temperature, osmotic pressure, etc.) that are involved in the lesion tissue. Using microagents as carriers to deliver these drugs or cells has been commonly recognized as a promising solution, and its feasibility has been verified in recent years. Microagents can be small particles in the range of a few microns or less, which can protect the drug from degradation and control drug release over a certain period of time; or relatively large microrobots ranging from tens to hundreds of microns, which can deliver cells on the basis of appropriately designed three-dimensional (3 D) structures to facilitate loading, adhesion, transport, and release of functional cells. As another example, microrobots may be used in harsh industrial environment that is dangerous for human beings or is difficult to access. In such harsh applications, microrobots may be expected to migrate towards a desirable site or area to perform certain tasks. 
     New methods and apparatus that assist in advancing technological needs and industrial applications in microagent control are desirable. 
     SUMMARY OF THE INVENTION 
     One embodiment provides a method for controlling a microagent in a workspace. The method includes providing a plurality of magnetic sources and generating a rotating gradient magnetic field by activating the plurality of magnetic sources differently such that a driving force is created to drive the microagent towards an aggregation center in the workspace. 
     Other example embodiments are discussed herein. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The patent or application file contains at least one drawing executed in color. Copies of this patent or patent application publication with color drawing(s) will be provided by the Office upon request and payment of the necessary fee. 
         FIG.  1    illustrates rotating gradient magnetic field actuation in accordance with certain embodiments. 
         FIG.  2 A  illustrates a magnetic field generation system in accordance with certain embodiments. 
         FIG.  2 B  illustrates a workspace generated by the magnetic field generation system of  FIG.  2 A . 
         FIG.  3 A  shows simulation results of magnetic field unit flux density in x direction (B x ) generated by a single magnetic coil in a platform with height h=0 in accordance with certain embodiments. 
         FIG.  3 B  shows simulation results of magnetic field unit flux density in y direction (B y ) generated by a single magnetic coil in a platform with height h=0 in accordance with certain embodiments. 
         FIG.  4 A  shows simulation results of magnetic field unit flux density in x direction (B x ) generated by a single magnetic coil in a platform with height h=10 in accordance with certain embodiments. 
         FIG.  4 B  shows simulation results of magnetic field unit flux density in y direction (B y ) generated by a single magnetic coil in a platform with height h=10 in accordance with certain embodiments. 
         FIG.  5 A  shows simulation results of magnetic field unit flux density in x direction (B x ) generated by a single magnetic coil in a platform with height h=20 in accordance with certain embodiments. 
         FIG.  5 B  shows simulation results of magnetic field unit flux density in y direction (B y ) generated by a single magnetic coil in a platform with height h=20 in accordance with certain embodiments. 
         FIG.  6 A  shows simulation results of magnetic field unit flux density in x direction (B x ) generated by a single magnetic coil in a platform with height h=30 in accordance with certain embodiments. 
         FIG.  6 B  shows simulation results of magnetic field unit flux density in y direction (B y ) generated by a single magnetic coil in a platform with height h=30 in accordance with certain embodiments. 
         FIG.  7    illustrates a sequential activation for a plurality of magnetic sources in accordance with certain embodiments. 
         FIG.  8 A  illustrates motion trajectories of a microagent moving from four directions to an aggregation center under parameter c=(1, 1, 1, 1) in accordance with certain embodiments. 
         FIG.  8 B  illustrates motion trajectories of a microagent moving from four directions to an aggregation center under parameter c=(1.22, 1.11, 1, 1) in accordance with certain embodiments. 
         FIG.  8 C  illustrates motion trajectories of a microagent moving from four directions to an aggregation center under parameter c=(1, 1.12, 1.11, 1) in accordance with certain embodiments. 
         FIG.  8 D  illustrates motion trajectories of a microagent moving from four directions to an aggregation center under parameter c=(1.01, 1, 1, 1.11) in accordance with certain embodiments. 
         FIG.  9    shows a mapping relationship between aggregation center position g(x, y) and c=(c 1 , c 2 , c 3 , c 4 ) in accordance with certain embodiments. 
         FIG.  10    illustrates simulation results of a converging trajectory in accordance with certain embodiments. 
         FIG.  11    illustrates force field distributions with two different aggregation centers in according with certain embodiments. 
         FIG.  12 A  shows simulation results of motion trajectory of a microagent in a working plane with h=0 in accordance with certain embodiments. 
         FIG.  12 B  shows simulation results of motion trajectory of a microagent in a working plane with h=10 in accordance with certain embodiments. 
         FIG.  12 C  shows simulation results of motion trajectory of a microagent in a working plane with h=20 in accordance with certain embodiments. 
         FIG.  12 D  shows simulation results of motion trajectory of a microagent in a working plane with h=30 in accordance with certain embodiments. 
         FIG.  13    illustrates experimental results of a single microagent convergence in accordance with certain embodiments where (A) shows moving trajectories of single microagents (Fe, 300 μm) from four different starting positions in 1,000 pcs dimethylsiloxane (I=2.5 A, f=20 Hz, c i =1); (B) shows moving trajectories of single microagents in 1,000 pcs dimethylsiloxane when the aggregation position is changed by adjusting current parameter c i  for the rotating gradient magnetic field. 
         FIG.  14 A  shows simulation results of agent-agent interaction in a magnetic field with a vertically downward direction in accordance with certain embodiments. 
         FIG.  14 B  shows simulation results of agent-agent interaction in a magnetic field with a sloped downward direction in accordance with certain embodiments. 
         FIG.  15 A  shows simulation results of agent-agent interaction in a fluid where microparticles are fixed at their positions in the fluid in accordance with certain embodiments. 
         FIG.  15 B  shows simulation results of agent-agent interaction in a fluid where microparticles are freely released in the fluid in accordance with certain embodiments. 
         FIG.  16    shows images of different microagents (A) spherical-shaped hematite microparticles; (B) superparamagnetic iron oxide microparticles; and (C) burr-like porous spherical structure in accordance with certain embodiments. 
         FIG.  17 A  illustrates an aggregation process of a microparticle swarm where microparticles are distributed in a chamber with low density in accordance with certain embodiments. 
         FIG.  17 B  illustrates gathering of microparticles at different aggregation areas under different parameters c=(c 1 , c 2 , c 3 , c 4 ) in accordance with certain embodiments. 
         FIG.  17 C  illustrates locomotion of a swarm of microparticles (diameter: 1 μm) by changing parameters c=(c 1 , c 2 , c 3 , c 4 ) in accordance with certain embodiments. 
         FIG.  17 D  illustrates locomotion of a group of  30  microrobots (diameter: 80 μm) by changing parameters c=(c 1 , c 2 , c 3 , c 4 ) in accordance with certain embodiments. 
         FIG.  18 A  illustrates a microparticle swarm on a working plane with h=20 mm, but at frequencies ranging from 6.66 Hz to 50 Hz in accordance with certain embodiments. 
         FIG.  18 B  illustrates a microparticle swarm on a working plane with different h values of 20, 25, 30, and 35 mm respectively at a frequency of 10 Hz in accordance with certain embodiments. 
         FIG.  19    illustrates motion performance characterization of microagent swarm in accordance with certain embodiments. 
         FIG.  20    illustrates a microparticle swarm tested on different working planes with h values ranging from 0 mm to 60 mm at different rotating frequencies in accordance with certain embodiments. 
         FIG.  21 A  illustrates flow simulation in binary channels (up) and nested channels (down) for in-vitro experiments of microagent aggregation control in microfluidic channels in accordance with certain embodiments. 
         FIG.  21 B  illustrates enrichment of microparticles in different binary channels by adjusting aggregation centers for in-vitro experiments of microagent aggregation control in microfluidic channels in accordance with certain embodiments where (i) the microparticles are evenly distributed in the entire fluid channel at a flow rate of 3 μl/min; (ii) the microparticles are enriched in upper part; (iii) the microparticles are enriched in lower diamond-shaped microfluidic channels; and (iv) the microparticles scatter. 
         FIG.  21 C  illustrates enrichment of microparticles in different nested channels at low flow rates for in-vitro experiments of microagent aggregation control in microfluidic channels in accordance with certain embodiments where (i) the microparticles are evenly distributed at a flow rate of 1 μl/min; (ii) the microparticles are enriched in the aggregation area A; (iii) the microparticles are scattered; and (iv) the microparticles are enriched in the aggregation area B. 
         FIG.  21 D  illustrates concentration degrees of microparticles of  FIG.  21 B  at different times. 
         FIG.  21 E  illustrates concentration degrees of microparticles in the nested channel of  FIG.  21 C . 
         FIG.  22 A  illustrates flow fluid simulation results in a microfluidic channel where liquid flow in binary channels with the input velocity of 1 μl/min in accordance with certain embodiments. 
         FIG.  22 B  illustrates flow fluid simulation results in a microfluidic channel showing microagent swarms in the flow channel when they are trapped by a rotating gradient magnetic field (I=2.5 A, f=20 Hz) in accordance with certain embodiments. 
         FIG.  23    shows calculation of concentration degrees in accordance with certain embodiments. 
         FIG.  24 A  illustrates ex-vivo experiments of microagent aggregation control and dispersion in a bovine eyeball in accordance with certain embodiments wherein (i) microparticles are injected into the fundus of the bovine eyeball; (ii) high-concentration suspension is dispersed to a uniformly distributed position through 2 D mechanical shaking and ultrasonic vibration; (iii) an observation area and scanning line of Optical Coherence Tomography (OCT); and (iv) an incised retina stained by the fluorescein released from the aggregated microparticles. 
         FIG.  24 B  illustrates an aggregation process of microparticles in 0-400 s and a dispersion process of microparticles in 400-750 s (I=2.5 A, f=15 Hz for aggregation, and f=66 Hz for dispersion) in the ex-vivo experiments of  FIG.  24 A . 
         FIG.  24 C  illustrates fluorescent microscopy images of the incised retina stained by fluorescence microparticles with and without magnetic actuation control in the ex-vivo experiments of  FIG.  24 A . 
         FIG.  24 D  shows quantitative data of the fluorescent microscopy images in  FIG.  24 C  where the intensity and area of fluorescein are used to simulate the drug release process. 
         FIG.  25    shows a reconstructed the OCT image with slice-array images of gathered microparticles in accordance with certain embodiments. 
         FIG.  26    illustrates a magnetic drive system in accordance with certain embodiments. 
         FIG.  27    is a flow chart illustrating a method for microagent control in accordance with certain embodiments. 
         FIG.  28    illustrates an apparatus for controlling a microagent or a microagent swarm in accordance with certain embodiments. 
         FIG.  29    illustrates a system for controlling a microagent or a microagent swarm in accordance with certain embodiments. 
     
    
    
     DETAILED DESCRIPTION 
     Example embodiments relate to methods and apparatus for microagent control by which a microagent or a swarm of microagents can migrate towards a desirable site or area effectively. 
     Take an application of microagent in therapy as an example. The success of targeted therapy largely depends on accuracy of delivery to a targeted lesion. To overcome limitations of the carrying capacity of a single microagent, a group of microagents (i.e., microagent swarm) must be used for delivery, which puts forward a high requirement for the actuation and control. The microagent swarm can be triggered and actuated by external field stimuli, such as ultrasound, optical tweezers, electricity, and magnetic actuation. Among these methods, electromagnetic actuation is popular for in-vivo applications for its advantages of noninvasive and good control ability, minimal damage to tissues, and insensitivity to biological substances. In this regard, two typical magnetic drive methods are used. One is based on torque-driven magnetic field, and the other is based on gradient magnetic field. The torque-driven magnetic field rotates microagents by first imposing a torque on them, and then converts the rotation into a driving force on the basis of the specifically designed shape and structure of microagents. Such a torque-driven mechanism has a strong driving capacity but limits the shape of the designed microagents. The gradient-based magnetic field can generate a magnetic force directly to drive microagents. The method liberates the constraint of the microagent shape design but requires a high magnetic field gradient to drive microagents. The imaging methods used for the above two drive mechanisms are limited by low resolution and/or shallow penetration depth, which hinders the application of microagent delivery in the in-vivo environment, especially in small and complex regions, such as tiny cavities or tortuous ducts across the blood circulation system. 
     Example embodiments solve one or more of the problems associated with the existing methods and systems and provide technical solutions with improved microagent control. With one or more methods and apparatus as described herein, a microagent or a microagent swarm can be effectively controlled and migrate to a desirable site or area. 
     According to one or more embodiments, a rotating gradient magnetic field is used to transport a microagent or a swarm of microagents to a target site precisely. The rotating gradient magnetic field can be generated by sequentially energizing each of magnetic sources (such as magnetic coils of a gradient-based electromagnetic coil system). Compared with the traditional gradient field drive, under the driving force of the rotating gradient magnetic field, rotation of microagent will reduce viscous resistance and friction of surrounding environment to the microagent, thereby greatly enhancing the motion ability of each microagent. Considering that the gradient magnetic field remains as the main driving force, the shape design of the microagent is unrestricted. The rotating gradient field will produce a volume of high gradient concentrated onto the target site, which attracts the microagent or microagent swarm to automatically converge to the target site from different directions under the action of centripetal force. 
     According to one or more embodiments, rotating gradient-based magnetic field is used to drive magnetic microswarms as carriers to precisely deliver drugs or cells. A sequentially energized electromagnetic coil system generates an equivalent centripetal force pointing to a target site, which will attract magnetic microswarms to converge to the target site in the lesion tissue from different directions. The target site can be adjustable through changing various factors, such as the current inputs of magnetic coils. 
     According to one or more embodiments, under a rotating gradient magnetic field, a microagent is driven to rotate while moving forward, thereby reducing the viscous resistance and friction on the microagent and improving its motion ability. 
     According to one or more embodiments, the microagent control does not rely on any specific trajectory plan and real-time visual guidance for each microagent navigation, which greatly simplifies practical applications. 
     According to one or more embodiments, a rotating gradient magnetic field is generated to drive different magnetic microagents despite their properties such as size, shape, and material. Further, the microagent control does not rely on the initial distribution density of microagents. 
     According to one or more embodiments, a rotating gradient magnetic field is used to gather and drive a swarm of magnetic agents, such as microparticles, microrobots, and other agents which can be magnetized, and make them aggregate in a designed target site or area or aggregation position in absence of imaging guide. The aggregation position can be changed by adjusting various factors, such as the input current of the magnetic system. The microagent control is suitable for precision targeted therapy by delivering drugs or therapeutic cells in complex or harsh environments or other industrial applications, such as harsh environment or environment that is difficult to access by human beings. 
     According to one or more embodiments, for microagent control, electric magnetic coils are used to form a dynamic magnetic field, which is more easily for the generating and adjusting process of the magnetic field by programming input current of the coils when compared with using a permanent magnet to force microagents. The microagent control is based on the principle of creating a zone of attraction in certain position which attracts all the magnetic microswarms. So the microagent control can drive different magnetic microswarms regardless of their properties such as size, shape, and material and does not rely on their distribution density. This is different from traditional methods that require a specific trigger mechanism. The microagent control can drive the microswarms accurately to move to different target positions by adjusting various factors, such as the input current of the coils. The aggregation area moves and attracts the microswarms from its initial position naturally. The control process is simple and can be more easily and effectively achieved than existing methods. No external navigation and feedback methods are needed. The control approach can overcome numerous problems that exist in traditional methods, such as maintaining pattern stability, stochasticity of initial distribution, and navigating in an unpredictable dynamic fluid environment. One or more advantages have been experimentally demonstrated in different microswarm environments including open area environment in chamber, constrained environment in microfluidic chip, and ex-vivo environment in bovine eyeball with different micro swarm agents. 
     According to one or more embodiments, a rotating magnetic field is generated for microagent control. By adjusting the rotating frequency of the magnetic field, different types of microagents are driven to converge to a produced aggregation center or scatter at different rates. Considering that the aggregation does not depend on mutual attraction of the microagents, there is no specific requirement on the distribution density of the microagents. A numerical model of rotating gradient magnetic field actuation is established, based on which the location of the microagent aggregation can be determined by adjusting the input current of each magnetic source, such as each magnetic coil. The relationship between the current input and the location of the aggregation center is characterized to ensure that the microagents are controllable in the entire workspace. 
     According to one or more embodiments, the driving ability of a rotating gradient magnetic field to transport microagents to a simulated blood flow environment is investigated. Given that the driving mechanism does not depend on the agent-agent interaction, the aggregation does not depend on the specific characteristics of the microagents, such as size, shape and material. Experiments performed in a microfluidic channel have confirmed that when an aggregation area is created, the majority of microagents passing through the area are firmly attracted by the magnetic field. 
     According to one or more embodiments, an ex-vivo test is conducted in a bovine eyeball to demonstrate the effectiveness of a rotating gradient magnetic field in driving microagents to a target site. No motion planning is needed for each microagent, and no guidance is required for real-time imaging. The experimental results show that the control method can enrich microagents in complex environments with good performance. 
     According to one or more embodiments, new actuation mechanism is developed that uses a rotating gradient-based magnetic field to drive magnetic microagents to the target site. By programming a microcontroller unit (MCU) of an actuator to sequentially energize electromagnetic coils, the gradient magnetic field can be rotated, and an equivalent centripetal force is generated on the microagents and converge the microagents to a common target position. By modifying the input currents of coils, the position of aggregation center can be adjusted. Experimental results verify the feasibility of this new magnetic drive mechanism. The effectiveness of the rotating gradient magnetic field is verified in a microfluidic chip network that simulates a vascular environment. The ex-vivo experiment has also been conducted successfully on a bovine eyeball model. The experimental results have confirmed the feasibility of the rotating gradient magnetic field in driving different kinds of microagents to a common site for targeted delivery. 
     According to one or more embodiments, the magnetic drive mechanism for microagent control is different from existing methods in several aspects. First, unlike the method that uses permanent magnet to force microagents to form a dynamic stable swarm, the rotating gradient magnetic field in accordance with one or more embodiments as described herein can be easily generated and adjusted by only programming the input current of the coil. Second, the rotating gradient magnetic field can drive different magnetic microagents regardless of their properties such as size, shape, and material and does not rely on the distribution density. This is different from many traditional methods that require a specific trigger mechanism. In addition, the generated swarm can have a large size (e.g., at millimeter scale) and be located in the entire workspace. Third, the microagent swarm can accurately move to different target positions by adjusting the input current of magnetic sources, such as coils. The control process is can be easily implanted. 
     According to one or more embodiments, the microagent control approach can overcome various problems that exist in traditional methods, such as maintaining pattern stability, stochasticity of initial distribution, and navigating in an unpredictable dynamic fluid environment. The experimental results have revealed that the low-density microagents can accumulate in a wide open area and finally form a dynamic equilibrium pattern in a desired aggregation area. 
       FIG.  1    illustrates a rotating gradient magnetic field actuation in accordance with certain embodiments. 
     By way of example,  FIG.  1    illustrates microagents  12  (For concise, only one microagent is referenced with a sign  12 ) in blood vessels  2  and microagents  14  (For concise, only one microagent is referenced with a sign  14 ) on the surface of the retina of an eyeball  4 . Magnetic sources  111 ,  112 ,  113 , and  114  are employed to generate a magnetic field. For concise, only magnetic field  120  is shown for illustrative purpose. By way of example, the magnetic sources have four orthogonal electromagnetic coils. When current flows through a magnetic coil, a static gradient magnetic field with a donut-shaped distribution is generated. By way of example, by sequentially inputting direct current (DC) to each coil, a rotating magnetic field can be created. A microagent or a swarm of magnetic microagents can be excited to migrate or navigate to and accumulate at an aggregation center or target site or target position. The position or location of the aggregation center can be adjusted by changing the input current of the coils. 
       FIG.  2 A  illustrates a magnetic field generation system. For concise, only a single magnetic source  211  is shown. The magnetic source can be a specific implementation of magnetic sources  111 ,  112 ,  113 , or  114  with reference to  FIG.  1   . 
     By way of example, the magnetic source includes a magnetic coil.  FIG.  2 A  illustrates a reference plane  26  and a working plane  28 . The reference plane  26  can be a horizontal plane where point dipoles of magnetic coils are located. The distance between the two planes is denoted by h, which is also height of the working plane  28  relative to the reference plane  26  along a direction perpendicular to the two planes  26 ,  28 . The working plane is also called h-plane in one or more embodiments. 
       FIG.  2 B  illustrates a workspace  20 . The workspace is a space where a microagent or a microagent swarm or a majority of a microagent swarm migrates. In reality, the workspace can be a 3 D space, such as substantially having a configuration of a sphere or cuboid. A working plane is a plane passing through the workspace and in parallel with the reference plane. The working plane typically passes through the center of a workspace with which it associates. In one or more embodiments as described herein, for concise, the workspace is illustrated as a two-dimensional (2 D) space, and as such, the workspace and the associated working plane are in a same plane. In the present embodiment, the workspace  20  is illustrated as a square area of 15×15 unit square areas in the working plan and defined by the four magnetic coils C 1 , C 2 , C 3 , and C 4 . 
       FIGS.  3 A- 6 B  shows simulation results of magnetic field unit flux density B unit (r, h) generated by a single magnetic coil in different platforms with different height h. B x , and B y  are the flux density in x and y directions respectively, and h is the height of h-plane relative to a reference plane.  FIGS.  3 A- 3 B  shows B x  and B y  at h=0 mm (i.e. the working plane and the reference plane are on a same plane) respectively.  FIGS.  4 A- 4 B  shows B x , and B y  at h=10 mm respectively.  FIGS.  5 A- 5 B  shows B x  and B y  at h=20 mm respectively.  FIGS.  6 A- 6 B  shows B x  and B y  at h=30 mm respectively. 
     In accordance with one or more embodiments, a rotating gradient magnetic field can be generated by activating multiple magnetic sources differently (such as activating the magnetic sources on a different time sequence, with a different current input, etc.) such that a driving force (such as a centripetal force) is created to drive a microagent towards an aggregation center in a workspace. The driving force can also drive a microagent swarm towards an aggregation area. 
     By way of example,  FIG.  7    illustrates a sequential activation for a plurality of magnetic sources for generating a centripetal force in accordance with certain embodiments. In the present embodiment, the magnetic sources are illustrated as four magnetic coils that are magnetic coils C 1 , C 2 , C 3 , and C 4  respectively with reference to  FIG.  2 B . The magnetic coils are energized by four DC power sources or power supplies. The current input feeding the magnetic coils are DC input. As illustrated, a sequentially DC input of the coils is performed so as to generated a rotating magnetic field. When applying the sequentially DC input I i , i=1, 2, 3, 4 in the present embodiment, the flux density B(r, h) is then rotated with a frequency f. Denoting I as the current amplitude from the power source, the current of the ith coil is expressed as: 
                       I   i   ′     =     I   ·     sin   ⁡   (     2   ⁢     π   ⁡   (       f   ⁢   t     -       i   -   1     n       )       )     ·     c   i         ⁢   
       I   i     =     {               I   i   ′     ⁢        when   ⁢                ⁢     I   i   ′       ≥   0                 0   ⁢         when   ⁢                ⁢     I   i   ′       &lt;   0                       (   1   )               
where f and t denote the rotating frequency of the magnetic field and time period respectively. In real-time applications, a current parameter c i  can be introduced to I i  to adjust the current of the ith coil. In this way, the position or location of the aggregation center can be changed. In the present embodiment, I can be adjusted by the power source, and the parameter c i  can be adjusted by a microcontroller unit or controller.
 
       FIGS.  8 A- 8 D  illustrate motion trajectories of a microagent moving from four directions to different aggregation centers under different parameter c=(c 1 , c 2 , c 3 , c 4 ) in accordance with certain embodiments. The microagent is initially located at (0, 3), (3, 0), (0, −3), (−3, 0). In  FIG.  8 A , c 1 =c 2 =c 3 =c 4 =1, under a rotating gradient magnetic field, the microagent converges to a center of the workspace, i.e. (0, 0). The trajectories of the microagent are denoted by dotted lines. It can be seen that the microagent converges to the center from four different positions successfully, which indicates that the rotating magnetic field can produce a centripetal force to attract the microagent to converge to a target position. 
     In  FIG.  8 B , (c 1 , c 2 , c 3 , c 4 )=(1.22, 1.11, 1, 1). Under a rotating gradient magnetic field, the microagent converges to (2, 1). In  FIG.  8 C , (c 1 , c 2 , c 3 , c 4 )=(1, 1.12, 1.11, 1). Under a rotating gradient magnetic field, the microagent converges to (−1, 1). In  FIG.  8 D , (c 1 , c 2 , c 3 , c 4 )=(1.01, 1, 1, 1.11). Under a rotating gradient magnetic field, the microagent converges to (0, −1). These figures show that the microagent moves to different aggregation centers when changing the parameter c. That is, the location of the aggregation center can be adjusted by adjusting the current parameter c. 
     In accordance with some embodiments, the following rules apply when adjusting c i  to determine the position of an aggregation center. First, c i  for the magnetic coils on the same axis cannot be adjusted simultaneously. That is, taking the magnetic sources with four coils as an example, when adjusting c 1  for the first coil, the c 3  for the third coil in the opposite direction should keep the base value of 1. This should be applied to c 2  and c 4  similarly. Second, the current change is always conducted incrementally, which means that c i  is no less than 1 when c i  starts to change from a base value of 1. Coil pairs that change the coil current have four types, which are coils 1-2, 2-3, 3-4, and 4-1. Considering c=(c 1 , c 2 , c 3 , c 4 ) as the parameter group for four coils. When c=(1, 1, 1, 1), the aggregation center is located at the physical center of the workspace, namely, (x, y)=(0, 0). By changing c i , the position of the new aggregation center can be calculated on the basis of Equation (5) as set forth below. Then, the reverse mapping relationship from g(x, y) to c can be established using a back propagation neural network (BPNN) model. Here, the BPNN model contains three layers, namely, an input layer g(x, y), an output layer c, and a hidden layer. By way of example, the number of hidden layer units is 10. The rectified linear unit and mean squared error functions are used as the activation function and loss function, respectively. When c i  is increased from 1 to 2 at a step of 0.01, 100×100 data will be used to train the BPNN model with Python, and the reduced state sequence estimation (RSSE) method will be used as the evaluation function. When the RSSE is less than 0.001 after 10,000 iterations, convergence is reached, and then the training model is established. In this way, the position of any desired aggregation center can be determined by setting the corresponding c. As an example,  FIG.  9    shows a mapping relationship between the aggregation center position g(x, y) and c when the workspace of 15 mm×15 mm is divided into 15×15 unit square areas. The unit square area with a length of 1 mm is accurate enough for most clinical treatments (e.g., tumor therapy). 
     The model of an individual microagent driven by a rotating gradient magnetic field in low-Reynolds (Re) number regimes was established as follows. Let μ 0 =4π×10 −7 Tm/A denote the permeability of a free space, m 0  denote the point dipole moment, E denote the identity matrix, r denote the position of a microagent in the field, and p denote the magnetized vector of point dipole starting from the center of a workspace to the point dipole of coil. Under unit electric current, the magnetic field unit flux density B unit (r′) of a single magnetic coil can be described as: 
                       B     u   ⁢   n   ⁢   i   ⁢   t       (     r   ′     )     =         μ   0       4   ⁢   π       ⁢     (         3   ⁢     (       m   0     ·     r   ′       )     ⁢     r   ′                r   ′          5       -       m   0              r   ′          3         )               (   2   )               
where r′=−r+p, representing the vector connecting the position of the microagent and the point dipole of the coil. Define a horizontal plane that includes the point dipole of coil as reference plane (or zero-plane) and a plane higher than the reference plane by a distance of h as h-plane. For a single magnetic coil, the flux density B unit (r, 0) in the h-plane (where h=0) can be simplified as B unit  (r, 0)=μ 0 m 0 /(2π||−r+p|| 3 ). Then, the unit flux density B unit (r, h) in the h-plane can be derived by extending as follows:
 
     
       
         
           
             
               
                 
                   
                     
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     When applying the sequentially DC input I i  described in equation (1) and  FIG.  7   , the flux density B(r, h) of the rotating gradient magnetic field is expressed by 
     
       
         
           
             
               
                 
                   
                     
                       
                         
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     where B i (r, h) is the flux density generated by the ith magnetic coil, I i  is the current input of the ith coil, n is the number of coils, and R i  is an orientation matrix of the ith coil expressed as 
                 R   1     =     [         1       0           0       1         ]       ,       R   2     =     [         0         -   1             1       0         ]       ,       R   3     =     [           -   1         0           0         -   1           ]       ,       R   4     =         [         0       1             -   1         0         ]     ⁢         when   ⁢         n     =     4   .               
Using Equation (4), the magnetic driving force F mag  can be estimated as
 
 F   mag =( m ·∇) B ( r, h )  (5)
 
where m=VTx/μ 0 (1+x), representing the magnetic moment of the microagent, and ∇ denotes the Hamiltonian operator representing the gradient of field. Given that the microagent always moves in a quasi-equilibrium state in a low Re number regime, the resistance force of the liquid, denoted by drag force F drag , is equal to F mag , namely, F mag =F drag . The drag force is calculated as F drag =6πηRv, where R is the equivalent radius of the microagent, η is the dynamic viscosity of the fluid, and v is the velocity of the microagent.
 
     Then, the position of the microagent at time t, denoted by r(t), can be derived as: 
     
       
         
           
             
               
                 
                   
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     As time t→∞, r(∞) represents an equilibrium position to which the microagent converges, which is defined as the aggregation center, denoted by g(x, y), where x and y are coordinates in the working plane. The point dipole moment m 0  and the magnetic moment m can be solved by Genetic Algorithm (Python, scikit-opt solver). As a function of r(t), p can be solved. Using r(t) in Equation (6), the velocity v of the microagent can be estimated; therefore, the drag force F drag  can be determined. Consequently, the magnetic force F mag , which is equal to F drag , can be estimated. 
       FIG.  10    illustrates simulation results of a converging trajectory r(t) in accordance with certain embodiments.  FIG.  11    illustrates force field distributions (magnetic force F mag ) with two different aggregation centers in according with certain embodiments. By way of example, for  FIG.  10    and the Aggregation position #1 of  FIG.  11   , frequency f=20 Hz, current I=2 A and c 1 =c 2 =c 3 =c 4 =1. As illustrated in  FIG.  10   , the microagent is initially located at four initial positions respectively, which are (0, 3), (3, 0), (0, −3), (−3, 0). Then the individual microagent converges to the center of the workspace, i.e. the aggregation center. The trajectory of the microagent is expressed with dotted lines. 
     The right of  FIG.  10    is an enlarged view of a trajectory portion  1010 . As can be seen, the microagent rotates around a centerline or central line  1020  and moves forward along the arrow of the centerline  1020 , where T represents time period, and t 1 , t 2 , t 3 , t 4  represent different time points. Given that actual motion of the microagent is an orbital revolution around the centerline  1020 , it can be treated as a movement along the centerline  1020 . It can be seen that the microagent converges to the aggregation center from four different positions successfully, showing that the rotating magnetic field can produce a centripetal force to attract the microagent to converge to a target position or site. 
       FIG.  11    displays field distributions of the estimated magnetic force F mag , which are calculated on the basis of Equation (6). The arrows represent directions of the magnetic force, and the contour maps and distribution represent the value of the estimated magnetic force. 
       FIGS.  12 A- 12 D  shows simulation results of motion trajectory of a microagent in the working planes with different h=0, 10, 20, and 30 mm respectively in accordance with certain embodiments. The solid dots represent microagents, and the dot lines represent trajectories. The calculation result shows that the flux density B(r, h) of the rotating gradient magnetic field is closely related to the height h of the working plane. In the planes of h=0 mm ( FIG.  12 A ) and h=10 mm ( FIG.  12 B ), the microagent moves near the boundary of the workspace, and the aggregation effect is not so obvious. In the planes of h=20 mm ( FIG.  12 C ) and h=30 mm ( FIG.  12 D ), the microagent moves towards a central position or an aggregation center, indicating that the microagent can be attracted by the rotating magnetic field in these two planes. 
       FIG.  13    illustrates experimental results of a single microagent convergence.  FIG.  13 (A)  shows moving trajectories of single microagents (Fe, 300 μm) from four different starting positions in 1,000 pcs dimethylsiloxane (I=2.5 A, f=20 Hz, c i =1). Scale bar=1 mm. Each starting point corresponds to a respective trajectory group, and therefore there are four trajectory groups #1, #2, #3, and #4. For each trajectory group, a dot line represents a defined trajectory while a solid line represents an actual trajectory.  FIG.  13 (B)  shows moving trajectories of single microagents in 1,000 pcs dimethylsiloxane when the aggregation position is changed by adjusting current parameter c i  for the rotating gradient magnetic field. As can be seen, when the current parameter c i  changes, the trajectory changes and accordingly a different aggregation center is reached. 
       FIGS.  14 A and  14 B  show simulation results of agent-agent interaction in a magnetic field in accordance with certain embodiments. By way of example and for the simulation, spherical-shaped hematite microparticles (diameter: 1  i m) are used. The simulation is performed using an AC/DC Module of COMSOL Multiphysics.  FIG.  14 A  illustrates magnetic field distributions of microparticle arrays with different distances. The distance between neighboring array centers decreases from 4 μm to 1 μm. Direction of the magnetic field is vertically downward. For  FIG.  14 B , the difference from  FIG.  14 A  is that the direction of the magnetic field slopes downward. As can be seen, when the distance between microparticles is small enough (e.g., &lt;1 μm), the magnetic field will affect the agent-agent interaction. 
       FIG.  15 A and  15 B  show simulation results of agent-agent interaction in a fluid in accordance with certain embodiments. By way of example and for the simulation, spherical-shaped hematite microparticles (diameter: 1 μm) are used.  FIG.  15 A  illustrates flow field distribution when the microparticles are fixed at their positions in the fluid. The simulation is performed using the Rotating Machinery Module of COMSOL Multiphysics. Each microparticle is assumed to rotate at a frequency of 10 Hz. When the distance between two adjacent microparticles is 4 μm, the fluid fields of the microparticles do not affect the interaction among microparticles. When the distance is reduced to 1.25 μm, the fluid fields of adjacent microparticles are merged, indicating that the particle-particle interaction are affected by the fluid.  FIG.  15 B  illustrates flow field distribution when five microparticles are freely released in fluid. The simulation is performed using the Fluid-Structure Interaction of COMSOL Multiphysics. Each microparticle is assumed to rotate at a frequency is 10 Hz. When t=0 s, the distance between two adjacent microparticles is 1.5 μm. After 12 ms, the microparticles form a chain-like structure, and the distance is reduced to 1.35 μm, indicating that the fluid affects the behavior of microparticles. 
       FIG.  16    shows images of different microagents in accordance with certain embodiments. The morphology of the microparticles and fabricated microrobots is observed under a scanning electron microscope (SEM). (A) shows spherical-shaped hematite microparticles with superparamagnetic core and polymer outsourcing layer with a diameter of 1 μm. (B) shows superparamagnetic iron oxide microparticles with superparamagnetic core. (C) shows a burr-like porous spherical structure and a diameter of 80 μm, manufactured by a two-photon lithography system using degradable materials doped with 2% superparamagnetic materials. 
       FIGS.  17 A- 17 D  illustrate an aggregation process of a microparticle swarm in accordance with certain embodiments. The magnetic microagents used in these experiments include microparticles (diameter: 1 μm) and spherical microrobots (diameter: 80 μm). The frequency of the rotating magnetic field is 10 Hz, and the current I from the power source is 2.5 A. 
     In  FIG.  17 A , the microparticles are distributed in a chamber with low density. At the beginning, the microparticles are distributed in a custom-made chamber with a density as low as 1 μg/ml. When a magnetic field is applied, the microparticles converge to a resulting aggregation center or are confined in an aggregation area. It can be seen that as time increases, more and more microparticles gather and are densely distributed around the aggregation center or in the aggregation area.  FIG.  17 B  illustrates that by changing current parameter c=(c 1 , c 2 , c 3 , c 4 ), the microparticles gather at different aggregation areas. From left to right, the parameters c are (1, 1, 1, 1), (1.22, 1.11, 1, 1), (1, 1.12, 1.11, 1) and (1.01, 1, 1, 1.11) respectively. A dotted circle represents boundary of the circle that covers 95% of the microparticles. 
       FIG.  17 C  illustrates locomotion of a swarm of microparticles (diameter: 1 μm). The swarm of microparticles is substantially confined in an aggregation area with a boundary denoted by a dot circle. At 1 s, the microparticle swarm is located at its original position by setting c=(1.11, 1, 1, 1.12). After changing c to (1.10, 1.02, 1, 1), the microparticle swarm moves to a new aggregation area at 160 s. By adjusting c to (1, 1.23, 1.01, 1), the microparticle swarm continues to move to a new aggregation area at 320 s. By adjusting c to (1, 1.12, 1.22, 1), the microparticle swarm then moves to a new aggregation area at 480 s. That is, with adjustment of the parameter c, the location or position of the aggregation area can be adjusted. 
       FIG.  17 D  illustrates locomotion of a group of 30 microrobots (diameter: 80 μm). By adjusting the parameter c, as can be seen, the microrobot swarm will migrate to a new aggregation area. 
     These results verify that a rotating gradient magnetic field, when properly designed, can accumulate different types of magnetic microagents, despite their size, shape, or material characteristics. Also, the driving mechanism does not depend on agent-agent interaction among microagents. 
       FIGS.  18 A and  18 B  illustrate aggregation states of microparticle swarms when changing working plane&#39;s height h and magnetic field&#39;s rotating frequency f in accordance with certain embodiments. Height h is the distance or height of a working plane relative to a reference plane. 
       FIG.  18 A  illustrates a microparticle swarm on the working plane with h=20 mm, but at various frequencies ranging from 6.66 Hz to 50 Hz. It can be seen that the size of the formed microparticle swarm increases as the rotating frequency increases. The increased size of the swarm indicates decreased aggregation effect. That is,  FIG.  18 A  indicates the increased frequency makes it harder to confine the microparticles. When the frequency reaches 50 Hz, the microparticles no longer stay together, but rather are scattered. 
     In  FIG.  18 B , the working planes are initialized with different h values of 20, 25, 30, and 35 mm respectively at a frequency of 10 Hz. It can be seen that when h increases, the size of the formed microparticle swarm increases, indicating a decreased aggregation ability or aggregation effect. 
       FIG.  19    illustrates motion performance characterization of microagent swarm in accordance with certain embodiments. Motions  1910  and  1920  are related to a swarm of microparticles (diameter: 1 μm) under two different rotating frequencies (10 Hz and 50 Hz) respectively. Motions  1930  and  1940  are related to a swarm of microrobots (diameter: 80 μm) under two different rotating frequencies (10 Hz and 50 Hz) respectively. 
     At 10 Hz, the distribution area of the microparticles is reduced from a larger area at 1 s to a smaller area at 120 s, indicating that the microparticles successfully aggregate. When changing the rotating frequency from 10 Hz to 50 Hz, the microparticles expands to a larger area from 1 s to 60 s, suggesting that the microparticles scatter when the frequency is increased to a certain high value. Motions  1930  and  1940  show similar performance for microrobots. 
       FIG.  20    illustrates a microparticle swarm tested on different working planes, with h values ranging from 0 mm to 60 mm at different rotating frequencies. Three different states are defined as “aggregation state,” “dispersion state,” and “unstable state”. When the rotating frequency is in a low level, the microparticles aggregate and in the “aggregation state.” When the rotating frequency increases to a high level, the microparticles scatter, and is in the “dispersion state.” When the rotating frequency is in a critical level between the above two states, the microparticles appear unstable and in the “unstable state.” 
     In certain embodiments, when the rotating frequency is in a range from 6 Hz to 34 Hz, the microparticles aggregate and in the “aggregation state.” When the rotating frequency increases to above 48 Hz, the microparticles scatter and in the “dispersion state.” When the rotating frequency falls in a range from 34 Hz to 48 Hz, the microparticles appear unstable and in the “unstable state.” 
       FIG.  21 A- 21 E  illustrate in-vitro experiments of microagent aggregation control in microfluidic channels in accordance with certain embodiments. 
     According to the embodiment, experiments of aggregating microparticles in a microfluidic chip are conducted. The microfluidic chip is designed to simulate a blood vessel network for targeted delivery. Under action of a rotating magnetic field, a specific agglomeration area or aggregation area is formed, attracting microparticles from different channels. When the location of the aggregation area is changed by adjusting parameter c to respond to other disease sites for treatment, the microparticles located in the existing aggregation area are released and accumulate in a new aggregation area. Two microfluidic chips with different internal structures are designed to mimic two vascular environments of blood vessels and capillary network. The blood vessels with large diameters are usually used for injection because they can be easily detected and pierced. 
       FIG.  21 A  illustrates simulation results of the flow that can be uniformly distributed (less than 5% dispersion). Flow simulation in binary channels  2102  and nested channels  2104  is shown. 
     In an experiment as shown in  FIG.  21 B , in the entire microfluidic channel, a microfluidic chip with a diameter of 300 μm is used as a main channel (such as the main channel  2110  as shown in  FIG.  21 B (i)), which is separated into two subchannels (such as the subchannels  2112  and  2114  as shown in  FIG.  21 B (i)). Each subchannel is further separated into two branch channels (diameter: 50 μm) (such as the branch channels  2112   a ,  2112   b ,  2114   a , and  2114   b  as shown in  FIG.  21 B (i)). 
       FIG.  21 B  shows enrichment of microparticles in different binary channels by adjusting the aggregation center or area.  FIG.  21 B (i) shows at a flow rate of 3 μl/min, the microparticles are evenly distributed in the entire fluid channel. Under the low-frequency rotating gradient magnetic field, the microparticles are enriched in upper part (see  FIG.  21 B (ii)) and lower diamond-shaped microfluidic channels (see  FIG.  21 B (iii)). Under a high-frequency rotating magnetic field, the microparticles scatter (see  FIG.  21 B (iv)). 
     Specifically, the microparticles are evenly distributed at the beginning ( FIG.  21 B (i)), and then are attracted to the upper and lower diamond-shaped microfluidic channels ( FIG.  21 B (ii) and  FIG.  21 B (iii)). These results suggest that under a rotating magnetic field, magnetic microparticles can move to different aggregation areas by entering different channels. When the frequency increases to 50 Hz, the microparticles first scatter and then are washed away by the fluid flow ( FIG.  21 B (iv)). A similar phenomenon can also be found in the nested channels of the simulated capillary network. 
       FIG.  21 C  illustrates enrichment of microparticles in different nested channels at low flow rates. At a flow rate of 1 μl/min, the microparticles are evenly distributed ( FIG.  21 C (i)), and then enriched in the aggregation area A ( FIG.  21 C (ii)) and the aggregation area B ( FIG.  21 C (iv)). The microparticles are scattered under a high-frequency rotating magnetic field ( FIG.  21 C (iii)). As shown in  FIG.  21 C , by changing the aggregation center or area defined by the rotating gradient magnetic field, magnetic particles are enriched in different areas of the channels. 
       FIG.  21 D  illustrates concentration degrees of microparticles of  FIG.  21 B  at different times. A concentration degree represents density of microparticles in aggregation, and its value can be calculated by image processing in Python OpenCV. Phase 0 represents the initial state where no microparticle passes through the fluid channel and can be used as a reference in image processing. When microparticles flow into a binary channel, the concentration degree is displayed in Phase 1, which is higher than that in Phase 0. Note that the concentration degrees of the aggregation areas 1 and 2 are close to each other, indicating that the flow is evenly distributed. Phase 2 represents the process of  FIG.  21 B (ii) where the microparticles are attracted by the rotating magnetic field in aggregation area 1. The concentration degrees of microparticles in aggregation area 1 increases sharply to a high level, whereas that in aggregation area 2 decreases. Phase 3 represents the process of  FIG.  21 B (iii) in which the concentration degree in the aggregation area 2 increases significantly, whereas that in aggregation area 1 decreases. Phase 4 represents the dispersion process where the concentration degrees of the two areas decrease at the initial level. 
       FIG.  21 E  illustrates concentration degrees of microparticles in a nested channel. Phases 1-4 represent the processes in  FIG.  21 C (i)-(iv) respectively. 
       FIGS.  22 A- 22 B  illustrate flow fluid simulation results in a microfluidic channel.  FIG.  22 A  shows liquid flow in binary channels with the input velocity of 1 μL/min.  FIG.  22 B  shows microagent swarms in the flow channel when they are trapped by a rotating gradient magnetic field (I=2.5 A, f=20 Hz). As the velocity increases, the microagent swarm is squeezed on the radial direction of the flow channel, demonstrating that the rotating gradient magnetic field can trap the microagents in a flow fluid environment. 
       FIG.  23    shows calculation of concentration degrees. By way of example, aggregation areas  2310 ,  2320 ,  2330 , and  2340  are aggregation areas 1, 2, A, and B in  FIGS.  21 A- 21 C . The images of flow channels are extracted from the original image, and the relationship between gray level and number of pixels is calculated at different time. When no microparticle passes through the fluid channel, the image is white (gray value=255), and the concentration degree is 0%; when the fluid channel is full of microparticles, the image is black (gray value=0), and the concentration degree is 100%. Using the statistical information of the imaging histogram, the concentration degrees of microparticles at different time can be calculated. 
       FIGS.  24 A- 24 D  illustrate ex-vivo experiments of microagent aggregation control and dispersion in a bovine eyeball.  FIG.  24 A  is schematic of an experiment.  FIG.  24 A (i) shows microparticles are injected into the fundus of the bovine eyeball.  FIG.  24 A (ii) shows that high-concentration suspension is dispersed to a uniformly distributed position through 2 D mechanical shaking and ultrasonic vibration. The red dashed square and red solid line in  FIG.  24 A (iii) show the observation area and scanning line of OCT, respectively. The green sketch in  FIG.  24 A (iv) shows the incised retina stained by the fluorescein released from the aggregated microparticles.  FIG.  24 B  illustrates an aggregation process of microparticles in 0-400 s and a dispersion process of microparticles in 400-750 s (I=2.5 A, f=15 Hz for aggregation, and f=66 Hz for dispersion).  FIG.  24 C  illustrates fluorescent microscopy image of the incised retina stained by fluorescence microparticles with and without magnetic actuation control. The yellow dashed circle shows the fluorescence area in different situations.  FIG.  24 D  shows quantitative data of the fluorescent microscopy image in  FIG.  24 C  where the intensity and area of fluorescein are used to simulate the drug release process. The scale bars in  FIGS.  24 B- 24 C  are 1 mm. 
     With regards to the ex-vivo experiments of controlling microparticles in the bovine eyeball, after being injected into the eyeball, the drug-loaded microparticles begin to slowly degrade, and the drugs are released through passive diffusion and stain the retina. 
     However, this passive diffusion to the retina can cause side effects and reduce the efficiency of passive diffusion. This problem can be overcome by using actively propelled microparticles. The physical properties of vitreous, such as density or viscoelasticity, may be unaffected by the small-dose injection of particle suspension, and the locomotion of microparticles may be also not dependent on the partial or overall dilution. In the present embodiment, a swarm of microparticles are injected into the bovine eyeball to demonstrate the feasibility of using rotating gradient magnetic field for microagent aggregation. The fluorescein bonded to the microparticles is used to demonstrate the drug release process. OCT and fluorescent microscopy are used to capture images. 0.1 ml of microparticle suspension (1 mg/mL) is injected into the posterior part of the eyeball ( FIG.  24 A (i)), and then subjected to 6 min of 2 D mechanical vibration and 0.5 min of ultrasonic vibration dispersion ( FIG.  24 A (ii))) to simulate the rehabilitation operation between the two consecutive treatment courses. Subsequently, a rotating gradient magnetic field is applied to trigger the aggregation process of the microparticles. The current of each coil is 2.5 A, and the rotating frequency is 15 Hz.  FIGS.  24 A (iii)-(iv) show aggregation process of the microparticle swarm. In  FIG.  24 A (iv), when the microparticles are degraded after 30 mins, the eyeball is stained by the released fluorescein, which can be used to simulate the drug release process for targeted therapy. 
     More specifically,  FIG.  24 B  shows the process of aggregation and dispersion, where the length of the OCT scan line is 5.8 mm. Under a rotating magnetic field, the uniformly distributed particles gather into many clusters, as represented by the white pattern marked by the yellow dashed circle. At the same time, the microparticles begin to move toward the center of the OCT view, which is the desired aggregation center. When the distribution area of the microparticles is reduced, the image contrast of OCT is improved. Finally, the microparticles are concentrated around the aggregation center at 400 s. After increasing the frequency of the rotating magnetic field to 66 Hz within a period from 400 s to 750 s, the microparticles scatter. 
     More specifically,  FIG.  24 C  shows the comparison result of the stained area with and without the rotating magnetic field. When the rotating magnetic field is applied, the fluorescence area shrinks from a large ellipse area at 5 mins to a small ellipse area at 30 mins. During this period, the brightness of the fluorescence stain increases, indicating that the microparticle swarm moves to the aggregation center and releases fluorescence. Note that due to the difference in the aggregation characteristics of the microparticles in the tangential and radial cross-sectional directions of the eyeball, the microparticles forms an elliptical pattern instead of a circle. The results of the control group show that when no magnetic actuation control is applied, the passive diffusion of fluorescence is weaker than that of actively propelled microparticles. Moreover, the distribution area is large and irregular.  FIG.  24 D  shows the quantitative data of intensity and area of fluorescein used to simulate the drug release process. A reconstructed OCT image with slice-array images of the gathered microparticles is shown in  FIG.  25   . 
       FIG.  26    illustrates a magnetic drive system in accordance with certain embodiments. The magnetic drive system includes four magnetic coils  2601 ,  2602 ,  2603 , and  2604  to generate magnetic field in two orthogonal directions, four DC power supplies  2620  (AMETEK SGX300X17D-0ASAR) to generate high-power steady electrical voltage, one MCU  2630  (ATMEL MEGA32U4) included in a computer device  2640 , and four voltage amplifiers  2622  controlled by MCU to transform DC current to the modified sinusoidal wave signals, such as what is shown in  FIG.  7   . The other components include a custom-designed chamber  2605 , a microfluidic chip, an inverted optical CCD camera (THORLABS 1500 M-GE with objective lens from 2× to 10×), and OCT  2660  (THORLABS, Telesto™ Series), and a microscope  2670  that enables observation of microagent migration. The workspace of the magnetic field is located in the central area of the coil system, which is a square area with side length of 15 mm. A micro-injection device  2610  is provided to inject microagents into the workspace. Further, a drive device, such as a motor  2652 , drives a lift platform  2650  such that the relative position of the workspace or working plane can be adjusted. 
     Consider a typical 2 D Helmholtz coil system with four coils where the first and third coils are in the positive and negative directions of the x-axis, and the second and fourth coils are in the positive and negative directions of the y-axis, respectively. The flux density of the rotating magnetic field is described as B(t)=B x cos(2πft)e x +B y sin(2πft)e y , where e x  and e y  denote the unit vectors in x and y directions respectively. For a Helmholtz coil system, B x  is determined by the first and third coils. When current I 1  and I 3  of the first and third coils are reciprocal functions, expressed as I 1 =−I 3 , the superposition magnetic field B x  is a unique vector field. Similarly, I 2  and I 4  are also reciprocal functions. 
     To generate a rotating gradient magnetic field, the two coils in the same direction should not be activated simultaneously. When I 1 &gt;0 and I 3 =0, the direction of B x  will point to the positive direction of the x-axis; when I 1 =0 and I 3 &gt;0,the direction of B x  will point to the negative direction of the x-axis. For B y  on the y-axis, I 2  and I 4  are the same. This sequential activation process can be presented by Heaviside step function. Then, the current I i  of the ith coil is presented in Equation (6). 
     Regarding microparticles and microrobots, by way of example, commercial spherical-shaped hematite microparticles (MagbeStar MP150FG-Plain, BEAVER Co., Ltd., China), with superparamagnetic core and polymer outsourcing layer with a diameter of 1 μm, are used for one or more in-vitro experiments. The microparticles can be loaded with various drugs via surface bonding. Commercial superparamagnetic iron oxide microparticles (SPIOm, Product 103 FG, NanoMicroTechnology Co., Ltd, China) are used for one or more ex-vivo experiments. The core of SPIOm is Fe 3 O 4 . The out layer of SPIOm is biocompatible polymers, and the fluorescein λmax absorption and λmax emission are 488 and 515 nm respectively. The particle size distribution (D50) is 0.5 μm. To adapt to high-viscosity environment, the microparticles can be processed with 1% Pluronic F-127 (Sigma Aldrich) in Deionized water solution as hydrophobic surface functionalization. The microrobots has a burr-like porous spherical structure and a diameter of 80 μm. They can be manufactured by a two-photon lithography system (Nanoscribe GmbH) using degradable materials doped with 2% superparamagnetic materials. Functional cells can be carried and delivered by such microrobots. The images of the microparticles and microrobots are shown in  FIG.  16   . 
     Regarding microfluidic chip design and fabrication, by way of example, a microfluidic chip is fabricated using soft-lithography technology. A four-inch-diameter silicon wafer is used as the substrate and spin-coated with a 100-μm-thick layer of negative photoresist SU-8 2050 (Microchem Corp.). After several processes, such as pre-bake, exposure, post-bake, and development, a SU-8 mold with a pattern of molded vascular microchannels is obtained. Appropriate amounts of polydimethylsiloxane (PDMS) (Sylgard 184, Dow Corning) and curing agent can are mixed at a ratio of 10:1 by weight and poured onto the SU-8 mold. The mold with PDMS mixture is placed in a vacuum oven and baked at 70° C. for 2 h after removing air bubbles. Finally, the cured PDMS microchannel is peeled off from the mold, punched at the inlet and outlets, and bonded with a clean glass substrate to form the final chip. 
     Regarding ex-vivo experiment on the bovine eyeball, by way of example, the bovine eyeball can be bought from local market and kept at 0° C.-4° C. environment. The fluorescein microparticle suspension with a volume of 1,000 μl is placed on a cell dish, mixed with 9 ml PBS (pH=7.6) buffer solution. After injecting 100 μl PBS buffer solution containing fluorescein microparticles into the eyeball using a micropipette, the eyeball incision is sealed with glue and then fixed on a custom-designed vibration chamber. Then, the eyeball with uniformly distributed fluorescein microparticles is placed in the operating area of the magnetic coil system. Before observation with OCT, the upper part of the eyeball can be removed. The eyeball is cut at its equator, excluding all other tissues (lens, cornea, pupil, iris, etc.) except the vitreous body. These images are taken with a complementary metal oxide semiconductor camera at a rate of 9-12 frames per second. After magnetic propulsion, the eyeball is cut with a scalpel, then the vitreous body is removed mechanically, and the retina is cut into a square (2 cm×2 cm). The fluorescence of the microparticles is excited by a light-emitting diode (Ts2R, Nikon eclipse) with a center wavelength of 488 nm. The experiment can be repeated three times or more. 
       FIG.  27    is a flow chart illustrating a method  2700  for controlling a microagent. The method  2700  can be used to control migration of a microagent or a swarm of microagents in a workspace. The microagent may be microparticle, microrobot, or other agents that can be magnetized. 
     Block  2710  states providing a plurality of magnetic sources. The magnetic sources can be activated to generate a magnetic field. The magnetic sources, when activated properly, can generated a rotating magnetic field. By way of example, the plurality of magnetic sources include magnetic coils, such as those as described with reference to  FIG.  1   ,  FIGS.  2 A- 2 B  or  FIG.  26   . The magnetic coils distribute evenly around the workspace and are energized sequentially with current input. The number of the magnetic sources can be determined according to practice needs. For example, there may be 2, 4, 6, 10, 12, 14, 18, or 20 magnetic sources. 
     Block  2720  states generating a rotating gradient magnetic field by activating the plurality of magnetic sources differently such that a driving force is created to drive the microagent towards an aggregation center in the workspace. By way of example, the method performs sequential activation for the plurality of magnetic sources such that direction of the rotating gradient magnetic field rotates. By way of example, the method adjusts position of the aggregation center by adjusting current input for the plurality of magnetic sources such that a magnetic flux density of the rotating gradient magnetic field in the workspace is adjusted. By way of example, the method adjusts position of the aggregation center by adjusting a rotating frequency at which the rotating gradient magnetic field rotates. By way of example, a workspace defines a working plane, and the plurality of magnetic sources defines a reference plane. The method adjusts position of the aggregation center by adjusting a height h of the working plane relative to the reference plane. 
     By way of example, the method energizes a plurality of magnetic coils sequentially at a frequency f from respective DC power source. A current I i  flowing through the ith magnetic coil is expressed as equation (1). The method adjusts position of the aggregation center by adjusting one or more of the amplitude I, the frequency f, and the current parameter. 
     By way of example, the method generates a mapping between the current parameter the aggregation center. The method solves motion functions with back propagation neural network (BPNN) model. 
     By way of example, the method controls migration of a swarm of microagents or microagent swarm in a workspace. The method generates a rotating gradient magnetic field by performing sequential activation for a plurality of magnetic sources such that a centripetal force is created to drive the microagent swarm towards an aggregation area in the workspace. The method increases size of the aggregation area by increasing a rotating frequency at which the rotating gradient magnetic field rotates. When the rotating frequency is less than a first threshold, the microagent swarm is in an aggregation state. When the rotating frequency is equal to or greater than the first threshold and is less than a second threshold, the microagent swarm is in an unstable state. When the rotating frequency is equal to or greater than the second threshold and is less than a second threshold, the microagent swarm is in a dispersion state. By way of example, the method further increases size of the aggregation area by increasing a height h of the working plane relative to the reference plane. 
       FIG.  28    illustrates an apparatus for controlling a microagent or a microagent swarm. The apparatus, for example, can execute one or more methods as described above (such as the method  2700 ) or one or more steps of a method as described above. The apparatus, when operated, can control migration or navigation of a microagent or a microagent swarm in certain area or space. The certain area or space can be an environment inside or outside a human body. The certain area or space can be an industrial environment that is dangerous or harsh to humans or difficult for humans to access. 
     As illustrated, the apparatus includes a magnetic field generation system  2810  and a controller  2820 . The magnetic field generation system  2810  generates a magnetic field. By way of example, the magnetic field generation system  2810  includes a plurality of magnetic sources, such as magnetic coils, and one or more power sources that energize the magnetic sources. In some embodiments, the magnetic field generation system  2810  includes other electrical components that performs one or more of functions including but not limited to signal filtration, rectification, conversion, amplification, comparison, etc. 
     The controller  2820  controls operation of the magnetic field generation system  2810  such that a rotating magnetic field can be generated to drive a microagent or a microagent swarm towards an aggregation center or aggregation area. For example, the controller  2820  can control the way of energization of the magnetic sources such that the magnetic sources are activated differently, such as sequentially, thereby rotating the magnetic field in a desirable way, such as at a desirable frequency. By way of example, the controller  2820  can control the rotating frequency of the magnetic field, the height of a working plane relative to a reference plane, one or more current parameters, etc. As a result, the migration behaviors, the location of the aggregation center or area, etc. of microagent or microagent swarm can be adjusted or controlled. 
     The controller  2820  can be implemented as a processor or processing unit of a computer device, such as a sever, a desktop, a tablet, a laptop, a smartphone, or the like, that communicates with the magnetic field generation system  2810  such that the magnetic field generation system  2810  can receive instructions from the controller  2820  and respond by following the same. 
       FIG.  29    illustrates a system  2900  for controlling a microagent or a microagent swarm. The system  2900 , for example, can execute one or more methods as described above (such as the method  2700 ) or one or more steps of a method as described above. 
     As illustrated, the system  2900  includes an apparatus  2901  that includes a magnetic field generation system  2910  and a controller  2920 . The magnetic field generation system  2910  can be a specific implementation of the magnetic field generation system  2810  with reference to  FIG.  28   . The controller  2920  can be a specific implementation of the controller  2820  with reference to  FIG.  28   . 
     By way of example, the magnetic field generation system  2910  includes multiple magnetic coils  2912  and DC power sources  2914  that energize the magnetic coils  2912 . The controller  2920  controls the DC power sources  2914  such that the magnetic coils  2912  are activated differently. For example, the magnetic coils  2912  can be energized sequentially to create a rotating magnetic field. The rotating magnetic field generates a centripetal force for driving a microagent or a microagent swarm towards a target site. The rotating magnetic field generates a target site acting as an attraction center that attracts a microagent or a microagent swarm. 
     Optionally, the apparatus  2901  includes a drive system  2930 , such as a motor and a transmission mechanism. The drive system  2930  can drive a platform  2950  for the microagent or microagent swarm, thereby changing positon of the workspace in the rotating magnetic field. The platform  2950  may be a human body, part of a human body, a microagent platform outside a human body, or a harsh environment in which microagents are expected to migrate to a target site to carry out a task in an industrial application. 
     Optionally, the apparatus  2901  includes a detection system  2940 . The detection system  2940  includes one or more of sensors, cameras, etc. for collecting information related to microagent migration. The detection system  2940  facilitates monitoring of microagent or microagent swarm in a workspace. In some embodiments, optionally, the collected data by the detection system  2940  can be used in a feedback loop such that microagent migration can be adjusted timely or in a real-time manner. In this way, migration of microagent or swarm into the target site can be achieved more effectively, such as within a shorter time period, reaching the target site more accurately, etc. 
     Optionally, the apparatus  2901  can communicate one or more devices or systems via one or more networks  2960 . As a result, microagent control can be achieved remotely. This is advantageous in applications where a close observation and control is difficult. For example, there may be scenarios where platform for carrying microagent or swarm must be kept in certain conditions, such as very low temperature or a limited space that is not easy to be accessed by operators or users. 
     By way of example, the system  2900  includes a server  2970  that communicates with the apparatus  2901  via one or more networks  2960 . The server  2970  includes a processor or processing unit  2972  (such as one or more processors, microprocessors, and/or microcontrollers), one or more components of computer readable medium (CRM) or memory  2974 , and a magnetic field application  2976 . The memory  2974  stores instructions that when executed cause the processor  2972  to execute one or more methods as discussed herein, or one or more steps of a method as discussed herein. 
     In certain embodiments, optionally the system  2900  includes a portable electronic device or PED  2980  and a storage or memory  2990 . The storage  2990  can include one or more of memory or databases that store one or more of image files, audio files, video files, software applications, and other information discussed herein. By way of example, the storage  2990  store image, instructions or software application that are retrieved by the server  2970  over the network  2960  such that one or more methods as discussed herein are executed, or one or more steps of a method as discussed herein are executed. For example, instructions for controlling the magnetic field generation system  2910  can be stored in the storage  2990  and retrieved by the server  2970  for execution. For example, the data collected by the detection system  2940  can be stored in the storage  2990  and retrieved by the server  2970 . 
     The PED  2980  includes a processor or processing unit  2982  (such as one or more processors, microprocessors, and/or microcontrollers), one or more components of computer readable medium (CRM) or memory  2984 , one or more displays  2986 , and a magnetic field application  2988 . The PED  2980  can execute one or more of methods as discussed herein or one or more steps of a method as discussed herein, and display an image related to microagent migration for review. Alternatively or additionally, the PED  2980  can retrieve files such as software instructions from the storage  2990  over the network  2960  and execute one or more methods as discussed herein or one or more steps of a method as discussed herein. 
     As used herein, a microagent is an agent with a size in a range of a few microns or less and can be magnetized. A microagent can be a microparticle or a microrobot, or the like. 
     The methods, apparatus, or systems in accordance with embodiments are provided as examples, and examples from one embodiment should not be construed to limit examples from another embodiment. 
     Unless otherwise defined, the technical and scientific terms used herein have the plain meanings as commonly understood by those skill in the art to which the example embodiments pertain. Embodiments are illustrated in non-limiting examples. Based on the above disclosed embodiments, various modifications that can be conceived of by those skilled in the art fall within scope of the example embodiments.