10.2.1.1 Micro-manipulation of biology specimens

The cells, nucleus, and other biological specimens that have been manipulated by the engineering methods include (i) mechanical, (ii) optical, and (iii) magnetic means. For mechanical means, one classical technique is micropipette aspiration. The micropipette can apply a low negative pressure to deform and elongate a portion of a cell into it. Based on the deformation, various continuum models [6–8] can be built for quantifying the cell's mechanical properties, such as elasticity and viscosity. One of typical optical methods is laser trapping, also known as optical trap or laser tweezer. The laser beam can create a potential well to trap micro-particles within a defined region. Thus, the cell can be precisely manipulated when attached to the micro-particle being trapped by the laser tweezer. The stretching force in between the micro-particle and cell is proportional to the applied laser power, where the force generated is approximately 0.1–1 nN. Applying the principle of laser trapping, various live entities have been investigated, including virus and bacteria [9], red blood cells [10], natural killer cells [11], and outer hair cells [12]. These laser tweezers have further been refined and innovated through optoelectronic tweezers [13], laser-tracking micro-rheology (LTM) [14], and surface plasmon resonance excited by polarized light [15]. Similar to the micro-particles in laser tweezer, magnetic micro-beads can serve as the handle for magnetic tweezer [16], where the manipulation force equals to the acting magnetic force. These magnetic micro-beads can be ligand-coated [17]. They can work in magnetic gradient [18] and magnetic twisting cytometry (MTC) [19].

10.2.1.2 Micro-force sensing

Beyond the more traditional micro-manipulation methods mentioned in the previous section, the progression of microelectromechanical system (MEMS) technology is significantly enhancing our capabilities in mechanical characterization of the biological specimens. For example, Galbraith et al. [20] measured traction forces generated by fibroblasts using a micro-fabricated device. Also with micro-fabricated force sensor, Yang and Saif et al. investigated the responses of adherent fibroblasts to stretching forces [21] and the role of mechanical tension in neurotransmission [22]. The representative working principles of MEMS micro-force sensors include piezoresistive sensors [23], strain gauges [24], and comb-capacitance structures [25,26]. They are able to sense the micro-forces in magnitudes of less than $1\text{ mN}$. These MEMS devices are not convenient for real biological applications in fluid environments due to their tethered complex electronics. Moreover, these delicate MEMS devices are vulnerable to mechanical impact and thus, susceptible to failure.

Another family of micro- and nano-force sensors takes advantage of the sensing functions of an atomic force microscope (AFM) [27] or scanning electron microscope (SEM) [28]. For example, a vertical micro-cantilever in AFM can be operated to scan and deform a cell. The deflection of the AFM tip can be recorded to generate a map of stiffness across the cell's surface. The cellular and molecular characterization using this method has been reviewed in [29,30]. These customized modules in AFM or SEM are able to detect forces down to nN or even pN levels. However, these micro- and nano-force sensors require even more complex and larger auxiliary drive equipment, compared to the micro-force sensor based on MEMS devices. This creates a difficult test setup to replicate and use in a biology lab.

In contrast, vision-based force sensing can overcome many of the drawbacks mentioned above associated with MEMS and AFM/SEM micro-force sensors. As shown in Fig. 10.3, a stiffness calibrated elastic structure is the critical component of vision based force sensing. When the force F acts on the sensing probe, i.e., when pushing an target “cell”, the probe tip will deflect a certain amount Δ. Based on the known stiffness K of the elastic structure, we can determine the force F from

$F=K\cdot \mathrm{\Delta }.$

In recent studies, the elastic object of low stiffness has been made of silicone elastomers with low Young's modulus and high failure strain. For example, a micro beam made of Polydimethylsiloxane (PDMS) has been used to sense one dimensional nano-Newton level forces for single cell studies [31]. Cappelleri et al. [32] have also used PDMS to develop a 2D vision based micro-force sensor for microrobotic and micromanipulation tasks. Park et al. [33] even made 3D structure out of PDMS for cell-polymer hybrid systems. Besides, micro-post arrays have also been micro-fabricated from silicone elastomer to measure forces exerted by single adhesion sites of a cell [34]. The image processing techniques for the deformation of micro-post arrays have been improved in [35,36]. These vision based micro-force sensors are able to provide force information feedback wirelessly. However, they cannot move to perform the manipulation task unless they are tethered to a motion module. Therefore, an untethered mobile micro-scale robot will be an ideal candidate to incorporate with the vision-based sensors perform wireless force controlled manipulation tasks.

10.3.2.1 Design specifications

For design goal (i), the force that μFSMM can exert onto cells, it directly depends on the magnetic microrobot body because the acting magnetic force is the source of the moving momentum and also the manipulation force. The acting magnetic force, $F_m$, can be evaluated as

$F_m=V\cdot \mathrm{\nabla }(M\cdot B)$

where V is the magnetic volume, M is its magnetization, and B indicates the external magnetic field strength. The magnetic body is a micro-sized nickel part. The volume V (width × height × thickness) is $w\times h\times t=300\text{μm}\times 450\text{μm}\times 76\text{μm}=1.0\times {10}^{-11}{\text{m}}^3$. The magnetization M is set for simplicity as constant value of $3.5\times {10}^5\text{A}{\text{m}}^{-1}$, which is based on the property of $99\text{\%}$ pure annealed nickel in a magnetic field of $2\text{ mT}$ [45]. The magnetic field is produced by the electromagnetic coil testbed shown in Fig. 10.4. The field gradient can be greater than $0.5\text{T}{\text{m}}^{-1}$ within the workspace. Therefore, a representative magnetic force, $F_m$, acting on the current μFSMM can be as large as $F_m=V\cdot (M\cdot \mathrm{\nabla }B)\approx 1.75\text{μN}$.

On the other hand, for the design goal (ii), this amount of force needs to be detected by the on-board micro-force sensor as well. For vision based force sensing, the sensed force, F, is determined by the known stiffness, K, of the elastic sensor structure and its detected deflection Δ due to the applied force. This is expressed as Eq. (10.1), namely, $F=K\cdot \mathrm{\Delta }$. Under this applied force, the micro-force sensor needs to deflect larger than the minimum displacement, ${\mathrm{\Delta }}_{\mathit{min}}$, that can be observed by the vision system. The ${\mathrm{\Delta }}_{\mathit{min}}$ of a vision system can be calculated as:

${\mathrm{\Delta }}_{\mathit{min}}=\frac{2\times \text{Field of View}}{\text{Camera Sensor Resolution}}.$

For our current overhead vision system, the field of view, camera sensor resolution, and other parameters are listed in Table 10.1. The vision system consists of a CMOS camera (FL3-U3-14E4C-C, http://www.ptgrey.com) and an adjustable $2.5\text{–}10\text{X}$ zoom imaging lens (VZM 1000i, http://www.edmundoptics.com). As shown in Table 10.1, the micro-force sensor must deflect more than ${\mathrm{\Delta }}_{\mathit{min}}=6.0\text{μm}$ in order to be detected.

Table 10.1

Specifications of the vision system

	Width (X)	Height (Y)	Unit	Notes
Sensor size	7.18	5.32	mm	Sensor format: 1/1.8”
Number of pixels	1280	1024	–	At 60 fps
Field of view	2.87	2.87	mm	Lens at 2.5X
Observable size, ${\mathrm{\Delta }}_{\mathit{min}}$	4.5	5.6	μm	From Eq. (10.3)

Therefore, the micro-force sensor should be no stiffer than the maximum stiffness, $K_{\mathit{max}}$, when the applied force F results in the minimum observable displacement ${\mathrm{\Delta }}_{\mathit{min}}$. It is obvious that F depends on the magnetic force $F_m$, which varies with the magnetic microrobot body and the applied external magnetic field. ${\mathrm{\Delta }}_{\mathit{min}}$ varies with the available hardware of the vision system. For a conservative estimate as the initial reference for μFSMM design, let $F=F_m/3$. Then the required stiffness of the micro-force sensor $K⩽K_{\mathit{max}}=F/{\mathrm{\Delta }}_{\mathit{min}}=F_m/3({\mathrm{\Delta }}_{\mathit{min}})\approx 0.1\text{N}{\text{m}}^{-1}$.

10.3.2.2 Design of micro-force sensor end-effector

After the stiffness requirement is determined, the detailed design of the micro-force sensor end-effector shown in Fig. 10.5 can be done. In order to meet the low stiffness requirement, the material of elastic section is selected as a silicone elastomer, Polydimethylsiloxane (PDMS), whose Young's modulus is no more than several MPa. The rest of the frame section and end-effector is made from silicon, which is selected for its mechanical strength to avoid out-of-plane deflection and easy workability with MEMS fabrication processes. Moreover, a micro-scale spring-type compliant structure is chosen to yield low planar stiffness. The geometry design is based on our previous studies on the meso-scale vision based force sensor [32]. Here, we introduce the lower stiffness spring structure design within a micro-scale envelope. In addition, the shuttle probe is customized into various shaped end-effectors to facilitate different manipulation processes (i.e., such as cell pushing).

The stiffness of the micro-force sensor design is analyzed with finite element analysis in COMSOL (http://www.comsol.com). A series of designs with tuned dimensions are modeled. The results indicate that four geometric parameters can have different influences on device stiffness. They are summarized in Table 10.2 (for the data in the table, only one design parameter was varied at a time). Geometric parameters impacting the structure's stiffness include: $t_{xy},l_1,l_2$, and d, as shown in Fig. 10.5, where $t_{xy}$ is the beam width, $l_1,l_2$ are the beam lengths, and d indicates the gap between the beams. As shown in Table 10.2, the beam width, $t_{xy}$, and the gap between beams, d, can tune the device stiffness significantly, while the beam lengths, $l_1,l_2$, impact the stiffness in a minor degree. Note that the thickness of the device, $t_z$, also impacts the stiffness proportionally. Thus, it is set as $50\text{μm}$ during the analysis.

Table 10.2

Impacts of geometric parameters on the stiffness of micro-force sensor

Impact	Beam width ($t_{xy}$) ↑	Beam length ($l_1$ & $l_2$) ↑	Gap between beams (d) ↑
Device stiffness in X axis	⇑	↓	⇓
Device stiffness in Y axis	⇑	↑	⇓

Note: This table illustrates the response of micro-force sensor stiffness with increases in the geometric parameters. “↑ / ↓” means slightly increase/decrease: when geometric parameter varies $>50\text{\%}$, stiffness changes $<5\text{\%}$. “⇑ / ⇓” means significant increase/decrease: when geometric parameter varies $<15\text{\%}$, stiffness changes $>50\text{\%}$.

The selected geometric parameters for the micro-force sensor designs are summarized in Table 10.3. The different combinations of these geometric parameters result in 32 different μFSMM designs (P1–P32). Their footprints are between $595\text{μm}\times 765\text{μm}$ to $890\text{μm}\times 875\text{μm}$, which meet the micro-scale dimension requirement. The FEA models show the largest stiffness is approximately $0.05\text{N}{\text{m}}^{-1}$, which is well less than $0.1\text{N}{\text{m}}^{-1}$, the estimated stiffness requirement.

Table 10.3

Geometric parameters of the micro-force sensor

Prototype # (1–32)	Beam width $t_{x}y$ (μm)	Gaps between beams d (μm)	Beam lengths $l_1$ & $l_2$ (μm)
1 – 4	10	45	(75, 75) (50, 50) (50, 75) (25, 50)
5 – 8		60
9 – 12	15	45
13 – 16		60
17 – 20	20	45
21 – 24		60
25 – 28	25	45
29 – 32		60

Note: The thickness of the device $t_z=50\text{μm}$.

10.3.4.1 Prototype calibration

At first, the stiffness of the micro-force sensor on the μFSMM is experimentally calibrated using an electrostatic MEMS micro-force sensing probe (FT-S1000, resolution $\approx 0.05\text{μN}\mathrm{@}10\text{ Hz}$, http://www.femtotools.com). As shown in Fig. 10.7, while the micro-force sensor of μFSMM is fixed, the micro-force sensing probe FT-S1000 is mounted on a micromanipulator system (MPC-200, http://www.sutter.com). This micromanipulator arm can translate along $X\text{–}Y\text{–}Z$ directions independently with a resolution of $1\text{μm}$. Thus, the micro-force sensing probe can be leveled and flushed with the micro-force sensor end-effector. During the calibration tests, the traveled distance of the force sensing probe is recorded in real-time. This corresponds to the deflection of the calibrating micro-force sensor, Δ. Therefore, the stiffness of the fabricated prototype, K, can be derived based on Eq. (10.1), namely, $K=F/\mathrm{\Delta }$, where F is the blocking force read out from the micro-force sensing probe. These stiffness calibrations also show that the vision based micro-force sensor on the μFSMM is able to sense the same level force that can be read by the MEMS device based micro-force sensing probe with tethered electronics.

The stiffness calibration results of the $\mathrm{\#}1\text{–}32$ micro-force sensor designs are summarized in Fig. 10.8. In the measurement testing, the micro-force sensor tip is pushed with a deflection of $20\text{μm}$ to $80\text{μm}$. Comparing with the FEA results, the stiffness of the actual prototypes are all stiffer, with values at most approximately $25\text{\%}$ stiffer. This can be explained by the variance of: (i) geometric dimensions; and (ii) material stiffness properties for the prototypes.

For reason (i), the geometric dimension of the fabricated prototype can be different from the nominal values. The planar geometric dimensions of the fabricated prototypes show a small deviation from nominal values ($⩽3\text{μm}$), which is essentially the resolution of photolithography process. This is a minor factor explaining the stiffness variance. The thickness of the device layer ($t_z$) is also one of the geometric parameters that can impact the stiffness of micro-force sensor. Any extra thickness on the elastic structure can be interpreted as two spring elements bundled in parallel. Therefore, the thickness deviation ($<5\text{\%}$) also cannot fully explain the increased stiffness ($\sim 25\text{\%}$) of the μFSMM prototypes.

For reason (ii), the material property of the PDMS elastomer may be different from the theoretical values plugged in the FEA model. The stiffness of PDMS is a function of curing temperature and aging [48]. The Young's modulus can even reach to $>2\text{ MPa}$ after a long curing under high temperatures (${100}^{\circ }\text{C}$). This can account for the PDMS hardening in μFSMM prototypes as they are exposed to high temperature during MEMS fabrication processes. After the PDMS is cured, the wafer sample still needs two steps of photolithography using $AZ1518$ and $AZ9260$, respectively. Both of them require soft bake at $>{100}^{\circ }\text{C}$ before exposure. This excessive baking process will increase the Young's modulus of the final PDMS structure, which is unavoidable. To verify this hardening, a higher Young's modulus is plugged in the FEA model. At approximately $800\text{kPa}\text{–}1.1\text{MPa}$, the FEA will have the same result as the calibration results (discrepancy $<5\text{\%}$).

Given this stiffness variance, the calibrated stiffness of the fabricated μFSMM prototypes (Fig. 10.8) are still well in the stiffness range required by our current vision and drive system ($100\times {10}^{-3}\text{N/m}$). Limited work has been done in microrobot force sensing, including the efforts from Kawahara et al. [49]. Table 10.4 shows a comparison of primary specifications between the work in [49] and the calibrated micro-scale μFSMM prototypes. These μFSMM prototypes have shown clear advantage when compared with this other microrobot with force sensing capabilities.

10.3.4.2 Mobility

Mobility tests are performed with assembled μFSMM prototypes. The microrobot is submerged into an oil bath and rests on a silicon substrate during the tests. The fluid medium is silicone oil (A12728, http://www.alfa.com), whose dynamic viscosity ν is $40\text{ c.s.t.}$ Actuated by the external magnetic field in the workspace, the first series of tests to demonstrate mobility drive the microrobot in a linear translation (Fig. 10.9(A)). With a $10\text{ mT}$ field, the microrobot is able to move at approximately $2\text{ mm/s}$ with these specific settings. The second mobility test rotates the microrobot in place (Fig. 10.9(B)). The ability to adjust orientation is needed for cell manipulation to control the specific location and approach angle of the robot when approaching and manipulating the cell. In order to realize steady controllable rotation without translation, a magnetic field with a low intensity is applied, less than $4\text{ mT}$. Under the applied field signal, the microrobot rotates in place with the end-effector tip of the microrobot following a circular trajectory, with a deviation error less than $20\text{μm}$.

10.3.4.3 Manipulation on cell analog with micro-force feedback

The μFSMM was then tested to evaluate its ability to push a cell analog (micro-disc with diameter $=200\text{–}400\text{μm}$, thickness $=50\text{μm}$) and simultaneously detect the acting force. The testing environment is the same as in the case of the mobility tests (oil bath, viscosity $\nu =40\text{ c.s.t.}$, silicon substrate). Snapshots for one such test are shown in Fig. 10.10. The μFSMM microrobot is first driven to the target “cell”. After a short pause, the microrobot is driven to push the cell. During the push, the micro-force sensor end-effector deflects up to $\mathrm{\Delta }\approx 30\text{μm}$. Eventually, the “cell” is nudged and displaces an amount approximately equal to the deflection, Δ, and the micro-force sensor returns to its original shape ($\mathrm{\Delta }=0$). This particular pushing test is performed with μFSMM prototype #9 from Table 10.3. According to the calibrated stiffness (Fig. 10.8), the stiffness of its micro-force sensor end-effector in the Y direction, $K_Y\approx 0.01\text{ N/m}$. Therefore, the maximum force during this pushing action is $F=K_Y\times \mathrm{\Delta }\approx 0.3\text{μN}$. The behavior of the μFSMM during this test is shown in Fig. 10.11.

In real cell manipulation tests, the desired micro-force information is the amount of force, $F_0$, that is purely applied on the cell. In the above pushing test, the sensed force F by the μFSMM not only consists of $F_0$, but actually

$F=F_0+f+F_D$

where $F_0$ indicates the force acted on the “cell”, f is the friction force against substrate, and $F_D$ represents the fluid drag during the motion of microrobot. Therefore, both the friction f and fluid drag $F_D$ also need to be evaluated before the actual force $F_0$ on cell is revealed.

Based on Coulomb's model, the friction $f=\mu \cdot G$, where G is the gravity of the microrobot prototype and μ is the friction coefficient. For estimation, G is calculated for a $600\times 500\times 50$ (${\text{μm}}^3$) silicon block, resulting in $G\approx 0.34\text{μN}$. The friction coefficient μ is plugged in as 0.03, similar scenario here as in [50]. Therefore, the friction force $f\approx 1\times {10}^{-2}\text{μN}$.

For the fluid drag, $F_D$, the Reynolds number Re is evaluated first, which is defined as

$Re=\rho vl/\nu$

where ρ is the mass density of the oil bath ($\approx 960{\text{kg/m}}^3$); v is the fluid velocity, which can be set as the microrobot's speed during the pushing action ($\approx 50\text{μm/s}$); l is the characteristic length, which is the length of the microrobot ($\approx 750\text{μm}$); and ν is the dynamic viscosity of the silicone oil ($\approx 40\text{c.s.t.}=0.04\text{Pa}\text{s}$). Thus, for this pushing test in Fig. 10.10, $Re\approx 9\times {10}^{-4}$, which is well within the laminar flow domain. In order to further evaluate the fluid drag force, $F_D$, the laminar flow model of μFSMM is built in COMSOL software (Fig. 10.12). Based on the pressure results (Fig. 10.12(B)), the fluid drag $F_D$ can be assessed by the surface integration of the Y component of the pressure on all the faces of the microrobot. This allows us to estimate the fluid drag, $F_D$, on the direction of microrobot movement (Y axis) as approximately $8\times {10}^{-3}\text{μN}$.

Summing up the friction, f, and fluid drag, $F_D$, accounts only for approximately $5\text{\%}$ of the sensed force, F in Eq. (10.4). Therefore, the micro-force sensor on the μFSMM is able to provide the in-situ feedback of the force acting on the “cell”, which is on the order of $0.1\text{μN}$, with an accuracy of $95\text{\%}$.

10.3.4.4 Path planned manipulation with force control

After verifying the mobility and micro-force sensing function of μFSMM, a comprehensive manipulation test is performed with both path planned motion and force controlled manipulation (Fig. 10.13). The working environment is the same as previous experimental tests.

As shown in Fig. 10.13(A), a μFSMM microrobot is placed preparing to push two object “cell” analogs into target position marked by an “L” bay. Then, the path navigated to the first “cell” is planned in MATLAB using the $A^{⁎}$ algorithm [51] (Fig. 10.13(B)). Thereafter, the microrobot executes the planned route approaching to the first “cell” analog (Fig. 10.13(C)). After approaching the manipulation object, the μFSMM microrobot is manually controlled pushing the “cell” into the target zone. The reason for conducting the manual control during manipulation is the non-prehensile essence of the micro-manipulation, which is difficult to automate and is not the focus of this particular work. Afterwards, the second objective “cell” analog is pushed and stacked into the target zone. After finishing all the manipulation tasks, the microrobot is automatically driven back to the original position. In this manipulation test, the applied forces can be controlled based on the force feedback from the vision based micro-force sensor end-effector. When manually controlling the μFSMM microrobot to push the “cell”, the manipulation can be stopped when the applied force is larger than the maximum allowed amount.