For disease progression, one vivid instance is the initiation of cancer metastasis 
, where the primary tumor evolves and generates delayed secondary tumors in distal organs 
. While many theories have been proposed to explain the process of cancer metastasis, the most accepted mechanism is through the formation of circulating tumor cells (CTCs) 
A). In brief, CTCs are rare cells that emigrate from the primary tumor, enter and circulate within the peripheral blood, and eventually settle down in different organs for growing 
. CTCs are generally considered as the seed of metastasis given their critical role during cancer migration 
and therefore have attracted significant attention as a general biomarker for monitoring and predicting cancer progression 
. However, one critical challenge of using CTCs is their rarity—the number of CTCs is extremely low, usually at the scale of a few CTCs in millions of normal cells 
For tissue regeneration, a representative example is the use of human hematopoietic stem/progenitor cells (HSPCs) for transplantation. HSPCs only represent 0.2% to 0.5% of the leukocyte population (or 0.0003–0.0008% of the blood cell population) in peripheral blood 
, but have the full potency to produce all types of blood cells (e.g., lymphocytes and monocytes, Figure 1
B). Therefore, the transplantation of HSPCs has been essential to the immune reconstruction post the treatment of leukemia 
. Besides, rare cells may modulate the fate of a specific regenerative therapy given to a patient. It has been reported that rare undifferentiated stem cells in therapeutic cells, such as cardiomyocytes 
and beta cells 
, may undergo uncontrolled growth in vivo in animal models 
and eventually convert regenerative therapies into stem cell cancers 
Thus far, over 50 different types of microfluidic devices have been designed and validated for the analysis of rare cells, including circulating tumor cells 
, circulating tumor clusters 
, circulating cancer stem cells 
, circulating fetal cells 
, and circulating endothelial cells 
in peripheral blood, as well as contaminating tumor cells 
in therapeutic cell products. Multiple strategies have been proposed, such as filtration, inertial fluidics, deterministic lateral displacement (DLD), and immunomagnetic sorting 
2. Micro-Magnetic Deflection
Magnetic deflection is a main approach of magnetophoresis. It relies on the dictated movement/migration of target cells to achieve separation. The main procedures of magnetic deflection include the specific magnetic labeling of target cells, the incorporation of an external magnetic field, and on-chip magnetic sorting.
The magnetic deflection of target cells is the result of interaction between magnetic force and hydrodynamic force on the cells. In the presence of an external magnetic field, magnetically labeled cells experience a magnetic force produced by the inserted magnetic gradient. In the meantime, the cells experience Stoke’s drag force from the fluid flow. The magnetic force given as
is the number of magnetic beads bound to the target cell, 𝑉𝑏𝑒𝑎𝑑
is the volume of a nanobead, ∆𝜒𝑏𝑒𝑎𝑑∆
is the relative magnetic susceptibility of nanobeads, 𝜇0
is the magnetic permeability of the free space, and 𝑩
is the magnetic field.
The drag force is expressed as
is the viscosity of the ambient fluid, 𝑅
is the radius of the t cell, and 𝑈
is the velocity magnitude of the target cells relative to the flow.
To dictate magnetic deflection, both magnetic force and hydrodynamic force can be designed based on applications. For magnetic force manipulation, the magnetic labeling of target cells and magnetic gradient in the microchannel can be designed. The optimization of magnetic labeling was discussed above. The change in magnetic gradients can be achieved by modifying the magnetic field. For the optimization of hydrodynamic force, the flow pattern in the microchannel can be designed.
2.2. Magnetic and Hydrodynamic Optimization
The design of magnetic field is an important aspect for the optimization of magnetic deflection. To achieve a good deflection, a large magnetic gradient is required. To increase the magnetic gradient, researchers have tried different types of permanent magnets and different ways to place the magnets. The easiest strategy is to apply a macroscale permanent magnet on the side or at the bottom of the microfluidic device to produce magnetic gradient 
. Target cells will be deflected due to the non-uniform magnetic field produced by the permanent magnet. However, the magnetic gradient may not be strong enough to achieve high-resolution magnetic deflection when target cells have low magnetic susceptibility. Alternatively, magnetic blocks arranged with opposing poles were used for a larger magnetic field gradient 
. Micro-magnet arrays have also been applied to create strong local magnetic gradients to increase magnetic deflection sensitivity 
Insertion of paramagnetic materials has also been used to further enhance local magnetic gradients in the microfluidic device. Soft magnetic materials such as nickel and ion oxide micro- or nanostructures were integrated in microfluidic devices to create strong local magnetic gradients in the microchannel 
. Tom Soh et al. have designed nickel microchannel strips to deflect magnetic labeled rare cells 
. The magnetic ratcheting cytometry system developed by the Di Carlo group also applied soft magnetic materials for magnetic field enhancement and adjustment. In this system, micropillars made of soft materials were arranged at various distances to create multiple magnetic ratcheting zones in the sorting chamber. Periodically switching magnetic fields were produced under the microchip through rotating permanent magnets. The micropillars activated by the switching magnetic field drove magnetically labeled cells across the sorting chamber, and cells with different magnetic loading levels would be stabilized at different ratcheting zones 
. In recent years, the Kelley group has developed a magnetic deflection-based microfluidic chip-termed PRISM 
. This system made use of the superb ferromagnetic property of an amorphous metal alloy ribbon called metglas to produce an extremely strong local magnetic field when external magnets were introduced. Through lithography and wet etching, metglas-based magnetic guide could be patterned on a glass substrate. SU8-based microchannels were then generated on top of the magnetic guide for sample processing and magnetic deflection. The magnetic guides embedded under the microchannel were designed to branch out from the middle to the sidewall of the microchannel with multiple magnetic deflection angles. Magnetically labeled rare cells were thus segregated into different subpopulations when following the magnetic guides.
Making use of hydrodynamic force is another way to dictate magnetic deflection. For example, designing microstructures in the microchannel to produce a low drag force zone can be used to isolate magnetically labeled cells for single-cell analysis 
. Using different materials for channel substrates and optimized channel shapes to obtain uniform flow profiles is another way for drag force manipulation 
. A third way is to introduce ‘flow pockets’ on the side the microchannel and apply permanent magnets along the ‘flow pockets’ 
. The flow velocity is close to zero in the ‘flow pockets’ and non-target cells flowing along the fluid flow will not enter the ‘flow pockets’, while magnetic labeled target cells will be deflected and trapped in the ‘flow pockets’. Table 1
summarizes different magnetic sorting methods and their relevant performance including throughput, target cell isolation efficiency, purity, sensitivity and their potential limitations.
Due to the miniaturized channel scale and strong inserted external magnetic field, microfluidics-based magnetic deflection can bring high deflection efficiency of target cells with good purity 
. Additionally, since magnetically labeled cells move continuously along the sorting chamber, deflected target cells can be easily collected in the designated outlet with few cell loss. However, this method solely depends on magnetic force added on the target cells, which may not be enough to address the heterogeneity of target cells. Rare cells such as CTCs are known to be heterogenous in both biological and physical properties 
. For example, CTCs undergoing epithelial to mesenchymal transition (EMT) will lose the expression of EpCAM 
. Targeting EpCAM alone cannot isolate CTCs with low EpCAM expression. To address this problem, researchers introduced multiplex marker targeting 
. In addition to EpCAM, biomarkers such N-cadherin, vimentin were used to differentiate CTCs under EMT from blood cells 
. Alternatively, magnetic deflection can be combined with physical-property based cell separation methods to achieve superb CTC isolation efficiency.
Table 1. Comparison of different magnetic deflection-based cell sorting strategies.
2.3. Fabrication of Magnetic Deflection-Based Microfluidic Devices
The functioning of magnetic deflection-based microfluidic devices requires two main components: microchannel/sorting chamber assembly and magnetic component combination. For most designs, the sorting chamber for magnetic deflection is integrated to the microchannels for sampling. Polydimethylsiloxane (PDMS) is the most common material for channel fabrication as it is transparent, air permeable, and biocompatible. PDMS substrates with microchannel/sorting chamber features can be conveniently fabricated using soft lithography 
. Briefly, a mold such as a silicon master containing the channel features can be first fabricated using photolithography, and then liquid PDMS mix (base: curing agent = 10:1) is casted on the mold and polymerized at 70 °C for 2 h. The PDMS substrate is then bonded with a cover (e.g., a thin glass slide) to form the microchannel. Other than PDMS, other materials such as negative photoresist (e.g., SU8) were also used in channel fabrication 
. SU8 channels can be fabricated through photolithography. For the integration of magnetic components, it can be direct integration by simply applying a permanent magnet at the top/bottom or on the side of the microchannel. It can also be a complicated process by adding soft magnetic materials. For the insertion of soft magnetic materials, there are multiple ways. The soft magnetic material can first be mixed in solution and then introduced to the bottom substrate of the device through injection molding 
. Another way is to use wet etching to generate magnetic deflection features. For this method, the soft magnetic materials are first coated on the device substrate through electron beam physical vapor deposition or epoxy taping 
. The soft magnetic layer is then patterned through wet etching masked by a photoresist layer. A third way to generate soft magnetic features is through electroplating 
. Different fabrications have pros and cons. For example, liquid soft magnetic material injection can plate magnetic materials easily, but it requires a mold with mirochannels for injection. Therefore, the shape and size of soft magnetic features can be limited. Deposited magnetic features can be highly accurate, but the thickness and magnetic strength of the material can be limited. For the taping of ferromagnetic material such as metglas, it can introduce an extremely strong local magnetic field. However, the taping process limits the smoothness of the substrate surface. Electroplated magnetic features can be generated with relatively high aspect ratio and brings strong local magnetic field. However, the resolution of electroplated feature is relatively low. As such, the fabrication methods chosen usually depends on the specific application of the microfluidic device.
2.4. Integration and Applications for Rare Cell Capture
Different approaches have been reported to combine magnetic deflection with other cell separation mechanisms, showing high compatibility of magnetic deflection. The integration of label-free cell sorting methods and magnetic deflection was widely explored since it usually shows advantages of both approaches. Label-free cell sorting methods generally give high throughput, while magnetic deflection shows high specificity. Toner et al. have developed an integrated microfluidic system that includes deterministic lateral displacement (DLD), inertial focusing and magnetic separation 
. This system was able to isolate CTCs from untreated whole blood, where nucleated cells were first separated from red blood cells (RBCs) through DLD, followed by magnetic depletion of magnetically labeled white blood cells (WBCs). Since RBCs are significantly smaller than nucleated cells, DLD can separate nucleated cells from RBCs with high purity. Inertial focusing re-aligns nucleated cell mixture into single-cell strips which reduces the cell–cell interaction. Therefore, in the last step, the magnetic depletion of WBCs brought high CTC efficiency and purity. Similarly, Nasiri et al. presented a hybrid device combing inertial focusing and magnetic deflection for CTC isolation 
. High isolation efficiency and purity can also be achieved. Several groups have combined dielectrophoresis (DEP) with magnetic separation for rare cell separation 
. Nucleated cells were separated by size using DEP and target cells were then isolated through magnetic deflection. Combing magnetic deflection with acoustic-based sorting for the isolation of rare cells from whole blood was also widely studied 
. Acoustics is a technology used for separating particles/cells based on the acoustic force which is proportional to the size of cells. As such, acoustics can also be used for the pre-sort of nucleated cells when integrated with magnetic deflection. Several other mechanisms incorporated with magnetic deflection were also reported to be highly efficient. For instance, Alipanah et al. developed a rare cell sorter using induced charged electroosmotic flow and magnetophoresis 
. Shamloo et al. presented a system combining centrifugal force with magnetic deflection for efficiency and high-purity isolation of rare cells 
. Javanmard et al. described a novel approach for the rapid assessment of surface markers on cancer cells using a combination of immunomagnetic separation and multi-frequency impedance cytometry. In this work, multi-frequency impedance cytometry was applied for target cell detection rather than separation