Effects of Shear and Extensional Stresses on Cells: Investigation in a Spiral Microchannel and Contraction–Expansion Arrays

Abstract

In recent decades, inertial microfluidic devices have been widely used for cell separation. However, these techniques inevitably exert mechanical stresses, causing cell damage and death during the separation process. This remains a significant challenge for their biological and clinical applications. Despite extensive research on cell separation, the effects of mechanical stresses on cells in microfluidic separation have remained insufficiently explored. This review focuses on the effects of mechanical stresses on cells, particularly in spiral microchannels and contraction–expansion arrays (Contraction and Expansion Arrays (CEAs)). We derived the approximated magnitude of shear stress in a spiral microchannel, extensional stress in CEAs and conventional methods, along with exposure time in a single map to illustrate cell damage and operational zones. Finally, this review serves as a practical guideline to help readers in evaluating stress damages, enabling the effective selection of appropriate techniques that optimize cell viability and separation efficiency for biological and clinical applications.

1. Introduction

Microfluidic technology has advanced in clinical and biological research with its portability, cost effectiveness, high throughput, and simplicity. It supports diverse applications such as capturing, culturing, mixing, detection, and separation, − making it a valuable tool for studying cell biology (e.g., RBCs, WBCs, cancer cells, and stem cells).

Microfluidic separation techniques widely used in various applications are classified as passive and active based on the source of manipulating forces. Passive techniques rely on the channel geometry and hydrodynamic forces. − In contrast, active techniques rely on external forces. − Active techniques may change biological properties due to external forces, while passive techniques rely on fluid flowoften low flow ratesand the channel geometry which can reduce device efficiency through clogging and cause cell loss during processing. In contrast, inertial microfluidics typically operating at higher flow rates without clogging have greater potential for cell separation compared to other techniques.

Inertial microfluidic techniques are categorized into four designs: straight channel, − spiral microchannels, − contraction–expansion arrays (Contraction and Expansion Arrays (CEAs)), − and serpentine microchannels. , Straight channels have limited sorting resolution due to multiple equilibrium positions and insufficient inertial effects. , To address this, secondary flow designs such as serpentine, spiral, and CEAs are used to enhance separation efficiency. The alternating curvature in serpentine channels generates complex and unsteady secondary Dean flows, leading to unpredictable particle trajectories and unclear inertial migration. − Until 2019, Zhang’s group investigated various focusing patternstwo-position, single-position, and defocused using low-aspect-ratio symmetric sinusoidal channels. This finding presents a predictive method using dimensionless parameters and an operational map to address the challenges of trajectory unpredictability in curved microchannels. However, if the flow rate is not optimal or changes slightly, it may shift the focusing pattern and then cause defocusing. Recently, several studies have been successful in cell focusing and separation by modifying serpentine designs and creating similar curved channels such as high-aspect-ratio asymmetric serpentine (HARAS), concave–convex obstacle, zigzag microchannel, and square wave microchannel. However, the available data on this technique remain insufficient for a detailed analysis of cell viability compared to the more extensively studied spiral microchannels and CEAs. Furthermore, serpentine microchannels involve a complicated design since multiple parameters simultaneously affect particle focusing and migration patterns. Therefore, spiral microchannels and CEAs have emerged as the primary topic of current research in inertial microfluidics and have been successfully applied in numerous and various biomedical and clinical applications.

In studies of fluids, hydrodynamic stressesshear − and extensional − present a big challenge due to their direct effects on cell viability, , morphology, , functions, phenotypes, , and intracellular delivery. , Our previous studies confirmed that strong hydrodynamic stresses in spiral microchannels and CEAs lead to cell damage and death. Key factors influencing cell damage include the type of stresses, magnitude, and exposure time. −

This article provides an overview of the effects of stresses on cells in conventional and inertial microfluidic methods with a focus on spiral microchannels and contraction–expansion arrays (CEAs). The first section discusses the effects of stresses on cells; the second compares stresses and other parameters in conventional and inertial microfluidic methods; and the final section compiles and evaluates key data on cell damage from literature specific to spiral microchannels and CEAs.

2. Effects of Stresses on Cells

Mechanical stresses cause two types of damages: macroscale damage and microscale damage. Macroscale damage involves high stresses leading to cell damage and death, while microscale damage involves low stresses causing the changes in the cell phenotype.

Cell death is the most extreme response to hydrodynamic stresses and occurs in three forms: apoptosis, necrosis, and autophagy. Apoptosis and necrosis lead to cell death, while autophagy serves as a defensive response. However, hydrodynamic stresses can directly cause necrosis by physically damaging cellular structures. −

Permanent deformation is another form of cell damage caused by high stress levels. When the stresses exceed the elastic limit of cells, they result in permanent deformation. , Even at below stress levels, it can impact cell morphology and cytoskeletal structure. ,

Loss of membrane integrity serves as an indirect indicator of cell damage and can be evaluated by examining factors such as nuclear membrane rupture, increased permeability, reduced cell–cell adhesion, and changes in membrane protein functions.

Lactate dehydrogenase (LDH) release is a common injury marker measured in suspending fluid, linked to cell damage, viability, stress magnitude, and exposure time. − For instance, stressed cells show higher LDH activity than unstressed cells and with increased shear stress or longer exposure time further increasing LDH release.

In addition to macroscale damage, microscale damage is another category caused by mechanical stresses involving changes in cell phenotypes and behaviors including cytoskeleton organization, , extracellular matrix (ECM) remodeling, ,, gene expression, and other cellular alterations. −

Intrinsic cell propertiestype, spreading, shape, and densityinfluence responses to mechanical stress. Excessive stress beyond cell-specific thresholds causes permanent deformation, while lower stress allows recovery. Spreading asymmetry aligns the cytoskeleton, stress alters shape and signaling, and high density enhances mechanical stability and stress distribution. These properties, along with stress levels and exposure time, are important to cellular stress responses.

Mechanical stresses impact physical and biological changes. Macroscale damage causes severe cell injury, , while microscale damage alters phenotypes or behaviors. Intrinsic cell properties also affect stress responses, potentially complicating their interpretation. Thus, this review focuses on key factors contributing to cell damage such as stress type, magnitude, and exposure time.

3. Studies of Stresses

In a 3-D Cartesian coordinate system, hydrodynamic stresses are described by a stress tensor with nine components: The stress tensor in a fluid can be expressed as follows.

The three normal stresses (σ _xx , σ _yy , and σ _zz ) act perpendicularly to the principal axes, representing forces causing stretching or compression per unit area. The six shear stresses (τ _xy , τ _xz , τ _yx , τ _yz , τ _zx , and τ _zy ) represent shear forces per unit area.

Mechanical stresses are classified as shear or extensional based on fluid flow dynamics. Shear stress acts parallel to the cell surface causing layers to slide (Figure A), while extensional stress acts perpendicularly, causing stretch or compress cells (Figure B).

$$\mathrm{H}\mathrm{y}\mathrm{d}\mathrm{r}\mathrm{o}\mathrm{d}\mathrm{y}\mathrm{n}\mathrm{a}\mathrm{m}\mathrm{i}\mathrm{c}\mathrm{s}\mathrm{t}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{e}\mathrm{s}=\left(\begin{array}{lll}{\sigma }_{xx}& {\tau }_{xy}& {\tau }_{xz}\\ {\tau }_{yx}& {\sigma }_{yy}& {\tau }_{yz}\\ {\tau }_{zx}& {\tau }_{zy}& {\sigma }_{zz}\end{array}\right)$$

1.

Schematic of cell deformation under (A) shear and (B) extensional stress.

3.1. Techniques Involving Shear Stress

Shear stress effects on cells have been studied using a viscometer, a rheometer, and an ektacytometer. Viscometers are commonly used, generating constant shear stress in a narrow gap (Figure A). A shear stress of 0–150 Pa increased abnormal RBCs, with hemolysis at 150 Pa and cell fragmentation above 250 Pa. Severe hemolysis occurred at 300–400 Pa, − reaching 90% at 450 Pa. Besides RBCs, WBCs showed functional changes at 15 Pa for 10 min, and T cells withstood up to 20 Pa for the same duration. Hybridoma cell viability dropped under 0.33 Pa, with >5 Pa and ∼50% loss at 78 Pa for 30 min or 19 Pa for 2 h. Insect cells lose viability at 1.5 Pa, with 50% loss after 3.5 h.

2.

Schematics of instruments for extensional stress studies: (A) concentric cylinder/ektacytometry with laser diffraction, (B) hyperbolic channel, (C) sharp entrance contraction channel, and (D) cross-slot channel.

Using a rheometer, hydrodynamic stresses of 1.09 and 3.05 Pa induce apoptosis in HEK and CHO cells, while a shear stress of 100–1000 Pa applied for 10–120 s using a plate-and-cone rheometer damages RSC96 and L8 cells.

An ektacytometer measures RBC deformation under shear stress, showing no changes below 16 Pa, mild impairments at 32 Pa, and significant deformation at 64 Pa. A shear stress of 56.4–112.8 Pa for 30 s significantly affected deformation, while extended exposure time at 56.4 Pa caused RBC damage.

Parallel Plate Flow Chambers (PPFCs) are used for cell adhesion studies. A shear stress of 0.4 and 0.8 Pa applied for 16 h increased caveolin-1 expression and eNOS phosphorylation, while a shear stress of 0.8 Pa for 15 h enhanced endothelial cell stiffness, elongation, and actin alignment.

A spinning disk device studies cell adhesion, migration, and mechanotransduction. A shear stress up to 6 Pa reduced adhesion by 60%, with near-complete detachment of ROS 17/2.8 cells at 9 Pa, while osteoblastic cells showed 50% detachment at ∼50 Pa.

Atomic Force Microscopy is a high-resolution technique for studying cell responses, operating within 10–10,000 pN. It measures cell stiffness and Young’s modulus. , For example, healthy cancer and fibroadenoma cell stiffness are 1.13 and 3.68 kPa. Stress relaxation on HeLa cells at 31–98 Pa significantly impacted behavior.

Acoustic Force Spectroscopy uses standing acoustic waves to study the biomechanical properties. A shear stress of 5.9–106.1 mPa or 320 mPa (24 h) had minimal impact on endothelial alignment and protein expression, while a shear stress of 0.6 Pa (48 h) enhances VE-cadherin localization and actin reorganization.

These findings emphasize the importance of measuring shear stress within specific ranges and highlight how responses vary across cell types, influenced by the stress magnitude and exposure time. It is noted that the compared results were obtained under varying exposure times and flow regimes. Table S1 summarizes the effects of shear stress on cells by different conventional methods.

3.2. Techniques Involving Extensional Stress

Shear stress was initially regarded as the primary cause of cell damage. However, recent evidence emphasizes the significant impact of extensional stress. Presented below are conventional and advanced methods for generating extensional stress.

The hyperbolic channel (Figure B) generates pure extensional flow at a constant rate. Studies on RBCs, , PBMCs, and platelets confirm extensional stress has a greater cellular impact than shear stress in this flow.

A contraction channel with a sharp (Figure C) or tapered entrance isolates various cell types, including RBCs, L929, HeLa S3, ATCC-TIB-18, HEK, CHO, RSC96, and L8 cells. While extensional stresses in these channels are nonuniform, they play a significant role in hemolysis, with threshold values reported at 1000 Pa, , 3000 Pa for short exposures, and 3000 Pa with <0.45 ms. Notably, in most cases, the extensional rate in a contraction channel is not constant.

Cross-slot channels (Figure D) generate pure extensional flow with precise stress control. Using this method, CHO cell viability decreased at ∼250 Pa, while HL60 cell viability reduced above 11.8 kPa. Leukemia cells exhibit bullet-shaped deformation in straight, long hyperbolic channels and elliptical deformation in cross-shaped, short hyperbolic channels.

Cell Traction Force Microscopy (CTFM) is a technique for measuring the forces generated by cells. One study showed human patellar tendon fibroblasts exerting traction forces of ∼250 Pa, causing a gel substrate displacements of ∼1.2 μm, , while 600 and 1200 Pa altered migration, cell shape, and E-cadherin expression.

Optical Tweezers use a focused laser to generate precise forces (0.1–100 pN), without causing damage of mechanical properties. They enable investigations into cell deformation, cell–cell interactions, and cellular responses.

Optical Stretcher (OS) uses dual lasers to trap and deform cells. Fibroblast deformation occurred at 7–18 Pa, while RBCs deform about 1–3 Pa, and then finally the cells ruptured. Furthermore, laser forces of 200–500 pN can deform in most cells.

Magnetic Tweezers (MT) apply forces of 50 fN to 20 pN for DNA stretching and 1–100 pN for studying mechanosensing proteins. They provide higher force output, precision, and deeper tissue penetration without heating or photodamage issues.

Table S2 summarizes conventional methods including hyperbolic, contraction, and cross-slot channels for measuring extensional stress causing macroscale damage, while CTFM, OS, and MT are excluded as they produce lower stresses causing only microscale damage. Notably, most methods cannot apply pure extensional stress as minor shear stress occurs during sample transport.

4. Studies of Exposure Time

Exposure time refers to the duration at which cells are exposed to stresses. The duration can range from milliseconds to days. High stresses with short exposure or low stresses with long exposure can cause cell damage or death. Therefore, the relationship between exposure time and stress is important for understanding cellular responses.

Shear stress for hemolysis was reported at 4000 Pa for 0.01 ms in turbulent jets, 450–700 Pa for 0.01 s in capillary, 150 Pa for 100 s, and 25 Pa for 1000 s in concentric cylinders. Hemolysis also occurred at ∼100 Pa after seconds and ∼400 Pa within milliseconds in capillary. On the other hand, extensional stress for hemolysis was observed at 1000 Pa for 0.06 ms, 1500 Pa for 0.45 ms, and 3000 Pa in the microsecond range. In viscometers, shear stress at 10–60 Pa for 10 min affected WBC function and viability, while 100 ms exposure preserved WBC count but impaired function. In hybridoma cells, higher shear rates or increased exposure caused cell death, with 870 s^–1 over 15 h, dropping it to 70% (85% in controls). Reducing shear stress by four times while increasing exposure time by four times caused 50% cell death. Endothelial cells exposed to 6 Pa for 1–48 h increased eNOS and TM mRNA expression (6–24 h) and reduced ET-1 mRNA by >90% at 48 h. Microbial cells reduced viability under 2770 Pa for several hundred milliseconds in capillaries.

Figure illustrates that conventional methods for shear stress including viscometers, rheometers, and spinning disk generate a wide range of stress magnitudes from 10^–1 to 10³ Pa with an exposure time of 10–10⁴ seconds. Among these, viscometers provide precise control over stress and exposure time. As a result, they are beneficial for long-term studies of biological samples. However, PPFCs operate within lower and narrower stress ranges with limited exposure time. Ektacytomers apply shear stress between 10 and 100 Pa for ∼10 s, making them suitable for measuring RBC deformation.

3.

Comparison of shear and extensional stresses vs exposure time using conventional and alternative measurement techniques highlights the inertial microfluidic operational zone (<100 Pa, <10 s).

Conventional methods for extensional stress such as capillary and contraction channels typically generate high stresses ranging from 10³ to 10⁴ Pa with an extremely short exposure time of 10^–5–10^–2 s. In contrast, methods such as OS and CTMS can achieve longer exposure times but typically operate at lower stress magnitudes. The narrow stress range in capillary and contraction channels along with the localized nature of extensional flow regions makes it challenging to accurately regulate exposure time under pure extensional stress and exceeding the operational ranges for inertial microfluidic applications.

Unlike conventional methods, inertial microfluidics generally function at stress levels below 100 Pa with an exposure time of less than 10 s. However, accurately quantifying these low stresses and short exposure times in microchannels remains challenging. Therefore, there is a pressing need to develop more precise measurement techniques for microfluidic systems.

5. Inertial Microfluidic Methods

5.1. Spiral Microchannel

In a spiral microchannel, particle separation is governed by the balance between the inertial lift force, which pushes particles toward channel walls, and the Dean drag force caused by vortices, which moves them toward the centerline of the channel (Figure A). Larger particles are dominated by inertial lift force, migrating to outer walls while smaller particles are influenced by the Dean drag force, shifting toward the inner walls.

4.

Schematics illustrating (A) particles experiencing inertial lift and Dean drag forces in a spiral microchannel. (B) Regions of high extensional and shear stress in a cross-section. Adapted from ref . Available under a CC-BY 4.0 license. Copyright 2019 Suwannaphan et al. (C) Cell damage caused by shear stress.

Stress distribution in spiral microchannels is influenced by inertial lift and Dean drag forces, causing significant shear stress damage along the walls (Figure B). A previous work confirmed shear stress as the primary cause of cell damage (Figure C), while other contribution forces such as Magnus, Saffman, and molecular interactions are negligible. Shear stress on cells in a spiral microchannel is estimated using eq .

$$\mathrm{S}\mathrm{h}\mathrm{e}\mathrm{a}\mathrm{r}\mathrm{s}\mathrm{t}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{s}:\tau =\mu (\partial \mathrm{v}/\partial y)$$ 1

where τ is the shear stress, ∂v/∂y is the velocity gradient (shear rate), v is the streamwise velocity, y is the distance from the channel wall, and μ is the dynamic viscosity. Assuming a PBS-diluted cell suspension, the viscosity is set at 0.00105 Pa·s. The velocity gradient is simplified as the average velocity divided by half of the channel height. The average velocity in a spiral microchannel is estimated using eq .

$$v_{\mathrm{a}\mathrm{v}\mathrm{e}}=Q/A$$ 2

where Q is the volumetric flow rate and A is the cross-sectional area of the microchannel. The total length of the spiral microchannel is calculated using eq .

$$L=(2\pi r_{\mathrm{a}\mathrm{v}\mathrm{e}})\mathrm{N}$$ 3

where r _ave is the average radius, calculated as (D/2 + d/2)/2 with D and d being the outer and inner diameters and N the number of turns. This approximation deviates from the exact value by less than 0.1%. Additionally, the exposure time is approximated using eq .

$$\mathrm{E}\mathrm{x}\mathrm{p}\mathrm{o}\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{e}\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{e}=L/v_{\mathrm{a}\mathrm{v}\mathrm{e}}$$ 4

These parameters are important for evaluating shear stress and exposure time. To prevent cells, shear stress can be reduced by decreasing flow rate, while exposure time can be minimized by increasing channel width or shortening channel length. However, excessively low flow rates may reduce the separation efficiency.

5.2. CEAs

CEAs utilize the balance between inertial lift and Dean drag forces for particle separation. In contraction regions, reduced cross-sections increase the flow velocity and inertial lift, pushing larger particles toward the walls. In expansion regions, increased cross-sections reduce lift forces, allowing larger particles to cross streamlines and trap in expansion zones. Dean vortices drive the particle center line, while inertial lift directs them to walls, enabling differential migration. This technique is applied in the separation of plasma, blood cell, cancer cell, and rare cell. −

Figure shows that maximum extensional stress occurs at the abrupt change in cross-section, while shear stress occurs at corners and along contraction regions. The smaller cross-section in the contraction region increases local flow velocity, generating periodic high–low extensional stress with short exposure time. In CEA, extensional stress can be approximated using eq .

$$\mathrm{E}\mathrm{x}\mathrm{t}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{a}\mathrm{l}\mathrm{s}\mathrm{t}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{s}:\sigma =\mu (\partial v/\partial x)$$ 5

5.

High extensional and shear stress regions at the corner of CEA. Adapted from ref . Available under a CC-BY 4.0 license. Copyright 2019 Suwannaphan et al.

The extensional stress (σ) is proportional to the elongational rate (∂v/∂x), with μ = 0.00105 Pa·s as the dynamic viscosity, v is the streamwise velocity, and x is the distance over which cells experience extensional stress. In CEA, the elongational rate is calculated using eq .

$$\partial v/\partial x=(v_{\max }-v_{\min })/(W_{\mathrm{c}})$$ 6

where v _max and v _min are the average flow velocities in the contraction and expansion regions and W _c is the width of the contraction region. Extensional flow is localized approximately one orifice diameter before the contraction. The total exposure time is approximated by multiplying the time spent in one array by the total number of expansion and contraction arrays in the CEA.

The exposure time in CEA is calculated using eq .

$$\mathrm{E}\mathrm{x}\mathrm{p}\mathrm{o}\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{e}\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{e}=N(W_{\mathrm{c}}/v_{\mathrm{a}\mathrm{v}\mathrm{e}})$$ 7

where N represents the number of CEA, W _c is the contraction width, and v _ave is the average velocity between the CEA region. Note that extensional flow occurs at the abrupt change in cross-section, approximately one orifice diameter or W _c. The average velocity between contraction and expansion regions is calculated by using eq .

$$v_{\mathrm{a}\mathrm{v}\mathrm{e}}=(v_{\max }+v_{\min })/2$$ 8

This formula estimates the extensional stress and exposure time at abrupt cross-sectional changes. It is noted that minimizing the difference between v _max and v _min by decreasing the expansion width and increasing the contraction width can lower extensional stress. Similarly, fewer CEA arrays can reduce exposure time, but improper microchannel sizing may reduce separation efficiency.

6. Biological Applications and Operating Conditions

6.1. Spiral Microchannel

Spiral microchannels are categorized as standard and nonstandard designs. Standard designs are typically designed as Archimedean spirals with rectangular cross-sections. The applications of standard spiral designs include separating cancer cells, − blood components, , single cells, stem cells, sperm cells, − embryos, and marine microbes. −

In addition to cell separation efficiency, the influence of spiral microchannel geometry on cell responses including cell viability, morphology, function, and behaviors has become an important consideration for biological and clinical applications. Typically, standard spiral designs operate under shear stress in the range of approximately 1–10 Pa while maintaining high cell viability of >90% for blood cells and cancer cells (Table S3). This suggests a balance between effective separation and minimal mechanical damage. On the other hand, nonstandard designs such as trapezoidal, − double spiral, − U-turn, , cascaded spiral, and other designs − alter velocity distributions and Dean vortex strength, enhancing separation efficiency while maintaining high cell viability of >90% (Table S4). For instance, double and cascaded spiral designs demonstrated enhanced cell separation while maintaining high cell viability. ,,

To enhance cell separation throughput, 3D and multiplexed spiral chips have been developed. A stacked multiplexed spiral chip enriched CTCs from whole blood with remaining cell viability. Based on this, a chip with three stacked spirals and two loops achieved ∼85% recovery and 99.99% WBC depletion. A membraneless microfiltration system using multiplexed inertial microfluidics achieved >99% recovery and >97% viability. , Recently, a 3D trapezoidal chip with stacked serpentines was developed for efficient CTC separation.

Tables S3 and S4 summarize data from standard and nonstandard designs with velocities and stress levels, for example, flow rates up to 1 mL/min, average velocities up to 0.26 m/s, and shear stress up to 1.32 Pa (eq ) for an exposure time of 4 s (eq ). Standard spiral microchannels achieved ∼90% separation efficiency for spherical samples, while nonspherical samples such as embryos, algae, and sperm cells showed lower efficiency due to their asymmetrical shapes, reducing focusing sharpness. Cell viability remained above 95% for blood cells and above 90% for cancer and stem cells, reflecting a greater robustness of blood cells.

6.2. Contraction–Expansion Array (CEA)

Symmetric contraction–expansion array (CEA) designs are extensively employed for cell separation including cancer cells, , WBCs, and CTCs from blood. − These symmetric designs consist of axisymmetric multiorifice chambers, − chambers with siphoning channels, ,, sharp corner structures, , and curved geometries. In contrast, asymmetric CEAs with a side chamber is designed for enhancing separation in specific flow directions, ,,,,− each design influencing focusing behavior and separation performance.

In addition to separation, CEA designs inherently subject cells to high extensional stress, particularly at the abrupt change in the cross-section, where flow accelerates rapidly. These high stresses can cause permanent deformation, loss of membrane integrity, or cell death. Several studies have reported decreased cell viability in CEAs with sharp corners or narrow orifices. − This design is similar to conventional contraction channels, where extensional stress is exerted at the contraction region. Recent designs including symmetric triangle and curved corners have been developed to improve flow patterns. These designs also help reduce extensional stress by providing smoother transitions at abrupt changes in cross-section. For instance, a tapered design reduces extensional stress by minimizing abrupt stress concentrations and facilitating smoother, more uniform flow transitions. ,

Tables S5 and S6 summarize the advancements in symmetric and asymmetric CEAs for biological applications. CEAs typically operate at flow rates lower than those of spiral microchannels. However, due to CEAs’ smaller contraction cross-sections (∼50 μm wide × ∼100 μm high), this may generate higher flow velocities, for example, velocity reaching up to ∼40 m/s and an extensional stress of ∼1,700 Pa (eq ) at ∼2.6 mL/min, with 0.07 ms (eq ). Consequently, CEAs may cause greater cell damage than spiral microchannels. However, cell damage depends on various parameters, including cell type, stress type, magnitude, and exposure time.

7. Discussion and Perspective

To investigate the relationship between velocity distributions and cell size in both methods, Figure compares the average velocities in a constant cross-section of a spiral microchannel and the contraction region of the CEA. The results show that most spiral microchannel applications operate at lower flow velocities (0.2–1.1 m/s), achieving high separation resolution while maintaining a high cell viability of above 90%. In contrast, most CEA applications require higher velocities (0.5–47 m/s) for cell separation due to the narrower contraction regions. In this region, cells experience strong extensional stress at abrupt change in cross-section and localized shear stress over short exposure time, which can increase cell damage depending on stress magnitude and exposure time.

6.

Scatter plots showing average fluid velocity and cell size in spiral and CEA channels. Note that some data lack documentation on cell viability percentages.

To understand the relationship between stress magnitude and cell viability, we plotted the calculated stress magnitudesshear stress and extensional stressand highlighted the operational zones of each technique (Figure ). As can be seen, spiral microchannels require a lower stress of ∼1–16 Pa with higher cell viability (∼90–98%). Under these stress levels, only minor cell changes possibly occur such as slight deformation, reduced respiration, cell functional alterations, cell detachment, LDH release, and phenotype changescytoskeleton, gene expression, and ECM remodeling. Thus, this technique is useful for rare cell or low-abundance cell separation and sensitive biological studies.

7.

Comparison of operational zones for spiral microchannels and CEAs based on stress magnitude and cell viability, with corresponding levels of cellular responses referenced from conventional methods.

In contrast, CEAs are utilized for separation between significantly different-sized samples under higher stress levels of ∼14–1700 Pa with a cell viability of ∼84–96%. According to the operational zone of CEAs, the stress magnitude range extends from moderate to severe levels of cell damage. This intense extensional stress can negatively impact cells including severe deformation, induce hemolysis, trigger differentiation, and reduce cell viability. Therefore, it is important to simultaneously analyze velocity distributions in relation to cell size (Figure ) and stress magnitude in relation to cell viability (Figure ), as these parameters are essential for selecting appropriate separation techniques for specific cell types that optimize efficient separation, minimize cell damage, and maintain cell viability.

To evaluate the effects of stress on cells, we also calculated shear stress and exposure time for spiral microchannels (eqs and ), and extensional stress and exposure time for CEAs (eqs and ), as summarized in Figure . The graph is divided into three zones: the microscale damage zone, the operational zone (where most microfluidics are operated), and the macroscale damage zone.

8.

Scatter plots of the approximated magnitude of shear stress for spiral microchannels and extensional stress for CEAs and conventional methods versus exposure time.

In the microscale damage zone, cells experience low stress levels and short exposure time, resulting in minimal damage. This area can affect cell phenotypes and behaviors, while cell viability remains above 90%. However, due to limited data availability, the scatter plots in this zone are not represented in the graph.

In the operational zone, spiral microchannels operate under a shear stress of ∼1–10 Pa with an exposure time of ∼0.1–10 s. Under this condition, cell viability remains ∼90%, which is suitable for applications requiring minimal cell damage. In contrast, CEAs operate under extensional stress ranging from ∼10 to 10³ Pa with a shorter exposure time of ∼10^–4–10^–2 s. These stress levels contribute to higher cell damage risks than in spiral microchannels. Although <10% of cell death is generally acceptable for most experiments, it may cause significant difficulties for the studies involving rare cells or low-abundance cells. Furthermore, the dashed trendline suggests a power law relationship between stress magnitude and exposure time. This trendline defines the operating conditions for common microfluidic applications using spiral microchannel and CEA techniques. Interestingly, the power law relationship indicates that if the magnitude of stress increases 10 times, the exposure time a cell can withstand is reduced by approximately 100 times.

Above the operational zone is the macroscale damage zone. In this zone, cells encounter severe stresses resulting in increased cell deathapoptosis and necrosis, permanent deformity, loss of membrane integrity, and release of LDH, as indicated by data on the effects of stress on cells. This zone is primarily occupied by conventional high-stress techniques, such as viscometers, rheometers, capillary, contraction, and CTFM. Interestingly, under extensional stress of approximately 10³ Pa for a few milliseconds, A549 cells exhibit a high viability of 96%, whereas MCF-7 viability decreased to ∼84%. This difference is probably due to variations in their mechanical robustness and ability to withstand stresses and exposure time.

It is important to note that the calculations of shear and extensional stress magnitude are lower than the actual stresses in microfluidic devices. One reason is that the velocity value used in the calculation represents the average velocity. For example, the maximum velocity at the centerline of a microchannel is generally twice the average velocity. Practically, cells often encounter a combination of extensional and shear stresses simultaneously, particularly when cells are delivered to sorting spot. As a result, the actual stress values are expected to be higher than those derived from the calculations. However, the observed trends in cell damage caused by shear stress, extensional stress, and exposure time remain consistent.

To achieve optimal future microfluidic designs, the systems must be engineered to minimize mechanical damage while maximizing separation efficiency. Several strategies are recommended. First, smoother transitions at abrupt cross-sectional changes should be implemented by creating tapered or curved geometries in CEAs to minimize extensional stress. Channel dimensions should also be optimized such as by increasing microchannel width or radius of curvature in the spiral microchannel. Increasing these values can reduce shear and extensional stresses along the walls. However, it is important to consider that increasing these dimensions may also reduce the Dean drag force. Similarly, reducing flow rates can directly lower the stress magnitudes. However, it must be carefully balanced to maintain a sufficient separation efficiency. Minimizing the exposure time by shortening channel lengths and reducing the number of chambers can further reduce cell damage. Furthermore, computational fluid dynamics simulations with experimental techniques should be incorporated to precisely assess stress levels and exposure time, particularly in critical areas such as abrupt changes in cross-sections and channel walls. To gain a deeper understanding of the effects of stresses on cell phenotypes, future research should focus on expanding the available data on the microscale damage zone. These findings will be valuable for rare cells or low-abundance cell separation. Using these strategies, future microfluidic systems can potentially improve cell separation efficiency while maintaining cell viability and expanding their applicability in biological and clinical research.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsbiomaterials.5c00555.

• Shear stress studies using conventional methods (PDF)

• Extensional stress studies using conventional methods (PDF)

• Biological applications using standard spiral microchannels (PDF)

• Biological applications using nonstandard spiral microchannels (PDF)

• Biological applications using contraction–expansion arrays with an symmetric pattern (PDF)

• Biological applications using contraction–expansion arrays with an asymmetric pattern (PDF)

The authors declare no competing financial interest.