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Microfluidic Technologies
for Single Cell Manipulation
Como, 23 May 2018
Gabriele Dubini
Department of Chemistry, Materials and Chemical Engineering
‘Giulio Natta’
Outline
Introduction
Elements of fluid dynamics
The micro / nano scale environment
Fabrication technologies
Commercial platforms for cell biology
Microfluidics is the science of designing, manufacturing, and formulating devices
and processes that deal with volumes of fluid on the order of nanoliters or
picoliters.
What is microfluidics?
• Sample and medium - and waste handling - savings: e.g. nL of enzyme,
not mL
• Faster - and cheaper - analyses: can heat, cool small volumes quickly
• Integration: combine lots of steps onto a single device (including
parallelization)
• Automated processes
• Novel physics: diffusion, surface tension, and surface effects dominate
- This can actually lead to faster reactions!
• New functionalities, often impossible at the macroscopic level
Why use microfluidics?
van Duinen, Trietsch, Joore, Vulto, Hankemeier. Microfluidic 3D cell culture: from tools to tissue models.
Current Opinion in Biotechnology, 2015; 35: 118-126.
Why use microfluidics?
Several reasons make microfluidic devices and systems
interesting also for cell manipulation:
• The increasing interest for living cells
• The integration of several standard analytical
operations
• The possibility to manipulate large numbers of cells
simultaneously
• The possibility of manipulate single objects with cellular
dimension by micromechanics device
http://yoon.eecs.umich.edu/microfluidics.html
Motivation for microfluidics in cell biology
Test tubes
Robotics
Microfluidics
Automation
Integration
Miniaturization
Automation
Integration
Miniaturization
Automation
Integration
Miniaturization
Motivation for microfluidics in cell biology
Timeline of the evolution of microfluidic technology
The lab-on-a-chip concept
An early-concept for an integrated device with two liquid samples
and electrophoresis gel present
Burns et al., Science, 1998
Blue, liquid sample (ready for
metering)
Green, hydrophobic surfaces
Purple, polyacrylamide gel
Zhang and Nagrath. Microfluidics and Cancer: Are we there yet? Biomed. Microdevices 2013
Outline
Introduction
Elements of fluid dynamics
The micro / nano scale environment
Fabrication technologies
Commercial platforms for cell biology
Laminar and turbulent flow: the Reynolds number
water
ink
µ
ρ
= cLw
Re
x
y
z
wx
τy+dy
τy
dxdydz
x
w
wdxdydz
Dt
Dw x
x
∂
∂
ρ=ρ=forces(inertial)convective
( ) dxdydz
y
w
dxdzdy
y
w
y
dxdzdy
y
dxdz xx
ydyy 2
2
forcesviscous
∂
∂
µ=





∂
∂
µ
∂
∂
=





∂
τ∂
=τ−τ= +
carat
x
L
w
x
w
∝
∂
∂
22
2
caratt
x
L
w
y
w
∝
∂
∂
conduitsindiameterhydraulic
4
lengthsticcharacteri ==== h
t
c D
P
A
L
wwx ∝
r
z
h
h
D
mDw
Re:section)-cross(circulartubeafor
πµ
=
µ
ρ
=
4














−=
2
max 1)(
R
r
wrw 7
1
max 1)( 





−=
R
r
wrw
In steady-state conditions:
Laminar and turbulent flow: the velocity profiles
flowslaminarinRe056.0 ⋅≈
hD
x
flowsntin turbule10≈
hD
x
r
x
The entry length
flowsicmicrofluidinRe056.0
Re0035.01
6.0
⋅+
⋅+
≈
hD
x
0=⋅∇ w
( ) gwww
w
ρ+∇µ+−∇=





∇⋅+
∂
∂
ρ 2
p
t
(mass conservation)
(momentum conservation)
Hypotheses: incompressible, homogeneous, Newtonian fluid
Incompressible, Newtonian fluids:
the Navier-Stokes equations
A particular case: 2-D Navier-Stokes equations for steady-state flow
𝜌
𝜕𝑤 𝑥
𝜕𝜕
+ 𝑤 𝑥
𝜕𝑤 𝑥
𝜕𝑥
+ 𝑤𝑧
𝜕𝑤 𝑥
𝜕𝑧
= −
𝜕𝜕
𝜕𝜕
+ 𝜇
𝜕2 𝑤 𝑥
𝜕𝑥2 +
𝜕2 𝑤 𝑥
𝜕𝑧2
𝜌
𝜕𝑤𝑧
𝜕𝜕
+ 𝑤 𝑥
𝜕𝑤𝑧
𝜕𝑥
+ 𝑤𝑧
𝜕𝑤𝑧
𝜕𝑧
= −
𝜕𝜕
𝜕𝜕
+ 𝜇
𝜕2
𝑤𝑧
𝜕𝑥2
+
𝜕2
𝑤𝑧
𝜕𝑧2
𝜕𝑤 𝑥
𝜕𝜕
+
𝜕𝑤𝑧
𝜕𝑧
= 0
𝜕𝜕
𝜕𝜕
= 𝜇
𝜕2
𝑤 𝑥
𝜕𝑧2
and, if the pressure gradient ∂P/∂x is constant and equal to ∆P/L:
𝑤 𝑥 𝑧 =
∆𝑃ℎ2
8𝜇𝜇
1 −
4𝑧2
ℎ2
= 𝑣 𝑚𝑚𝑚 1 −
4𝑧2
ℎ2
−
ℎ
2
≤ 𝑧 ≤ +
ℎ
2
for
x
y
z
L
w
h
h « L
h « w
𝑤 𝑥 =
1
𝐴 𝑡
� 𝑤 𝑥 𝑧 𝑑𝑑
+
ℎ
2
−
ℎ
2
=
2
3
∆𝑃ℎ2
8𝜇𝜇
Pressure (P) and shear stress (τ) are different:
• Pressure is the force per unit area acting in the normal direction to an (ideal)
surface within a fluid.
• Shear stress is the force per unit area acting in the tangential direction to an
(ideal) surface within a moving fluid.
Under steady-state conditions, force equilibrium in the longitudinal direction for
the yellow volume of fluid yields:
𝑃𝜋𝑟2
− 𝑃 − ∆𝑃 𝜋𝑟2
= 𝜏 2𝜋𝜋𝜋
∆𝑃
𝑙
=
2𝜏
𝑟
→ 𝜏 𝑟 =
∆𝑃
𝑙
∙
𝑟
2
Pressure and shear stress in a steadily moving fluid
Height of the channel (mm)
Pressure and shear stress in a steadily moving fluid
Outline
Introduction
Elements of fluid dynamics
The micro / nano scale environment
Fabrication technologies
Commercial platforms for cell biology
Definition Range of channel dimension
Conventional channels Dh > 3 mm
Minichannels 3 mm ≥ Dh > 200 µm
Microchannels 200 µm ≥ Dh > 10 µm
Transitional microchannels 10 µm ≥ Dh > 1 µm
Transitional nanochannels 1 µm ≥ Dh > 0,1 µm
Nanochannels Dh ≤ 0,1 µm = 100 nm
𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝐷ℎ =
4𝐴 𝑡
𝑝
Micro and nanochannels
Scale effects
Comparison between volume densities of culture conditions in
traditional, macroscale culture in 6-well plates and in microscale,
microchannel culture (750 µm wide, 5 mm long, and 250 µm tall).
Paguirigan and Beebe, BioEssays, 2008
Scale effects
1 mm 1 mm3 = 1 µl
10 µm 103 µm3 = 1 pl
100 µm 106 µm3 = 1 nl
Scale effects
∆𝑃 =
128𝜇𝜇
𝜋𝑑4
𝑄
∆𝑃~
∆𝑉
𝑉𝐾𝑠
=
𝑄∆𝑡
𝜋
4
𝐷2 𝐿𝐾𝑠
∆𝑡 =
32𝜇𝜇𝐷2 𝐿𝐾𝑠
𝑑4
D, L d, l
𝐾𝑠 = −
1
𝑣
𝜕𝜕
𝜕𝜕 𝑠
= 49 × 10−11 𝑃𝑃−1
𝜇 = 10−3 𝑃𝑃 ∙ 𝑠, 𝐿 = 10 𝑐𝑐, 𝐷 = 1 𝑐𝑐
, 𝑙 = 1 𝑐𝑐, 𝑑 = 1 𝑚𝑚 ∆𝑡~ 0 𝑠
A counter-intuitive effect in microfluidics: the bottleneck effect
Scale effects
∆𝑃 =
128𝜇𝜇
𝜋𝑑4
𝑄
∆𝑃~
∆𝑉
𝑉𝐾𝑠
=
𝑄∆𝑡
𝜋
4
𝐷2 𝐿𝐾𝑠
∆𝑡 =
32𝜇𝜇𝐷2 𝐿𝐾𝑠
𝑑4
D, L d, l
𝐾𝑠 = −
1
𝑣
𝜕𝜕
𝜕𝜕 𝑠
= 49 × 10−11 𝑃𝑃−1
𝜇 = 10−3 𝑃𝑃 ∙ 𝑠, 𝐿 = 10 𝑐𝑐, 𝐷 = 1 𝑐𝑐
, 𝑙 = 1 𝑐𝑐, 𝑑 = 10 𝜇𝑚 ∆𝑡~𝑚𝑚𝑚𝑚𝑚𝑚𝑚
A counter-intuitive effect in microfluidics: the bottleneck effect
Scale effects
Scale effects
Effects of micro domain
– laminar flow
– surface tension
– surface effect
– electrowetting
– diffusion
The behavior of fluids at the microscale
Active flow mixers
Laminar flow
Cortelezzi, Ferrari and Dubini. A scalable active micro-
mixer for biomedical applications. Microfluidics and
Nanofluidics 2017; 21(3): article no. 31.
Capillary pressure
Pcap > Patm Pcap < Patm
Hydrophilic microchannel 100 µm (water-air): Pcap = 0,015 bar
Nanochannel 100 nm (water-air): Pcap = 15 bar
http://web.mit.edu/nnf/education/wettability/gravity.html
Cell responses on surface chemistry of channel walls:
1) surface hydrophobicity
2) protein adsorption
3) surface charge
4) surface roughness
5) surface softness and stiffness
Pinning fluid–fluid interfaces by chemically
inhomogeneous surfaces in static (c) and
flowing systems (d). Altering the wetting
properties using chemically homogeneous,
micro- and nanostructured surfaces: (e, f ).
(Gűnther and Jensen, Lab on a Chip, 2006)
Surface effects
Driving force for fluid
motion and the
channel
characteristics can
be chosen
independently
A flow driven by either a pressure
gradient, an electric field, or a
surface tension gradient.
A surface modified chemically in stripes. A surface modified with topography.
Stone et al. Annu. Rev. Fluid Mech., 2004
Surface effects
Electrical modulation of the solid-liquid interfacial tension
No Potential
A droplet on a hydrophobic
surface originally has a
large contact angle.
Applied Potential
The droplet’s surface
energy increases, which
results in a reduced contact
angle. The droplet now
wets the surface.
Electrowetting
Analyte D (m2/s) Pe
Na+ (100 pm) 10-9 10
Glucose 6×10-10 17
Albumine (BSA, 10 nm) 10-11 103
Viron (100 nm) 10-12 104
Bacterial Cell (1 µm) 10-13 105
Erythrocyte (10 µm) 10-14 106
Polystyrene Bead (100 µm) 10-15 107
Diffusivities and representative Péclet numbers for dilute analytes
in water at 25 °C (100 mm wide channel, 100 mm/s mean velocity)
Smith et al., Electrophoresis, 2012
Diffusion
Continuous-flow : Permanently etched microchannels, micropumps and
microvalves
Digital microfluidic : Manipulation of liquids as discrete droplets
Biosensors:
Optical: SPR, Fluorescence, etc.
Electrochemical: Amperometric,
Potentiometric, Impedence-based, etc.
Mixing: Static,
Diffusion Limited
Multiplexing
Microfluidic platforms
𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝐷ℎ =
4𝐴 𝑡
𝑝
𝑊𝑊𝑊𝑊 𝑠ℎ𝑒𝑒𝑒 𝑠𝑠𝑠𝑠𝑠𝑠 𝜏 𝑤 = 𝜇𝛾̇ =
6𝑈𝜇
𝑠
𝑀𝑀𝑀𝑀 𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣 𝑈 =
𝑚̇
𝜌𝐴 𝑡
𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 𝑓𝑓𝑓𝑓𝑓𝑓 𝑓 =
𝐷ℎ∆𝑃
2𝜌𝑈2 𝐿
Parameters from ‘macroscopic’ transport phenomena - 1
𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 𝐷 =
𝑘 𝐵 𝑇
6𝜋𝜋𝜋
𝑃𝑃𝑃𝑃𝑃𝑃 𝑁𝑁𝑁𝑁𝑁𝑁 𝑃𝑃 =
𝑈𝐷ℎ
𝐷
𝑆ℎ𝑒𝑒𝑒𝑒𝑒𝑒 𝑁𝑁𝑁𝑁𝑁𝑁 𝑆ℎ =
ℎ𝐷ℎ
𝐷
Diffusivity characteristic time vs
convective characteristic time
Convective mass flux vs
diffusive mass flux
Parameters from ‘macroscopic’ transport phenomena - 2
(a)-(d) Contours of fluorescent light intensity (FLI), which indicate bacterial
concentration, plotted for RP437 E. coli at different time snapshots.
(e)-(h) Bacteria collect in the vortex pair as shown by FLI contours overlaid on the
flow streamlines (solid blue lines) (Yazdi and Ardekani, Biomicrofluidics, 2012).
Local fluid dynamics and cell adhesion
Smith et al., Electrophoresis, 2012
𝑆𝑆𝑆𝑆𝑆𝑆 𝑁𝑁𝑁𝑁𝑁𝑁 𝑆𝑆 =
𝜌 𝑝 𝐷 𝑝
2 𝑈
18𝜇𝐷ℎ
Particle time scale vs
flow time scale
PCTC: prostate circulating tumor cell
Local fluid dynamics and cell displacement
Smith et al., Electrophoresis, 2012
Local fluid dynamics and cell displacement
• rely on a diffusive process to cause cells to randomly move
transverse to streamlines,
• apply a body force (e.g., gravity or dielectrophoresis) to move the
cells transverse to streamlines,
• create geometries in the flow so that flow is accelerated,
streamlines are compressed and the cells are effectively brought in
proximity to the wall by motion along a streamline,
• make the wall permeable and allow the streamlines to cross the
interface.
Possible ways to bring cells in contact to a wall
𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝑁𝑁𝑁𝑁𝑁𝑁 𝐶𝐶 =
𝜇𝑈 𝑑
𝜎
𝐵𝐵𝐵𝐵 𝑁𝑁𝑁𝑁𝑁𝑁 𝐵𝐵 =
∆𝜌 𝑔𝐷ℎ
2
𝜎
𝑊𝑊𝑊𝑊𝑊 𝑁𝑁𝑁𝑁𝑁𝑁 𝑊𝑊 =
𝜇𝑈 𝑑
2
𝐷ℎ
𝜎
Gravity vs interfacial forces
Viscous vs interfacial forces
Inertial vs interfacial forces
Presence of suspended cells multiphase flows
Parameters from ‘macroscopic’ transport phenomena - 3
Inertial, viscous and gravitational body forces, relative to interfacial forces,
as a function of the channel size and characteristic velocity in microfluidic
multiphase systems
Gűnther and Jensen, Lab on a Chip, 2006
Parameters from ‘macroscopic’ transport phenomena - 4
Strain rates can be large in the microflows.
In the simplest case, τ ≈ U/h, which can yield 103 - 104 s−1.
Such values are sufficiently large to cause non-Newtonian
rheological effects, if suspended deformable objects are
present.
𝐷𝐷𝐷𝐷𝐷𝐷ℎ 𝑁𝑁𝑁𝑁𝑁𝑁 𝐷𝐷 =
𝑡 𝑐
𝑡 𝑝
Material stress relaxation time vs
characteristic time scale
Presence of suspended cells non-Newtonian fluids
A well known effect - since 1929 - is the Fåhraeus effect for
blood flowing in small tubes (I.D. < 0,3 mm).
Parameters from ‘macroscopic’ transport phenomena – 5
Bianchi et al. Journal of Biomechanics, 2012
Example 1:
Shear-stress dependent leukocyte adhesion assays
mediators
Ronen Alon , Immunity ,2007
Blood flow
Particles interactions
(platelets –
erithrocytes)
τω
Fdragτm
Normal and shear
stresses on the
cell membrane
Normal and shear
stresses on the
endothelial wall
Multiple steps cascades controlled by
integrated chemoattractant-dependent
signals and adhesive events
Endothelial ligands involved in that second step
of firm adhesion are intercellular adhesion
molecules (ICAMs) and vascular cell
adhesion molecules (VCAMs).
inflammation
Leukocyte Shear dependent adhesion and
transmigration across vessel wall in
inflammation
Example 1:
Shear-stress dependent leukocyte adhesion assays
Example 1:
Shear-stress dependent leukocyte adhesion assays
Kobel et al., Lab on a Chip, 2010
100 µm
10 µm
Example 2:
Single cell trapping
Nason et al., COUPLED PROBLEMS 2013
Example 2:
Single cell trapping
Example 3:
A microfluidic in vitro model for specificity of breast cancer
metastasis to bone
Bersini et al., Biomaterials, 2014
45-107
µm/s
120-500
µm/s
CFD
fibers cells
Particles Velocity
FLOW
Cell tracking
CFD and µ-PIV
Campos Marin et al., Ann Biomed Eng. 2017
Example 4:
Cell seeding within a 3D porous scaffold
4 mm total diameter
Each fiber is 400 ÷ 500 µm diameter
Outline
Introduction
Elements of fluid dynamics
The micro / nano scale environment
Fabrication technologies
Commercial platforms for cell biology
Material for the fabrication
of microfluidic channels
Silicon / Si compounds
 Classical MEMS approach
 Etching involved
Polymers / plastics
 New methods
 Easy fabrication
Fabrication by laser ablation
Micromachining of silicon and glass
Laser ablation
Powder blasting
70°
d
d
d
Hydrofluoric Isotropic Etching
Thermic
bonding
Thermic
bonding
Borofloat glass
Glass microchips
There are two types of photoresist:
• Positive: Exposure to UV light removes resist
• Negative: Exposure to UV light maintains resist
Mask
Positive Resist Negative Resist
Photolithography
Replica molding
Polymers
• Inexpensive
• Flexible
• Easily molded
• Surface properties easily modified
• Improved biocompatibility
Polymethyl methacrylate (PMMA)
• Often used as an alternative to glass
• Easily scratched
• Not malleable
• It can come in the form of a powder mixed
with liquid methyl methacrylate, which is an
irritant and possible carcinogen
Polydimethylsiloxane (PDMS)
• Silicon-based organic polymer
• Non toxic
• Non flammable
• Gas permeable
• Most organic solvents can diffuse and cause it to swell
SU8 mold
preparation
PDMS 5:1
pouring
Pre-curing
10min@80°C
Peeling
Blank wafer
PDMS 20:1
pouring
Pre-curing
8 min@80°C
Adhesion
Curing 1h@80°C
Peeling and
structure realising
Soft lithography
Outline
Introduction
Elements of fluid dynamics
The micro / nano scale environment
Fabrication technologies
Commercial platforms for cell biology
• Access for colture medium (nutrients, GFs, etc.)
• Access for drug adminstration
• Compatible with robotic system access
• Compatible with micropipetting access
• Suitable for incubator use
• Pressurized vs. open wells
Design requirements
https://www.10xgenomics.com/
https://www.dolomite-bio.com/
PDMS bonded on glass
many valves and tubings
280 wells - up to 600 cells/well
Provides nutrients through lateral
channels and sieves/valves
Up to 5 wells in series
Wells are not accessible with a
pipetting manual/robotic system
Unsuitable for incubator
192 single-cell processing units accessed
through four cell loading inlets
48 single-cell processing units
Fully automated, including:
• Cell selection and isolation
• Cell culture
• Imaging
• Exposure to drug
• Cell lysis and generation of
cDNA from mRNA
• PCR and cDNA harvesting
https://www.fluidigm.com/products/polaris#components
Fluidigm Polaris movie
https://www.fluidigm.com/products/polaris
http://cn-bio.com/
18 wells
https://insphero.com/
LABORATORY OF BIOLOGICAL
STRUCTURE MECHANICS
www.labsmech.polimi.it
gabriele.dubini@polimi.it
Thank you for your attention!

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CDAC 2018 Dubini microfluidic technologies for single cell manipulation

  • 1. Microfluidic Technologies for Single Cell Manipulation Como, 23 May 2018 Gabriele Dubini Department of Chemistry, Materials and Chemical Engineering ‘Giulio Natta’
  • 2. Outline Introduction Elements of fluid dynamics The micro / nano scale environment Fabrication technologies Commercial platforms for cell biology
  • 3. Microfluidics is the science of designing, manufacturing, and formulating devices and processes that deal with volumes of fluid on the order of nanoliters or picoliters. What is microfluidics?
  • 4. • Sample and medium - and waste handling - savings: e.g. nL of enzyme, not mL • Faster - and cheaper - analyses: can heat, cool small volumes quickly • Integration: combine lots of steps onto a single device (including parallelization) • Automated processes • Novel physics: diffusion, surface tension, and surface effects dominate - This can actually lead to faster reactions! • New functionalities, often impossible at the macroscopic level Why use microfluidics?
  • 5. van Duinen, Trietsch, Joore, Vulto, Hankemeier. Microfluidic 3D cell culture: from tools to tissue models. Current Opinion in Biotechnology, 2015; 35: 118-126. Why use microfluidics?
  • 6. Several reasons make microfluidic devices and systems interesting also for cell manipulation: • The increasing interest for living cells • The integration of several standard analytical operations • The possibility to manipulate large numbers of cells simultaneously • The possibility of manipulate single objects with cellular dimension by micromechanics device http://yoon.eecs.umich.edu/microfluidics.html Motivation for microfluidics in cell biology
  • 8. Timeline of the evolution of microfluidic technology
  • 10. An early-concept for an integrated device with two liquid samples and electrophoresis gel present Burns et al., Science, 1998 Blue, liquid sample (ready for metering) Green, hydrophobic surfaces Purple, polyacrylamide gel
  • 11. Zhang and Nagrath. Microfluidics and Cancer: Are we there yet? Biomed. Microdevices 2013
  • 12. Outline Introduction Elements of fluid dynamics The micro / nano scale environment Fabrication technologies Commercial platforms for cell biology
  • 13. Laminar and turbulent flow: the Reynolds number water ink µ ρ = cLw Re x y z wx τy+dy τy dxdydz x w wdxdydz Dt Dw x x ∂ ∂ ρ=ρ=forces(inertial)convective ( ) dxdydz y w dxdzdy y w y dxdzdy y dxdz xx ydyy 2 2 forcesviscous ∂ ∂ µ=      ∂ ∂ µ ∂ ∂ =      ∂ τ∂ =τ−τ= + carat x L w x w ∝ ∂ ∂ 22 2 caratt x L w y w ∝ ∂ ∂ conduitsindiameterhydraulic 4 lengthsticcharacteri ==== h t c D P A L wwx ∝
  • 14. r z h h D mDw Re:section)-cross(circulartubeafor πµ = µ ρ = 4               −= 2 max 1)( R r wrw 7 1 max 1)(       −= R r wrw In steady-state conditions: Laminar and turbulent flow: the velocity profiles
  • 15. flowslaminarinRe056.0 ⋅≈ hD x flowsntin turbule10≈ hD x r x The entry length flowsicmicrofluidinRe056.0 Re0035.01 6.0 ⋅+ ⋅+ ≈ hD x
  • 16. 0=⋅∇ w ( ) gwww w ρ+∇µ+−∇=      ∇⋅+ ∂ ∂ ρ 2 p t (mass conservation) (momentum conservation) Hypotheses: incompressible, homogeneous, Newtonian fluid Incompressible, Newtonian fluids: the Navier-Stokes equations
  • 17. A particular case: 2-D Navier-Stokes equations for steady-state flow 𝜌 𝜕𝑤 𝑥 𝜕𝜕 + 𝑤 𝑥 𝜕𝑤 𝑥 𝜕𝑥 + 𝑤𝑧 𝜕𝑤 𝑥 𝜕𝑧 = − 𝜕𝜕 𝜕𝜕 + 𝜇 𝜕2 𝑤 𝑥 𝜕𝑥2 + 𝜕2 𝑤 𝑥 𝜕𝑧2 𝜌 𝜕𝑤𝑧 𝜕𝜕 + 𝑤 𝑥 𝜕𝑤𝑧 𝜕𝑥 + 𝑤𝑧 𝜕𝑤𝑧 𝜕𝑧 = − 𝜕𝜕 𝜕𝜕 + 𝜇 𝜕2 𝑤𝑧 𝜕𝑥2 + 𝜕2 𝑤𝑧 𝜕𝑧2 𝜕𝑤 𝑥 𝜕𝜕 + 𝜕𝑤𝑧 𝜕𝑧 = 0 𝜕𝜕 𝜕𝜕 = 𝜇 𝜕2 𝑤 𝑥 𝜕𝑧2 and, if the pressure gradient ∂P/∂x is constant and equal to ∆P/L: 𝑤 𝑥 𝑧 = ∆𝑃ℎ2 8𝜇𝜇 1 − 4𝑧2 ℎ2 = 𝑣 𝑚𝑚𝑚 1 − 4𝑧2 ℎ2 − ℎ 2 ≤ 𝑧 ≤ + ℎ 2 for x y z L w h h « L h « w 𝑤 𝑥 = 1 𝐴 𝑡 � 𝑤 𝑥 𝑧 𝑑𝑑 + ℎ 2 − ℎ 2 = 2 3 ∆𝑃ℎ2 8𝜇𝜇
  • 18. Pressure (P) and shear stress (τ) are different: • Pressure is the force per unit area acting in the normal direction to an (ideal) surface within a fluid. • Shear stress is the force per unit area acting in the tangential direction to an (ideal) surface within a moving fluid. Under steady-state conditions, force equilibrium in the longitudinal direction for the yellow volume of fluid yields: 𝑃𝜋𝑟2 − 𝑃 − ∆𝑃 𝜋𝑟2 = 𝜏 2𝜋𝜋𝜋 ∆𝑃 𝑙 = 2𝜏 𝑟 → 𝜏 𝑟 = ∆𝑃 𝑙 ∙ 𝑟 2 Pressure and shear stress in a steadily moving fluid
  • 19. Height of the channel (mm) Pressure and shear stress in a steadily moving fluid
  • 20. Outline Introduction Elements of fluid dynamics The micro / nano scale environment Fabrication technologies Commercial platforms for cell biology
  • 21. Definition Range of channel dimension Conventional channels Dh > 3 mm Minichannels 3 mm ≥ Dh > 200 µm Microchannels 200 µm ≥ Dh > 10 µm Transitional microchannels 10 µm ≥ Dh > 1 µm Transitional nanochannels 1 µm ≥ Dh > 0,1 µm Nanochannels Dh ≤ 0,1 µm = 100 nm 𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝐷ℎ = 4𝐴 𝑡 𝑝 Micro and nanochannels
  • 23. Comparison between volume densities of culture conditions in traditional, macroscale culture in 6-well plates and in microscale, microchannel culture (750 µm wide, 5 mm long, and 250 µm tall). Paguirigan and Beebe, BioEssays, 2008 Scale effects
  • 24. 1 mm 1 mm3 = 1 µl 10 µm 103 µm3 = 1 pl 100 µm 106 µm3 = 1 nl Scale effects
  • 25. ∆𝑃 = 128𝜇𝜇 𝜋𝑑4 𝑄 ∆𝑃~ ∆𝑉 𝑉𝐾𝑠 = 𝑄∆𝑡 𝜋 4 𝐷2 𝐿𝐾𝑠 ∆𝑡 = 32𝜇𝜇𝐷2 𝐿𝐾𝑠 𝑑4 D, L d, l 𝐾𝑠 = − 1 𝑣 𝜕𝜕 𝜕𝜕 𝑠 = 49 × 10−11 𝑃𝑃−1 𝜇 = 10−3 𝑃𝑃 ∙ 𝑠, 𝐿 = 10 𝑐𝑐, 𝐷 = 1 𝑐𝑐 , 𝑙 = 1 𝑐𝑐, 𝑑 = 1 𝑚𝑚 ∆𝑡~ 0 𝑠 A counter-intuitive effect in microfluidics: the bottleneck effect Scale effects
  • 26. ∆𝑃 = 128𝜇𝜇 𝜋𝑑4 𝑄 ∆𝑃~ ∆𝑉 𝑉𝐾𝑠 = 𝑄∆𝑡 𝜋 4 𝐷2 𝐿𝐾𝑠 ∆𝑡 = 32𝜇𝜇𝐷2 𝐿𝐾𝑠 𝑑4 D, L d, l 𝐾𝑠 = − 1 𝑣 𝜕𝜕 𝜕𝜕 𝑠 = 49 × 10−11 𝑃𝑃−1 𝜇 = 10−3 𝑃𝑃 ∙ 𝑠, 𝐿 = 10 𝑐𝑐, 𝐷 = 1 𝑐𝑐 , 𝑙 = 1 𝑐𝑐, 𝑑 = 10 𝜇𝑚 ∆𝑡~𝑚𝑚𝑚𝑚𝑚𝑚𝑚 A counter-intuitive effect in microfluidics: the bottleneck effect Scale effects
  • 28. Effects of micro domain – laminar flow – surface tension – surface effect – electrowetting – diffusion The behavior of fluids at the microscale
  • 29. Active flow mixers Laminar flow Cortelezzi, Ferrari and Dubini. A scalable active micro- mixer for biomedical applications. Microfluidics and Nanofluidics 2017; 21(3): article no. 31.
  • 30. Capillary pressure Pcap > Patm Pcap < Patm Hydrophilic microchannel 100 µm (water-air): Pcap = 0,015 bar Nanochannel 100 nm (water-air): Pcap = 15 bar http://web.mit.edu/nnf/education/wettability/gravity.html
  • 31. Cell responses on surface chemistry of channel walls: 1) surface hydrophobicity 2) protein adsorption 3) surface charge 4) surface roughness 5) surface softness and stiffness Pinning fluid–fluid interfaces by chemically inhomogeneous surfaces in static (c) and flowing systems (d). Altering the wetting properties using chemically homogeneous, micro- and nanostructured surfaces: (e, f ). (Gűnther and Jensen, Lab on a Chip, 2006) Surface effects
  • 32. Driving force for fluid motion and the channel characteristics can be chosen independently A flow driven by either a pressure gradient, an electric field, or a surface tension gradient. A surface modified chemically in stripes. A surface modified with topography. Stone et al. Annu. Rev. Fluid Mech., 2004 Surface effects
  • 33. Electrical modulation of the solid-liquid interfacial tension No Potential A droplet on a hydrophobic surface originally has a large contact angle. Applied Potential The droplet’s surface energy increases, which results in a reduced contact angle. The droplet now wets the surface. Electrowetting
  • 34. Analyte D (m2/s) Pe Na+ (100 pm) 10-9 10 Glucose 6×10-10 17 Albumine (BSA, 10 nm) 10-11 103 Viron (100 nm) 10-12 104 Bacterial Cell (1 µm) 10-13 105 Erythrocyte (10 µm) 10-14 106 Polystyrene Bead (100 µm) 10-15 107 Diffusivities and representative Péclet numbers for dilute analytes in water at 25 °C (100 mm wide channel, 100 mm/s mean velocity) Smith et al., Electrophoresis, 2012 Diffusion
  • 35. Continuous-flow : Permanently etched microchannels, micropumps and microvalves Digital microfluidic : Manipulation of liquids as discrete droplets Biosensors: Optical: SPR, Fluorescence, etc. Electrochemical: Amperometric, Potentiometric, Impedence-based, etc. Mixing: Static, Diffusion Limited Multiplexing Microfluidic platforms
  • 36. 𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝐷ℎ = 4𝐴 𝑡 𝑝 𝑊𝑊𝑊𝑊 𝑠ℎ𝑒𝑒𝑒 𝑠𝑠𝑠𝑠𝑠𝑠 𝜏 𝑤 = 𝜇𝛾̇ = 6𝑈𝜇 𝑠 𝑀𝑀𝑀𝑀 𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣 𝑈 = 𝑚̇ 𝜌𝐴 𝑡 𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 𝑓𝑓𝑓𝑓𝑓𝑓 𝑓 = 𝐷ℎ∆𝑃 2𝜌𝑈2 𝐿 Parameters from ‘macroscopic’ transport phenomena - 1
  • 37. 𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 𝐷 = 𝑘 𝐵 𝑇 6𝜋𝜋𝜋 𝑃𝑃𝑃𝑃𝑃𝑃 𝑁𝑁𝑁𝑁𝑁𝑁 𝑃𝑃 = 𝑈𝐷ℎ 𝐷 𝑆ℎ𝑒𝑒𝑒𝑒𝑒𝑒 𝑁𝑁𝑁𝑁𝑁𝑁 𝑆ℎ = ℎ𝐷ℎ 𝐷 Diffusivity characteristic time vs convective characteristic time Convective mass flux vs diffusive mass flux Parameters from ‘macroscopic’ transport phenomena - 2
  • 38. (a)-(d) Contours of fluorescent light intensity (FLI), which indicate bacterial concentration, plotted for RP437 E. coli at different time snapshots. (e)-(h) Bacteria collect in the vortex pair as shown by FLI contours overlaid on the flow streamlines (solid blue lines) (Yazdi and Ardekani, Biomicrofluidics, 2012). Local fluid dynamics and cell adhesion
  • 39. Smith et al., Electrophoresis, 2012 𝑆𝑆𝑆𝑆𝑆𝑆 𝑁𝑁𝑁𝑁𝑁𝑁 𝑆𝑆 = 𝜌 𝑝 𝐷 𝑝 2 𝑈 18𝜇𝐷ℎ Particle time scale vs flow time scale PCTC: prostate circulating tumor cell Local fluid dynamics and cell displacement
  • 40. Smith et al., Electrophoresis, 2012 Local fluid dynamics and cell displacement
  • 41. • rely on a diffusive process to cause cells to randomly move transverse to streamlines, • apply a body force (e.g., gravity or dielectrophoresis) to move the cells transverse to streamlines, • create geometries in the flow so that flow is accelerated, streamlines are compressed and the cells are effectively brought in proximity to the wall by motion along a streamline, • make the wall permeable and allow the streamlines to cross the interface. Possible ways to bring cells in contact to a wall
  • 42. 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝑁𝑁𝑁𝑁𝑁𝑁 𝐶𝐶 = 𝜇𝑈 𝑑 𝜎 𝐵𝐵𝐵𝐵 𝑁𝑁𝑁𝑁𝑁𝑁 𝐵𝐵 = ∆𝜌 𝑔𝐷ℎ 2 𝜎 𝑊𝑊𝑊𝑊𝑊 𝑁𝑁𝑁𝑁𝑁𝑁 𝑊𝑊 = 𝜇𝑈 𝑑 2 𝐷ℎ 𝜎 Gravity vs interfacial forces Viscous vs interfacial forces Inertial vs interfacial forces Presence of suspended cells multiphase flows Parameters from ‘macroscopic’ transport phenomena - 3
  • 43. Inertial, viscous and gravitational body forces, relative to interfacial forces, as a function of the channel size and characteristic velocity in microfluidic multiphase systems Gűnther and Jensen, Lab on a Chip, 2006 Parameters from ‘macroscopic’ transport phenomena - 4
  • 44. Strain rates can be large in the microflows. In the simplest case, τ ≈ U/h, which can yield 103 - 104 s−1. Such values are sufficiently large to cause non-Newtonian rheological effects, if suspended deformable objects are present. 𝐷𝐷𝐷𝐷𝐷𝐷ℎ 𝑁𝑁𝑁𝑁𝑁𝑁 𝐷𝐷 = 𝑡 𝑐 𝑡 𝑝 Material stress relaxation time vs characteristic time scale Presence of suspended cells non-Newtonian fluids A well known effect - since 1929 - is the Fåhraeus effect for blood flowing in small tubes (I.D. < 0,3 mm). Parameters from ‘macroscopic’ transport phenomena – 5
  • 45. Bianchi et al. Journal of Biomechanics, 2012 Example 1: Shear-stress dependent leukocyte adhesion assays
  • 46. mediators Ronen Alon , Immunity ,2007 Blood flow Particles interactions (platelets – erithrocytes) τω Fdragτm Normal and shear stresses on the cell membrane Normal and shear stresses on the endothelial wall Multiple steps cascades controlled by integrated chemoattractant-dependent signals and adhesive events Endothelial ligands involved in that second step of firm adhesion are intercellular adhesion molecules (ICAMs) and vascular cell adhesion molecules (VCAMs). inflammation Leukocyte Shear dependent adhesion and transmigration across vessel wall in inflammation Example 1: Shear-stress dependent leukocyte adhesion assays
  • 47. Example 1: Shear-stress dependent leukocyte adhesion assays
  • 48. Kobel et al., Lab on a Chip, 2010 100 µm 10 µm Example 2: Single cell trapping
  • 49. Nason et al., COUPLED PROBLEMS 2013 Example 2: Single cell trapping
  • 50. Example 3: A microfluidic in vitro model for specificity of breast cancer metastasis to bone Bersini et al., Biomaterials, 2014
  • 51. 45-107 µm/s 120-500 µm/s CFD fibers cells Particles Velocity FLOW Cell tracking CFD and µ-PIV Campos Marin et al., Ann Biomed Eng. 2017 Example 4: Cell seeding within a 3D porous scaffold 4 mm total diameter Each fiber is 400 ÷ 500 µm diameter
  • 52. Outline Introduction Elements of fluid dynamics The micro / nano scale environment Fabrication technologies Commercial platforms for cell biology
  • 53. Material for the fabrication of microfluidic channels Silicon / Si compounds  Classical MEMS approach  Etching involved Polymers / plastics  New methods  Easy fabrication
  • 54. Fabrication by laser ablation Micromachining of silicon and glass
  • 56. Powder blasting 70° d d d Hydrofluoric Isotropic Etching Thermic bonding Thermic bonding Borofloat glass Glass microchips
  • 57. There are two types of photoresist: • Positive: Exposure to UV light removes resist • Negative: Exposure to UV light maintains resist Mask Positive Resist Negative Resist Photolithography
  • 59. Polymers • Inexpensive • Flexible • Easily molded • Surface properties easily modified • Improved biocompatibility
  • 60. Polymethyl methacrylate (PMMA) • Often used as an alternative to glass • Easily scratched • Not malleable • It can come in the form of a powder mixed with liquid methyl methacrylate, which is an irritant and possible carcinogen
  • 61. Polydimethylsiloxane (PDMS) • Silicon-based organic polymer • Non toxic • Non flammable • Gas permeable • Most organic solvents can diffuse and cause it to swell
  • 62. SU8 mold preparation PDMS 5:1 pouring Pre-curing 10min@80°C Peeling Blank wafer PDMS 20:1 pouring Pre-curing 8 min@80°C Adhesion Curing 1h@80°C Peeling and structure realising Soft lithography
  • 63. Outline Introduction Elements of fluid dynamics The micro / nano scale environment Fabrication technologies Commercial platforms for cell biology
  • 64. • Access for colture medium (nutrients, GFs, etc.) • Access for drug adminstration • Compatible with robotic system access • Compatible with micropipetting access • Suitable for incubator use • Pressurized vs. open wells Design requirements
  • 65.
  • 68. PDMS bonded on glass many valves and tubings 280 wells - up to 600 cells/well Provides nutrients through lateral channels and sieves/valves Up to 5 wells in series Wells are not accessible with a pipetting manual/robotic system Unsuitable for incubator
  • 69. 192 single-cell processing units accessed through four cell loading inlets
  • 70. 48 single-cell processing units Fully automated, including: • Cell selection and isolation • Cell culture • Imaging • Exposure to drug • Cell lysis and generation of cDNA from mRNA • PCR and cDNA harvesting https://www.fluidigm.com/products/polaris#components
  • 73.
  • 75. LABORATORY OF BIOLOGICAL STRUCTURE MECHANICS www.labsmech.polimi.it gabriele.dubini@polimi.it Thank you for your attention!