LABORATORY OF BIOLOGICAL STRUCTURE MECHANICS
www.labsmech.polimi.it
PROGETTAZIONE DEL MICROAMBIENTE
Gabriele Dubini, Elena Bianchi, Francesca Nason
XXXII Scuola GNB “Approccio integrato per la medicina rigenerativa”,
Bressanone, 16-19 settembre 2013
What microfluidic environment is induced on cells?
A quantitative understanding of the interplay among:
• pore geometry
• culture medium flow behaviour
• nutrient/waste mass transport
• cellular behaviour (proliferation/migration)
at the cell scale is required for rational design of scaffold materials and
bioreactor systems
Pietrabissa, CMBBE , Porto, 2008
G. Dubini - Progettazione del microambiente
A pioneering CFD analysis
89
100
shear stress [mPa]
150
pore dimension [µm]
50
59
scaffold porosity [%]
65
77
27.0
24.3
21.6
16.2
13.5
10.8
8.1
5.4
2.7
0.0
Boschetti et al. J Biomechanics, 2006
G. Dubini - Progettazione del microambiente
An example of state-of-the-art scaffold CFD analysis
Representative pressure distribution at inlet and outlet crosssections used to calculate (A) the pressure drop and (B) the velocity
distribution in the modelled region of interest for the HR-SP model.
The data are shown for the high-porosity scaffold for an inlet velocity
of 0.1 mm s−1.
Truscello et al., Acta Biomater., 2012
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Outline
The micro / nano scale environment
Cell size vs channel size
Parameters from ‘macroscopic’ transport phenomena
Local fluid dynamics and cell adhesion
Examples
Concluding remarks
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The micro / nano scale environment
G. Dubini - Progettazione del microambiente
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
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1 mm
1 mm3 = 1 µl
100 µm
106 µm3 = 1 nl
10 µm
103 µm3 = 1 pl
G. Dubini - Progettazione del microambiente
A counter-intuitive effect in microfluidics: the bottleneck effect
D, L
1 𝜕𝜕
𝐾𝑠 = −
𝑣 𝜕𝜕
d, l
𝑠
= 49 ×
10−11
𝑃𝑃−1
128𝜇𝜇
∆𝑃 =
𝑄
𝜋𝑑 4
32𝜇𝜇𝐷 2 𝐿𝐾𝑠
∆𝑡 =
𝑑4
𝜇 = 10−3 𝑃𝑃 ∙ 𝑠, 𝐿 = 10 𝑐𝑐, 𝐷 = 1 𝑐𝑐,
𝑙 = 1 𝑐𝑐, 𝑑 = 1 𝑚𝑚
G. Dubini - Progettazione del microambiente
∆𝑉
𝑄∆𝑡
∆𝑃~
=
𝑉𝐾𝑠 𝜋 𝐷 2 𝐿𝐾𝑠
4
∆𝑡~ 0 𝑠
A counter-intuitive effect in microfluidics: the bottleneck effect
D, L
1 𝜕𝜕
𝐾𝑠 = −
𝑣 𝜕𝜕
d, l
𝑠
= 49 ×
10−11
𝑃𝑃−1
128𝜇𝜇
∆𝑃 =
𝑄
𝜋𝑑 4
32𝜇𝜇𝐷 2 𝐿𝐾𝑠
∆𝑡 =
𝑑4
𝜇 = 10−3 𝑃𝑃 ∙ 𝑠, 𝐿 = 10 𝑐𝑐, 𝐷 = 1 𝑐𝑐,
𝑙 = 1 𝑐𝑐, 𝑑 = 10 𝜇𝑚
G. Dubini - Progettazione del microambiente
∆𝑉
𝑄∆𝑡
∆𝑃~
=
𝑉𝐾𝑠 𝜋 𝐷 2 𝐿𝐾𝑠
4
∆𝑡~𝑚𝑚𝑚𝑚𝑚𝑚𝑚
Capillary pressure
Pcap > Patm
Pcap < Patm
Hydrophilic microchannel 100 µm (water-air): Pcap = 0,015 bar
Nanochannel 100 nm (water-air): Pcap = 15 bar
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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
4𝐴𝑡
𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝐷ℎ =
𝑝
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Design considerations for microflows: 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
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An early integrated device with two liquid samples
and electrophoresis gel present
Blue, liquid sample (ready
for metering)
Green, hydrophobic
surfaces
Purple, polyacrylamide gel
Burns et al., Science, 1998
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Cell size vs channel size
Microfluidic devices for manipulating fluids:
a vast experience!
What about fluids with suspended cells?
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Ex. #1 - In vivo: Lymphocyte homing
Ex. #2 - In vitro: Inflammation – Leukocyte
adhesion cascade - THP1 adhesion to VCAM-1 at
0.5 dyn/cm²
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Cell responses on surface chemistry of tissue
engineering scaffolds:
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)
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Cell responses on architecture of tissue engineering
scaffolds:
1) pore size of tissue engineering scaffold
2) porosity of tissue engineering scaffold
3) connectivity and tortuosity of tissue engineering scaffold
4) cell responses to dynamic scaffolds
Schematic of the different pore types
found in tissue engineering scaffolds
(Wang et al., Tissue Engineering Part C
Methods, 2010).
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Determination of tortuosity through a porous
material using the arc-chord ratio (O'Connell et
al., BioMedical Engineering , 2010).
Fluid dynamic approaches to cell suspensions
•
•
•
•
•
Navier-Stokes eq. for the sole carrier fluid
Lagrangian approach (dilute suspensions)
Two-phase flow
Non-Newtonian flow
Fluid-structure interaction
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Parameters from ‘macroscopic’ transport phenomena
4𝐴𝑡
𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝐷ℎ =
𝑝
𝑚̇
𝑀𝑀𝑀𝑀 𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣 𝑈 =
𝜌𝐴𝑡
𝐷ℎ ∆𝑃
𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 𝑓𝑓𝑓𝑓𝑓𝑓 𝑓 =
2𝜌𝑈 2 𝐿
6𝑈𝜇
𝑊𝑊𝑊𝑊 𝑠𝑠𝑠𝑠𝑠 𝑠𝑠𝑠𝑠𝑠𝑠 𝜏𝑤 = 𝜇𝛾̇ =
𝑠
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𝑘𝐵 𝑇
𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 𝐷 =
6𝜋𝜋𝜋
𝑈𝐷ℎ
𝑃𝑃𝑃𝑃𝑃𝑃 𝑁𝑁𝑁𝑁𝑁𝑁 𝑃𝑃 =
𝐷
ℎ𝐷ℎ
𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 𝑁𝑁𝑁𝑁𝑁𝑁 𝑆𝑆 =
𝐷
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Diffusivity characteristic time vs
convective characteristic time
Convective mass flux vs
diffusive mass flux
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 µm wide channel, 100 µm/s mean velocity)
Smith et al., Electrophoresis, 2012
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Local fluid dynamics and cell adhesion
(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).
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PCTC: prostate circulating tumor cell
𝜌𝑝 𝐷𝑝 2𝑈
𝑆𝑆𝑆𝑆𝑆𝑆 𝑁𝑁𝑁𝑁𝑁𝑁 𝑆𝑆 =
18𝜇𝐷ℎ
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Particle time scale vs
flow time scale
Smith et al., Electrophoresis, 2012
Possible ways to bring cells in contact to a wall
• 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.
G. Dubini - Progettazione del microambiente
Smith et al., Electrophoresis, 2012
G. Dubini - Progettazione del microambiente
Presence of suspended cells
∆𝜌 𝑔𝐷ℎ 2
𝐵𝐵𝐵𝐵 𝑁𝑁𝑁𝑁𝑁𝑁 𝐵𝐵 =
𝜎
𝜇𝑈𝑑
𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝑁𝑁𝑁𝑁𝑁𝑁 𝐶𝐶 =
𝜎
𝜇𝑈𝑑 2 𝐷ℎ
𝑊𝑊𝑊𝑊𝑊 𝑁𝑁𝑁𝑁𝑁𝑁 𝑊𝑊 =
𝜎
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multiphase microflows
Gravity vs interfacial forces
Viscous vs interfacial forces
Inertial vs interfacial forces
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
G. Dubini - Progettazione del microambiente
Presence of suspended cells
non-Newtonian fluids
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.
A well known effect - since 1929 - is the Fåhraeus effect for
blood flowing in small tubes (I.D. < 0,3 mm).
𝑡𝑐
𝐷𝐷𝐷𝐷𝐷𝐷𝐷 𝑁𝑁𝑁𝑁𝑁𝑁 𝐷𝐷 =
𝑡𝑝
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Material stress relaxation time vs
characteristic time scale
A further issue: cell population dynamics
Galbusera et al., Biomed. Microdevices,2008
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http://people.physics.anu.edu.au/~mak110/
Example 1:
Shear-stress dependent leukocyte adhesion assays
Bianchi et al. Journal of Biomechanics, 2012
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Schematics of a flow chamber (a), its computing model (b), a half
computing model with active test region (c), micropatterned osteoblasts (d),
and a unit with a single cell of computational model (e). In the current
models, seven or fifteen units were placed in one row, and seven rows were
used for simplicity of calculation (Cui et al. Ann. Biomed. Eng., 2011)
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Example 2:
Single cell trapping
100 µm
10 µm
Kobel et al., Lab on a Chip, 2010
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Nason et al., COUPLED PROBLEMS 2013
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Example 2a:
Red blood cells in microvessels
Simulation of blood flow (Hct 30% and 95 ± 5 s-1shear rate; Dh = 19 µm
(left) and Dh = 24 µm (right). The domains are cut at the centerplane of
the vessels (Alizadehrad et al., Journal of Biomechanics, 2012).
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Concluding remarks
• the study of fluid dynamics of cell suspensions and the
design of the microfluidic environment are challenging tasks
• much information/expertise is available from other
disciplines
• the need for mechanical microenvironmental control in
materials/devices for regenerative medicine can be met with
an accurate design
• physico-chemical and biochemical aspects not discussed
here
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