Open Access Article

This Open Access Article is licensed under a Creative Commons Attribution-Non Commercial 3.0 Unported Licence

A. M. Jötten^{ab},
S. Angermann^{a},
M. E. M. Stamp^{ab},
D. Breyer^{a},
F. G. Strobl^{a},
A. Wixforth^{abc} and
C. Westerhausen*^{abcd}
^{a}Chair for Experimental Physics I, University of Augsburg, Germany. E-mail: christoph.westerhausen@gmail.com
^{b}Nanosystems Initiative Munich, Schellingstraße 4, 80799 Munich, Germany
^{c}Center for NanoScience (CeNS), Ludwig-Maximilians-Universität, Munich 80799, Germany
^{d}Zentrum für Interdisziplinäre Gesundheitsforschung (ZIG), University of Augsburg, 86135 Augsburg, Germany

Received
5th September 2018
, Accepted 15th December 2018

First published on 2nd January 2019

Investigating cell adhesion behavior on biocompatible surfaces under dynamic flow conditions is not only of scientific interest but also a principal step towards development of new medical implant materials. Driven by the improvement of the measurement technique for microfluidic flow fields (scanning particle image velocimetry, sPIV), a semi-automatic correlation of the local shear velocity and the cell detachment probability became possible. The functionality of customized software entitled ‘PIVDAC’ (Particle Image Velocimetry De-Adhesion Correlation) is demonstrated on the basis of detachment measurements using standard sand-blasted titanium implant material. A thermodynamic rate model is applied to describe the process of cell adhesion and detachment. A comparison of the model and our experimental findings, especially in a mild regime, where the shear flow does not simply tear away all cells from the substrate, demonstrates, as predicted, an increase of detachment rate with increasing shear force. Finally, we apply the method to compare experimentally obtained detachment rates under identical flow conditions as a function of cell density and find excellent agreement with previously reported model simulations that consider pure geometrical effects. The demonstrated method opens a wide field of applications to study various cell lines on novel substrates or in time dependent flow fields.

Within the last years, miniaturized setups to study cell adhesion phenomena using Surface Acoustic Wave (SAW) induced flow have been established.^{14–16} Basically there exist two options to generate the flow. On the one hand, the cells, e.g. covered by a droplet of cell culture medium, and the SAW-generating transducer can be located on the same piezoelectric substrate. Due to the setup concept, the field of applications is very limited here. On the other hand, setups are employed, where cells being seeded on arbitrary substrates are exposed to the microfluidic flow jet induced by a SAW chip at the opposite site of a micro reactor. Such a closed chamber system enables to cover a wide range of shear velocities applied to an ensemble of cells without risking an unintended temperature increase or an unintended possible SAW-effect as reported earlier^{17} and in contrast to the first option. Employing this approach allows to quantify the influence of the acting shear forces on the detachment of single cells from a non-confluent cell layer. Within a single measurement studying one ensemble of cells the complete shear force range of interest is covered. Here, we used a setup as described earlier^{16} to investigate the adhesion behavior of SaOs-2 cells on medical implants under microfluidic shear flow. The analysis capability of the setup was tremendously enhanced by the implementation of custom software entitled ‘Particle Image Velocimetry De-Adhesion Correlation’ (PIVDAC) that correlates the detachment of the cells with the local shear velocity of the streaming fluid. To be more precise, the combination of scanning particle image velocimetry and fluorescence microscopy allows the correlation of local acting shear velocity and detachment for a cell population time dependently.

While meanwhile a considerable number of reports on cell detachment can be found, the role of the cell density finds sparsely particular attention.^{18} Therefore, we here focus additionally on this aspect in such in vitro experiments and compare experimental measurements with simulation results published earlier.^{19}

The flow velocities as function of lateral and vertical position and the resulting distribution of the shear velocities were analyzed employing scanning particle image velocimetry (sPIV) based on Thielicke's time-resolved particle image velocimetry (PIV) software. Here, latex beads (Polysciences, Inc., Polybead® polystyrene, size 3 μm) were added to the fluid in the chamber, which follow the streamlines and are recorded using the high speed camera FASTCAM 1024PCI, Photron. The sPIV software enables to calculate the velocity distribution within particle image pairs, leading to the velocity field as function of the position above the SAW-chip. From measurements of velocity in several layers, the shear rate distribution in the plane as close as possible to the sample surface (∼20 μm) was extracted. The values range between ∼300 s^{−1} and ∼8000 s^{−1} and are interpolated from the large PIV grid of 39 × 23 pixels (72.5 × 109 μm pixel size) to obtain consistent resolution of the shear map and the micrographs of the adhered cells (2.59 μm pixel size, 923 × 1035 pixel, 2.39 × 2.68 mm), (Fig. 1D).

The fluorescence micrographs of the cells on the samples are recorded with an Axiovert 200 M (Zeiss) inverted microscope, a 2.5× objective and a digital camera (Hamamatsu Orca 5G) with 1344 × 1024 pixels. That implies an observable area of 3.48 mm × 2.65 mm, from which the sPIV analysed section is chosen (2.39 × 2.68 mm).

Zone | Mean ± standard deviation of shear velocity (1/s) |
---|---|

1 | 6882 ± 367 |

2 | 5132 ± 552 |

3 | 3231 ± 570 |

4 | 1746 ± 505 |

The detachment rate R turned out to be constant after a very short time after the beginning of each measurement, as soon as loosely bound cells, that persisted the washing step, are removed. Therefore, A(t) for the whole sample, as well as for each bin of shear velocity can be described by an exponential function as shown in Fig. 2:

A(t) = A_{∞} + (1 − A_{∞})e^{−Rt}
| (1) |

Be aware, that A_{∞} is a proportion referred to the area covered initially A_{c,ini,} while A_{c,ini} itself refers to the total area A_{tot}.

Fig. 3 (A) Gibbs potential as a function of an appropriate reaction coordinate. The two local minima at x_{A} and x_{B} correspond to the adhered and detached state of a cell adhesion molecule. (B) FEM simulations show that the stress inside an attached homogenous elastic hemisphere can be very inhomogeneous [adapted from ref. 24]. |

In an equilibrium of adherent (A) and free (B) bonds, the reaction equation with the coefficients k_{on} for adhesion and k_{off} for detachment reads as follows.

(2) |

The number of bonds in state A changes with time as

(3) |

The detachment rate k_{off} depends on the reaction's activation energy E_{AA}, which is the potential difference between state A and the transition state between A and B, according to the Arrhenius equation. Rebinding k_{on} scales with the potential difference E_{AB} between state B and the transition state, accordingly.

(4) |

Applying a constant external force F, in our case the shear flow, the potential G is adjusted by a linear term to = G − Fx. The reaction's activation energy follows to be Ẽ_{A} = E_{A} − F_{T} (see Fig. 3A). Therefore the new rate constant _{off} results as

(5) |

The applied force F is the part acting on a single bond of the overall shear force acting on a cell. The bond here can be described as a spring with spring constant k expanded by the distance z.

(6) |

From here on we follow an earlier argumentation^{21} to correlate the detachment rate of the bonds of a cell to the detachment rate of the entire cell. Due to their calculations, there are three regimes for the ratio of the applied force F and the adhesive force. In all our experiments included in this study, we intentionally applied comparably mild shear forces in the order of magnitude of the cell adhesion forces, as we consider this the most interesting regime. However, to relate these experiments with other reported ones and to complete the model, we here briefly summarize the model for the whole force range. The regimes differ in influence on the cells' peeling velocity v as described in eqn (7)–(9). Forces slightly exceeding a threshold force F_{C}, which is the minimum force required to peel cells of by shear flow, are declared as low forces. Here, F_{0} is a characteristic force scale. The peeling velocity increases linearly in the low force regime scaling with a constant factor depending on the equilibrium detachment rate R_{e}. Under the impact of significantly larger forces, we distinguish between a low velocity (strong adhesion) and a high velocity limit. In the medium force regime, where the adhesion is strong enough to account for a low peeling velocity, the thermo-activated process is still in progress. This induces an exponential relation between shear force and peeling velocity. When the shear force reaches a value, where the potential barrier vanishes and Kramer's theory fails, the cells directly follow the flow (high forces), and the progression is linear again. Thus, peeling velocity and shear force can be related as follows.^{21}low force – low velocity

(7) |

(8) |

(9) |

The shear force F acting on an object depends linearly on the fluid's shear velocity , the viscosity η and its area β parallel to the flow.

F = ηβ | (10) |

Approximating the peeling velocity v as the diameter of the attached cell divided by the time constant of the detachment process results in a linear dependency of the peeling velocity and the cell detachment rate R. Thus, the eqn (7)–(9) also relate the detachment rate R and the shear velocity . We introduce a characteristic shear velocity _{c} for simplification.low shear velocity

R() = R_{0}( − _{c})
| (11) |

(12) |

(13) |

The temporal devolution of the number of adherent cells can thus be described by an exponential decay as also found experimentally (see Fig. 2).

A(t) = A_{∞} + (1 − A_{∞})e^{−R()t}
| (14) |

Eqn (14) is used to describe the flow-induced detachment experiments to determine the appropriate regime of shear forces (low, medium or high). The experiments in this study reflect the low shear force regime, as we find R() = R_{0}( − _{c}) as shown in Fig. 2C. In contrast to earlier reports we find a positive R( = 0). This most likely originates from the inverted layout of our setup with cells adhering at the facing down surface of the lid of the microreactor.

To understand whether an almost linear dependency is reasonable and due to a lack of published data on SaOs-2 cells on titanium implants, we here compare our results to those on various cell-substrate-combinations and classify the applied shear forces according to our model. In doing so, we start with the most unsimilar combination reported by Décavé et al.,^{25} who studied shear flow-induced detachment of D. discoideum cells from glass. The authors also predict and show an exponential behavior at high shear velocities. The shear stress in our experiments ranges from 0.2 Pa to 5.6 Pa, while the above mentioned study covers a range up to 20 Pa.

As a rough first order approach to compare the detachment of different cell types on different substrates, we compare the intrinsic detachment rate R_{0} under static conditions. While in the reported study cited above R_{0} = 1.2 × 10^{−2} min^{−1}, we determine it to be R_{0} = 1.5 × 10^{−4} min^{−1}, which is only 1% as high. From this fact, we deduce that our cells adhere much stronger to the surface. Additionally, we apply lower shear velocities. Thus, low detachment rates and a linear slope, as predicted for a low force regime in the studied shear velocity range, seem reasonable, while the shear stress applied in the report cited above^{21} ranges in the medium force regime.

In an earlier similar publication García et al.^{1} describe a spinning disk device to investigate osteoblast-like cell adhesion on fibronectin coated glass. They report a non-linear decrease in the fraction of adherent cells vs. shear stress in a range of shear stress similar and above ours up to 10 Pa. Again, the here studied SaOs-2 cells seem to exhibit stronger adhesion, as the adherent cells are reduced to ∼60% at ∼5 Pa in both our case and García's at shorter incubation (15 min) and shorter exposure to shear (10 min). Therefore, those experiments reach up to the regime of medium forces. The stronger adhesion presumably originates from the higher surface roughness of the titanium substrate used in our study.

For drawing further comparisons, we consider the work of Fritsche et al.^{26} who measured bone cell adhesion using a spinning disc device. Comparable to our setup the authors studied bone cells adhered on titanium, but on a mirror-like polished surface and at far higher shear stresses (≈50 Pa). These experimental conditions and the linear increase of detachment with the shear velocity suggest the categorization into the high force regime (high force, low adhesion).

A substrate of comparable surface roughness to ours (R_{q} = 3.8 μm) is found in the work of Deligianni et al.^{27} Therein, cell detachment of human bone marrow cells on hydroxylapatite substrates of different surface roughness from R_{q} = 0.7 μm to 4.7 μm were studied at very high shear rates up to 60 Pa using a rotating disc device. In the shear range of our experiments, no detachment occurs. The apparent much stronger adhesion in the study of Deligianni et al. is most likely a result of the significantly longer incubation (4 h), smaller cell size and the similarity of the artificial bone material substrate to actual human bones.

Concluding, we can classify the specific cell-substrate combination and shear field we applied in the low force regime due to the mild application of shear flow and the conducive roughness of the surface for cell adhesion. This specific combination of cell-type, substrate and applied shear force regime has to be taken into account for each study. Thus, to bring the cells in their cell-type-specific low force regime it is necessary to ensure hydrodynamic comparability which includes careful adjustment of cell adhesion relevant parameters. Or, from another point of view, such measurements allow to assess the strength of cell-substrate combinations by their sensitivity towards shear forces. Furthermore, low detachment rates can result from the fact that, starting from a certain adhesion strength depending on the substrate conformation, cells can adapt to the application of shear forces. The integrins binding to the extracellular matrix respond to shear stress with a greater binding affinity.^{28} Moreover, cells develop more filopodial extensions responsive to low shear flow compared to their static state and start to round up only at high shear stress.^{29} In the relatively long time interval of our measurements (135 min from seeding to the end of the measurement), this effect is probably not negligible and another possible repressing factor for the increase of detachment with shear velocity.

However, the presented method allows to determine the detachment rate R() for whole cell ensembles simultaneously with a variable shear field and bears the potential to represent a platform for a variety of exciting experimental studies, e.g. on time dependent shear force modulation. In the last section of the paper, we demonstrate its potential to study the role of cell density for shear flow induced detachment.

We here performed detachment experiments as described above but varying the cell density, while all other parameters are kept constant. Fig. 4A–C show micrographs of the selected cell densities and the time dependent surface coverage A(t) with the shear zones employing PIVDAC. These detachment kinetics show a significant decrease of the detachment rate with increasing cell density. To avoid removal of whole pieces of tissue and to exclude a significant effect of cell–cell-adhesion, we do not include measurements of confluent cell layers in the further analysis steps to compare with previous simulations. These simulations simply do not account for such effects. However, for confluent cell layers within the error bars we even do not see cell detachment at all in the applied regime of shear forces (data not shown).

Fitting the cell covered area A(t) with eqn (1), we obtain the detachment rate R as function of cell density and shear stress as shown in Fig. 5A. To understand the dependency of R(ρ) we use results of finite element simulations published earlier^{19} and combine it with the minimal thermodynamic model proposed above.

Fig. 5 (A) Detachment rate R as function of cell density ρ for the four shear velocity zones. The shown values are mean ± standard deviation of five independent preparations. (B) Illustration of the top view of an idealized cell array under flow: the cell in the middle (hollow symbol) experiences lower shear forces due to the presence of neighboring cells. (C) Influence factor Ψ (see eqn (15)) for the cell in the middle of the cell array in B as function of cell density [adapted from ref. 19]. |

To do so, we use eqn (5) and consider the applied force as a function of cell density F(ρ). Following our previous publication,^{19} with increasing ρ the influence of neighboring cells on a distinct cell increases, reducing the effective acting forces compared to an identical situation but without neighboring cells. This is a pure geometrical effect, reducing the flow velocities of ‘downstream’ cells and thus the acting tension within these cells. Due to the design of these simulations, they are only valid in the regime below confluence, as they do not take into account cell–cell-contacts. As we here use the main result of that study, we briefly summarize it in the following paragraph.

By employing numerical Finite Element Method (FEM) simulations of deformable objects under shear flow, we investigated the occurring stress within elastic adherent cells and the influence of neighboring cells on these quantities. The influence factor Ψ is defined as

(15) |

Here, we now assume that the influence factor is a proportional measure for the shear forces acting on the cell adhesion molecules

F(ρ) = F_{0}Ψ ≈ F_{0}(Ψ_{0} − mϱ)
| (16) |

Here, m is a constant depending on the fluid velocity and the cell shape, while m increases with increasing fluid velocity. Combining eqn (5) and (16) then results in

(17) |

Assuming as described above, further results in

R ∼ e^{−mϱ}.
| (18) |

Comparing Fig. 5A with the predicted relation of eqn (18) seems convincing. While for zone 1 (with the highest fluid velocities and shear forces) the prediction fits perfectly to the data, in zones of lower shear force some deviations appear which are most likely linked to ‘nominal’ cell density, i.e. the seeded cell density, and the actual cell density. For clarity we here stress that the specific value of m depends on the fluid velocity and the exact value of R depends on k_{off}, what in turn implicitly depends very strong on the cell substrate combination. However, considering the fact that in the simulations we assume perfectly shaped, evenly distributed, homogeneous elastic objects without any biochemical interaction, while the data in Fig. 5A show the result of living cells seeded at different concentrations, is astonishing.

Thus, our method provides a powerful dynamical platform for various applications like, e.g. cell detachment under dynamically modulated shear fields. As a first application, and additionally to the demonstration of the method, our main finding is the strong dependence of cell detachment on the cell density. In agreement with earlier theoretical predictions, these experimental data strongly suggest to always take the cell density into account to compare results of different cell adhesion and detachment studies under flow.

- A. J. García, P. Ducheyne and D. Boettiger, Biomaterials, 1997, 18, 1091–1098 CrossRef.
- W. M. Saltzman and T. R. Kyriakides, in Principles of Tissue Engineering 4th edn, 2014, pp. 385–406 Search PubMed.
- A. S. Goldstein, T. M. Juarez, C. D. Helmke, M. C. Gustin and A. G. Mikos, Biomaterials, 2001, 22, 1279–1288 CrossRef CAS PubMed.
- A. Khalili and M. Ahmad, Int. J. Mol. Sci., 2015, 16, 18149–18184 CrossRef CAS PubMed.
- L. Weiss, Exp. Cell Res., 1961, 8, 141–153 CrossRef.
- A. Fuhrmann and A. J. Engler, Biophys. J., 2015, 109, 57–65 CrossRef CAS PubMed.
- R. Maan, G. Rani, G. I. Menon and P. A. Pullarkat, Phys. Biol., 2018, 15, 046006 CrossRef PubMed.
- C. D. Reyes and A. J. García, J. Biomed. Mater. Res., Part A, 2003, 67A, 328–333 CrossRef CAS PubMed.
- S. Usami, H.-H. Chen, Y. Zhao, S. Chien and R. Skalak, Ann. Biomed. Eng., 1993, 21, 77–83 CrossRef CAS.
- C. Couzon, A. Duperray and C. Verdier, Eur. Biophys. J., 2009, 38, 1035–1047 CrossRef PubMed.
- L. S. L. Cheung, X. Zheng, A. Stopa, J. C. Baygents, R. Guzman, J. A. Schroeder, R. L. Heimark and Y. Zohar, Lab Chip, 2009, 9, 1721 RSC.
- H. Lu, L. Y. Koo, W. M. Wang, D. a. Lauffenburger, L. G. Griffith and K. F. Jensen, Anal. Chem., 2004, 76, 5257–5264 CrossRef CAS PubMed.
- Z. Tang, Y. Akiyama, K. Itoga, J. Kobayashi, M. Yamato and T. Okano, Biomaterials, 2012, 33, 7405–7411 CrossRef CAS PubMed.
- A. Hartmann, M. Stamp, R. Kmeth, S. Buchegger, B. Stritzker, B. Saldamli, R. Burgkart, M. F. Schneider and A. Wixforth, Lab Chip, 2014, 14, 542–546 RSC.
- A. Bussonnière, Y. Miron, M. Baudoin, O. Bou Matar, M. Grandbois, P. Charette and A. Renaudin, Lab Chip, 2014, 14, 3556 RSC.
- M. Stamp, A. Jötten, P. Kudella, D. Breyer, F. Strobl, T. Geislinger, A. Wixforth and C. Westerhausen, Diagnostics, 2016, 6, 38 CrossRef CAS PubMed.
- M. S. Brugger, M. E. M. Stamp, A. Wixforth and C. Westerhausen, Biomater. Sci., 2016, 4, 1092–1099 RSC.
- K. S. Furukawa, T. Ushida, T. Nagase, H. Nakamigawa, T. Noguchi, T. Tamaki, J. Tanaka and T. Tateishi, Mater. Sci. Eng., C, 2001, 17, 55–58 CrossRef.
- M. Djukelic, A. Wixforth and C. Westerhausen, Biomicrofluidics, 2017, 11, 024115 CrossRef PubMed.
- C. A. Schneider, W. S. Rasband and K. W. Eliceiri, Nat. Methods, 2012, 9, 671–675 CrossRef CAS.
- D. Garrivier, E. Décavé, Y. Bréchet, F. Bruckert and B. Fourcade, Eur. Phys. J. E, 2002, 8, 79–97 CrossRef CAS.
- U. S. Schwarz and S. A. Safran, Rev. Mod. Phys., 2013, 85, 1327–1381 CrossRef CAS.
- G. Bell, Science (80-), 1978, 200, 618–627 CrossRef CAS.
- M. Djukelic, Modellierung und Simulation der Wechselwirkung zwischen adhärenten Zellen und Fluid bei kleinen Reynoldszahlen, Master thesis, University of Augsburg, 2015.
- E. Décavé, D. Garrivier, Y. Bréchet, B. Fourcade and F. Bruckert, Biophys. J., 2002, 82, 2383–2395 CrossRef.
- A. Fritsche, F. Luethen, U. Lembke, B. Finke, C. Zietz, J. Rychly, W. Mittelmeier and R. Bader, Materwiss. Werksttech., 2010, 41, 83–88 CrossRef CAS.
- D. D. Deligianni, N. D. Katsala, P. G. Koutsoukos and Y. F. Missirlis, Biomaterials, 2000, 22, 87–96 CrossRef.
- J. Y.-J. Shyy, Circ. Res., 2002, 91, 769–775 CrossRef CAS.
- T. G. van Kooten, J. M. Schakenraad, H. C. Van der Mei and H. J. Busscher, J. Biomed. Mater. Res., 1992, 26, 725–738 CrossRef CAS PubMed.

This journal is © The Royal Society of Chemistry 2019 |