Skip to main content
SpringerLink
Log in

Unraveling the Vascular Fate of Deformable Circulating Tumor Cells Via a Hierarchical Computational Model

  • Published:
Cellular and Molecular Bioengineering Aims and scope Submit manuscript

Abstract

Introduction

Distant spreading of primary lesions is modulated by the vascular dynamics of circulating tumor cells (CTCs) and their ability to establish metastatic niches. While the mechanisms regulating CTC homing in specific tissues are yet to be elucidated, it is well documented that CTCs possess different size, biological properties and deformability.

Methods

A computational model is presented to predict the vascular transport and adhesion of CTCs in whole blood. A Lattice–Boltzmann method, which is employed to solve the Navier-Stokes equation for the plasma flow, is coupled with an Immersed Boundary Method.

Results

The vascular dynamics of a CTC is assessed in large and small microcapillaries. The CTC shear modulus \({k}_{\text{ctc}}\) is varied returning CTCs that are stiffer, softer and equally deformable as compared to RBCs. In large microcapillaries, soft CTCs behave similarly to RBCs and move away from the vessel walls; whereas rigid CTCs are pushed laterally by the fast moving RBCs and interact with the vessel walls. Three adhesion behaviors are observed—firm adhesion, rolling and crawling over the vessel walls—depending on the CTC stiffness. On the contrary, in small microcapillaries, rigid CTCs are pushed downstream by a compact train of RBCs and cannot establish any firm interaction with the vessel walls; whereas soft CTCs are squeezed between the vessel wall and the RBC train and rapidly establish firm adhesion.

Conclusions

These findings document the relevance of cell deformability in CTC vascular adhesion and provide insights on the mechanisms regulating metastasis formation in different vascular districts.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9

Similar content being viewed by others

References

  1. Bagnall, J.S., Byun, S., Begum, S., Miyamoto, D.T., Hecht, V.C., Maheswaran, S., Stott, S.L., Toner, M., Hynes, R.O., Manalis, S.R.: Deformability of tumor cells vs. blood cells. Sci Rep 5, 18542 (2015)

    Google Scholar 

  2. Coclite, A., Mollica, H., Ranaldo, S., Pascazio, G., de Tullio, M.D., Decuzzi, P.: Predicting different adhesive regimens of circulating particles at blood capillary walls. Microfluidics and Nanofluidics 21(11), 168 (2017)

    Google Scholar 

  3. Cross, S.E., Jin, Y.S., Rao, J., Gimzewski, J.K.: Nanomechanical analysis of cells from cancer patients. Nat Nanotechnol 2, 780–3 (2007)

    Google Scholar 

  4. Falcucci, G., Ubertini, S., Chiappini, D., Succi, S.: Modern lattice boltzmann methods for multiphase microflows. IMA Journal of Applied Mathematics 76(5), 712–725 (2011)

    MathSciNet  Google Scholar 

  5. Fedosov, D., Caswell, B., Karniadakis, G.: A multiscale red blood cell model with accurate mechanics. Biophysical Journal 98(10), 2215–2225 (2010)

    Google Scholar 

  6. Fedosov, D., Caswell, B., Popel, A., Karniadakis, G.: Blood flow and cell-free layer in microvessels. Microcirculation 17(8), 615–628 (2010)

    Google Scholar 

  7. Fedosov, D., Gompper, G.: White blood cell margination in microcirculation. Soft Matter 10(8), 2961–70 (2014)

    Google Scholar 

  8. Fedosov, D., Peltmäki, M., Gompper, G.: Deformation and dynamics of red blood cells in flow through cylindrical microchannels. Soft Matter 10(24), 4258–67 (2014)

    Google Scholar 

  9. Gekle, S.: Strongly accelerated margination of active particles in blood flow. Biophysical Journal 110(2), 514 – 520 (2016)

    Google Scholar 

  10. Guz, N., Dokukin, M., Kalaparthi, V., Sokolov, I.: If cell mechanics can be described by elastic modulus: Study of different models and probes used in indentation experiments. Biophysical Journal 107, 564–575 (2014)

    Google Scholar 

  11. Hammer, D.A., Apte, S.: Simulation of cell rolling and adhesion on surfaces in shear flow: general results and analysis of selectin-mediated neutrophil adhesion. Biophys. J. 63(1), 35–57 (1992)

    Google Scholar 

  12. Joyce, J.A., Pollard, J.W.: Microenvironmental regulation of metastasis. Nat. Rev. Cancer 9(4), 239–252 (2009)

    Google Scholar 

  13. King, M., Hammer, D.A.: Multiparticle adhesive dynamics: Hydrodynamic recruitment of rolling leukocytes. Proc. Natl. Acad. Sci. U.S.A. 98(26), 14919 – 14924 (2001)

    Google Scholar 

  14. King, M., Phillips, K., Mitrugno, A., Lee, T., de Guillebon, A., McGuire, S.C., Carr, R., Baker-Groberg, S., Riggand, R., Kolatkar, A., Luttgen, M., Bethel, K., Kuhn, P., Decuzzi, P., McCarty, O.: A physical sciences network characterization of circulating tumor cell aggregate transport. Am. J. Physiol. Cell Physiol. 308(10), C792–C802 (2015)

    Google Scholar 

  15. Krastev, V.K., Falcucci, G.: Simulating engineering flows through complex porous media via the lattice Boltzmann method. Energies 11(4), 715 (2018)

    Google Scholar 

  16. Krüger, T.: Effect of tube diameter and capillary number on platelet margination and near-wall dynamics. Rheol. Acta. 55(6), 511–526 (2016)

    Google Scholar 

  17. Krüger T, Raabe, D.: Efficient and accurate simulations of deformable particles immersed in a fluid using a combined immersed boundary Lattice Boltzmann finite element method. Comput. Math. Appl. 61(12), 3485–3505 (2011)

    MathSciNet  MATH  Google Scholar 

  18. Lac, E., Barthes-Biesel, D., Pelekasis, N., Tsamopoulos, J.: Spherical capsuls in three- dimensional unbounded stokes flow: Effect of the membrane constitutive law and onset of buckling. Journal of Fluid Mechanics 516, 303–334 (2004)

    MathSciNet  MATH  Google Scholar 

  19. Lee, T.R., Choi, M., Kopacz, A., Yun, S.H., Liu, W., Decuzzi, P.: On the near-wall accumulation of injectable particles in the microcirculation: smaller is not better. Sci. Rep. 3, 2079 (2013)

    Google Scholar 

  20. Lekka, M., Laidler, P., Gil, D., Lekki, J., Stachura, Z., Hrynkiewicz, A.Z.: Elasticity of normal and cancerous human bladder cells studied by scanning force microscopy. Eur Biophys J 28, 312–6 (1999)

    Google Scholar 

  21. Li, J., Dao, M., Lim, C.T., Suresh, S.: Spectrin-level modeling of the cytoskeleton and optical tweezers stretching of the erythrocyte. Biophysical Journal 88(1), 3707–3719 (2005)

    Google Scholar 

  22. Li, Y., Stroberg, W., Lee, T.R., Kim, H., Man, H., Ho, D., Decuzzi, P., Liu, W.: Multiscale modeling and uncertainty quantification in nanoparticle-mediated drug/gene delivery. Computational Mechanics 53, 511–537 (2014)

    Google Scholar 

  23. Maeda, N., Suzuki, Y., Tanaka, J., Tateishi, N.: Erythrocyte flow and elasticity of microvessels evaluated by marginal cell-free layer and flow resistance. Am J Physiol. 516(6), H2454–H2461 (1996)

    Google Scholar 

  24. McWhirter, J., Noguchi, H., Gompper, G.: Nonlinear elastic and viscoelastic deformation of the human red blood cell with optical tweezers. Proceedings of the National Academy of Sciences of the United States of America 106(15), 6039–6043 (2009)

    Google Scholar 

  25. Mendez, S., Gibaud, E., Nicoud, F.: An unstructured solver for simulations of deformable particles in flows at arbitrary reynolds numbers. Journal of Computational Physics 256(1), 465–483 (2014)

    MathSciNet  MATH  Google Scholar 

  26. Mills, J., Qie, L., Dao, M., Lim, C., Suresh, S.: Nonlinear elastic and viscoelastic deformation of the human red blood cell with optical tweezers. Mech Chem Biosyst 1(3), 169–180 (2004)

    Google Scholar 

  27. Mody, N.A., Lomakin, O., Doggett, T.A., Diacovo, T.G., King, M.R.: Mechanics of transient platelet adhesion to von willebrand factor under flow. Biophys. J. 88(2), 1432–1443 (2005)

    Google Scholar 

  28. Mollica, H., Coclite, C., Miali, M., Pereira, R., Paleari, L., Manneschi, C., DeCensi, A., Decuzzi, P.: Deciphering the relative contribution of vascular inflammation and blood rheology in metastatic spreading. Biomicrofluidics 12(4), 042205 (2018)

    Google Scholar 

  29. Nguyen, D.X., Bos, P., Massagué, J.: Metastasis: from dissemination to organ-specific colonization. Nat. Rev. Cancer 9(4), 274–284 (2009)

    Google Scholar 

  30. Peer, D., Karp, J., Hong, S., Farokhzad, O., Margalit, R., Langer, R.: Nanocarriers as an emerging platform for cancer therapy. Nat Nanotechnol 2(12), 751–60 (2007)

    Google Scholar 

  31. Peskin, C.: The immersed boundary method. Acta Numerica 11(3-4), 479–511 (2002)

    MathSciNet  MATH  Google Scholar 

  32. Pozrikidis, C.: Numerical simulation of the flow-induced deformation of red blood cells. Annals of Biomedical Engineering 31(10), 1194–1205 (2003)

    Google Scholar 

  33. Qian, Y., Dhumieres, D., Lallemand, P.: Lattice bgk models for navier-stokes equation. Europhysics Letters 17(6), 479–484 (1992)

    MATH  Google Scholar 

  34. Rejniak, K.: Circulating tumor cells: when a solid tumor meets a fluid microenvironment. Front. Oncol. 2(111), 93–106 (2012)

    Google Scholar 

  35. Remmerbach, T.W., Wottawah, F., Dietrich, J., Lincoln, B., Wittekind, C., Guck, J.: Oral cancer diagnosis by mechanical phenotyping. Cancer ResEur Biophys J 69, 1728–32 (2009)

    Google Scholar 

  36. Riahi, R., Gogoi, P., Sepehri, S., Zhou, Y., Handique, K., Godsey, J., Wang, Y.: A novel microchannel-based device to capture and analyze circulating tumor cells (ctcs) of breast cancer. Int J Oncol 44, 1870–8 (2014)

    Google Scholar 

  37. Saadat, A., Iaccarino, G., Shaqfeh, E.: Immersed-finite-element method for deformable particle suspensions in viscous and viscoelastic media. Phys. Rev. E 98, 16 (2018)

    MathSciNet  Google Scholar 

  38. Schiller, U., Krüger, T., Henrich, O.: Mesoscopic modelling and simulation of soft matter. Soft Matter 14(1), 9–26 (2017)

    Google Scholar 

  39. Sigüenza, J., Mendez, S., Ambard, D., Dubois, F., Jourdan, F., Mozul, R., Nicoud, F.: Validation of an immersed thick boundary method for simulating fluid–structure interactions of deformable membranes. Journal of Computational Physics 322(1), 723–746 (2016)

    MathSciNet  MATH  Google Scholar 

  40. Skalak, R.: Strain energy function of red blood cell membranes. Biophys J 13(3), 245–264 (2009)

    Google Scholar 

  41. Sollier, E., Go, D.E., Che, J., Gossett, D.R., O’Byrne, S., Weaver, W.M., Kummer, N., Rettig, M., Goldman, J., Nickols, N., McCloskey, S., Kulkarni, R.P., Carlo, D.D.: Size-selective collection of circulating tumor cells using vortex technology. Lab Chip 14, 63–77 (2014)

    Google Scholar 

  42. Succi, S.: The lattice Boltzmann equation: for fluid dynamics and beyond. Oxford University Press (2001)

    MATH  Google Scholar 

  43. Succi, S.: Lattice boltzmann across scales: from turbulence to dna translocation. European Physical Journal B 64(3-4), 471–479 (2008)

    Google Scholar 

  44. Succi, S., Amati, G., Bernaschi, M., Falcucci, G., Lauricella, M., Montessori, A.: Towards exascale lattice boltzmann computing. Computers and Fluids 181, 107–115 (2019)

    MathSciNet  MATH  Google Scholar 

  45. Sui, Y., Chew, Y., Chen, HT., Low: Transient deformation of elastic capsules in shear flow: effect of membrane bending stiffness. Phys. Rev. E 75(6), 301 (2007)

    Google Scholar 

  46. Sun, C., Migliorini, C., Munn, L.: Red blood cells initiate leukocyte rolling in postcapillary expansions: a lattice boltzmann analysis. Biophys J 85(1), 208–22 (2003)

    Google Scholar 

  47. Takeishi, N., Imai, Y., Yamaguchi, T., Ishikawa, T.: Flow of a circulating tumor cell and red blood cells in microvessels. Phys. Rev. E 92, 3011 (2015)

    Google Scholar 

  48. Tan, S.J., Yobas, L., Lee, G.Y., Ong, C.N., Lim, C.T.: Microdevice for the isolation and enumeration of cancer cells from blood. Biomed. Microdev. 11, 883–892 (2009)

    Google Scholar 

  49. Wang, W., Mody, N.A., King, M.R.: Multiscale model of platelet translocation and collision. J. Comput. Phys. 244, 223–235 (2005)

    MathSciNet  MATH  Google Scholar 

  50. Wirtz, D., Konstantopoulos, K., Searson, P.C.: The physics of cancer: The role of physical interactions and mechanical forces in metastasis. Nat. Rev. Cancer 11(7), 512–522 (2011)

    Google Scholar 

  51. Xiao, L., Liu, Y., Chen, S., Fu, B.: Effects of flowing rbcs on adhesion of a circulating tumor cell in microvessels. Biomech. Model. Mechanobiol 16(2), 597–610 (2017)

    Google Scholar 

  52. Yan, W., Liu, Y., Fu, B.: Effects of curvature and cell-cell interaction on cell adhesion in microvessels. Biomech. Model. Mechanobiol 9(5), 629–40 (2010)

    Google Scholar 

  53. Ye, H., Shen, Z., Li, Y.: Cell stiffness governs its adhesion dynamics on substrate under shear flow. Journal of IEEE Transactions on Nanotechnology 17(3), 407–411 (2017)

    Google Scholar 

  54. Ye, H., Shen, Z., Li, Y.: Shear rate dependent margination of sphere-like, oblate-like and prolate-like micro-particles within blood flow. Soft Matter 14(36), 7401–7419 (2018)

    Google Scholar 

  55. Yin, X., Zhang, J.: Cell-free layer and wall shear stress variation in microvessels. Biorheology 49, 261–70 (2012)

    Google Scholar 

  56. Zhang, J., Johnson, P., Popel, A.: Effects of erythrocyte deformability and aggregation on the cell free layer and apparent viscosity of microscopic blood flows. Microvasc. Res. 77(3), 265–272 (2009)

    Google Scholar 

Download references

Acknowledgments

This project was partially supported by the European Research Council, under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ERC Grant Agreement No. 616695, by the Italian Association for Cancer Research (AIRC) under the Individual Investigator Grant No. 17664, and by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska–Curie Grant Agreement No. 754490.

Conflict of interest

Dr. Lenarda, Dr. Coclite and Dr. Decuzzi declare that they have no conflicts of interest.

Research Involving Human and Animal Rights

No animal studies or experiments with human samples were carried out by the authors for this article.

Author information

Authors and Affiliations

  1. Laboratory of Nanotechnology for Precision Medicine, Fondazione Istituto Italiano di Tecnologia, Via Morego 30, 16163, Genoa, Italy

    Pietro Lenarda, Alessandro Coclite & Paolo Decuzzi

Authors
  1. Pietro Lenarda
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alessandro Coclite
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Paolo Decuzzi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Paolo Decuzzi.

Additional information

Associate Editor Michael R. King oversaw the review of this article.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Electronic supplementary material

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lenarda, P., Coclite, A. & Decuzzi, P. Unraveling the Vascular Fate of Deformable Circulating Tumor Cells Via a Hierarchical Computational Model. Cel. Mol. Bioeng. 12, 543–558 (2019). https://doi.org/10.1007/s12195-019-00587-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12195-019-00587-y

Keywords

Search

Navigation