A nonlinear two-degree-of-freedom mass–damper–spring model to predict the isolation of circulating tumor cells in microfluidic-elasto-filtration devices

  • Huahuang Luo
  • Cong Zhao
  • Kui Song
  • Dayu Liu
  • Wenjuan Ma
  • Xingsu Yu
  • Huifang Su
  • Zhenfeng Zhang
  • Yitshak Zohar
  • Yi-Kuen LeeEmail author
Research Paper


Circulating tumor cell (CTC) isolation has made positive impacts on metastatic detection and therapy analysis for cancer patients. Microfluidic-elasto-filtration (MEF) device based on the critical elasto-capillary number (Ca e * ) has been proposed to utilize the optimal multi-parameter conditions, including cell diameter (dc), the diameter of cylindrical filter pores (dp), nonlinear cell elasticity and hydrodynamic drag force, for selectively capturing CTCs and depleting white blood cells (WBCs). In this paper, we propose a novel two-degree-of-freedom nonlinear mass–damper–spring (m–c–k) model to predict the dynamic behaviors of CTCs and WBCs in a generic MEF device. This model enables the optimization of the device design to achieve extremely high CTC capture efficiency and WBC depletion efficiency. In particular, the function of nonlinear cell stiffness specific to different cell types and MEF’s pore diameters is first determined by finite element method with neo-Hookean hyperelastic model, based on which the mechanical behaviors of CTCs and WBCs in MEF devices are systematically studied. Herein, the predicted normalized deformations of a CTC and WBC as a function of Cae are used to determine the optimized Cae of 0.043, consistent with the experimental results from the fabricated MEF devices using MCF-7 cells (0.04 ± 0.006). In addition, the normalized cell diameter versus Cae phase diagram is proposed for the first time as a useful tool for design optimization of MEF devices and other microfiltration devices.


Circulating tumor cells Mass–damper–spring model Microfluidic-elasto-filtration Elasto-capillary number Capture efficiency WBC depletion 



The authors would like to acknowledge the support of a Grant from HKUST-BME Division, the Grants from NSFC (nos. 81372274, 8141101080 and 11702236), Guangzhou Science and Technology Innovation Commission (no. 201704030101), Guangdong Science and Technology Grant (no. 2017B050506001) and Hong Kong ITF Grant (no. GHP/076/17GD).

Supplementary material

10404_2019_2240_MOESM1_ESM.mp4 (5.9 mb)
Supplementary material 1 (MP4 6036 kb)
10404_2019_2240_MOESM2_ESM.docx (16.7 mb)
Supplementary material 2 (DOCX 17149 kb)


  1. Adams DL et al (2014) The systematic study of circulating tumor cell isolation using lithographic microfilters. RSC Adv 9:4334–4342. CrossRefGoogle Scholar
  2. Aghaamoo M, Zhang Z, Chen X, Xu J (2015) Deformability-based circulating tumor cell separation with conical-shaped microfilters: concept, optimization, and design criteria. Biomicrofluidics 9:034106. CrossRefGoogle Scholar
  3. Alix-Panabieres C, Pantel K (2013) Circulating tumor cells: liquid biopsy of cancer. Clin Chem 59:110–118. CrossRefGoogle Scholar
  4. Bain BJ (2006) Blood cells: a practical guide, 4th edn. Blackwell Publishing Asia Pty Ltd., AustraliaCrossRefGoogle Scholar
  5. Caille N, Thoumine O, Tardy Y, Meister J-J (2002) Contribution of the nucleus to the mechanical properties of endothelial cells. J Biomech 35:177–187. CrossRefGoogle Scholar
  6. Carpenter A et al (2006) Cell profiler: image analysis software for identifying and quantifying cell phenotypes. Genome Biol 7:R100CrossRefGoogle Scholar
  7. Chang H, Zhou P, Xie Z, Gong X, Yang Y, Yuan W (2013) Theoretical modeling for a six-DOF vortex inertial sensor and experimental verification. J Microelectromech Syst 22:1100–1108CrossRefGoogle Scholar
  8. Chen J (2014) Nanobiomechanics of living cells: a review. Interface Focus 4:20130055CrossRefGoogle Scholar
  9. Chen M, Boyle FJ (2014) Investigation of membrane mechanics using spring networks: application to red-blood-cell modelling. Mater Sci Eng C 43:506–516. CrossRefGoogle Scholar
  10. Chen C-L et al (2013) Single-cell analysis of circulating tumor cells identifies cumulative expression patterns of EMT-related genes in metastatic prostate cancer. Prostate 73:813–826. CrossRefGoogle Scholar
  11. Cong Z et al (2015) The capillary number effect on the capture efficiency of cancer cells on composite microfluidic filtration chips. In: Micro electro mechanical systems (MEMS), 2015 28th IEEE international conference on, 18–22 January 2015, pp 459–462.
  12. Cong Z et al (2016) Capillary number effect on the depletion of leucocytes of blood in microfiltration chips for the isolation of circulating tumor cells. In: Proceedings of the 11th annual IEEE international conference on nano/micro engineered and molecular systems (IEEE-NEMS 2016), Matsushima Bay and Sendai MEMS City, Japan, p 1Google Scholar
  13. Corbin EA, Kong F, Lim CT, King WP, Bashir R (2015) Biophysical properties of human breast cancer cells measured using silicon MEMS resonators and atomic force microscopy. Lab Chip 15:839–847. CrossRefGoogle Scholar
  14. Coumans FAW, van Dalum G, Beck M, Terstappen LWMM (2013) Filtration parameters influencing circulating tumor cell enrichment from whole blood. PLoS One 8:e61774. CrossRefGoogle Scholar
  15. Cross SE, Jin Y-S, Rao J, Gimzewski JK (2007) Nanomechanical analysis of cells from cancer patients. Nat Nano 2:780–783CrossRefGoogle Scholar
  16. Dao M, Lim CT, Suresh S (2003) Mechanics of the human red blood cell deformed by optical tweezers. J Mech Phys Solids 51:2259–2280. CrossRefGoogle Scholar
  17. Desitter I et al (2011) A new device for rapid isolation by size and characterization of rare circulating tumor cells. Anticancer Res 31:427–441Google Scholar
  18. Ding Y, Xu G-K, Wang G-F (2017) On the determination of elastic moduli of cells by AFM based indentation. Sci Rep 7:45575. CrossRefGoogle Scholar
  19. Estridge BH, Reynolds AP, Walters NJ (2000) Basic medical laboratory techniques. Delmar Cengage Learning, Albany, NYGoogle Scholar
  20. Grover WH, Bryan AK, Diez-Silva M, Suresh S, Higgins JM, Manalis SR (2011) Measuring single-cell density. PNAS 108:10992–10996. CrossRefGoogle Scholar
  21. Harouaka RA, Nisic M, Zheng S-Y (2013) Circulating tumor cell enrichment based on physical properties. JALA 18:455–468. CrossRefGoogle Scholar
  22. Harouaka RA et al (2014) Flexible micro spring array device for high-throughput enrichment of viable circulating tumor cells. Clin Chem 60:323–333. CrossRefGoogle Scholar
  23. Hochmuth RM, Ting-Beall HP, Beaty BB, Needham D, Tran-Son-Tay R (1993) Viscosity of passive human neutrophils undergoing small deformations. Biophys J 64:1596–1601CrossRefGoogle Scholar
  24. Hosokawa M, Hayata T, Fukuda Y, Arakaki A, Yoshino T, Tanaka T, Matsunaga T (2010) Size-selective microcavity array for rapid and efficient detection of circulating tumor cells. Anal Chem 82:6629–6635. CrossRefGoogle Scholar
  25. Kaiser J (2010) Cancer’s circulation problem. Science 327:1072–1074. CrossRefGoogle Scholar
  26. Kim J-D, Waleed M, Lee Y-G (2013) Stiffness measurement of a biomaterial by optical manipulation of microparticle. In: Proceedings of SPIE 8595: 85951G.
  27. Kuznetsova TG, Starodubtseva MN, Yegorenkov NI, Chizhik SA, Zhdanov RI (2007) Atomic force microscopy probing of cell elasticity. Micron 38:824–833. CrossRefGoogle Scholar
  28. Lee SS, Antaki JF, Kameneva MV, Dobbe JG, Hardeman MR, Ahn KH, Lee SJ (2007) Strain hardening of red blood cells by accumulated cyclic supraphysiological stress. Artif Organs 31:80–86. CrossRefGoogle Scholar
  29. Lee HJ et al (2013) Efficient isolation and accurate in situ analysis of circulating tumor cells using detachable beads and a high-pore-density filter. Angew Chem Int Ed 52:8337–8340. CrossRefGoogle Scholar
  30. Li QS, Lee GYH, Ong CN, Lim CT (2008) AFM indentation study of breast cancer cells. BBRC 374:609–613. CrossRefGoogle Scholar
  31. Lim C, Zhou E, Quek S (2006) Mechanical models for living cells—a review. J Biomech 39:195–216CrossRefGoogle Scholar
  32. Lim LS et al (2012) Microsieve lab-chip device for rapid enumeration and fluorescence in situ hybridization of circulating tumor cells. Lab Chip 12:4388–4396. CrossRefGoogle Scholar
  33. Luo Y et al (2014) A constriction channel based microfluidic system enabling continuous characterization of cellular instantaneous Young’s modulus. Sens Actuators B Chem 202:1183–1189CrossRefGoogle Scholar
  34. McFaul SM, Lin BK, Ma H (2012) Cell separation based on size and deformability using microfluidic funnel ratchets. Lab Chip 12:2369–2376. CrossRefGoogle Scholar
  35. Milovanovic L, Ma H (2012) Method for measurement of friction forces on single cells in microfluidic devices. Anal Methods 4:4303–4309. CrossRefGoogle Scholar
  36. Munson BR, Young DF, Okiishi TH, Huebsch WW (2006) Fundamentals of fluid mechanics, vol 69. Wiley, Hoboken, p 520Google Scholar
  37. Park K et al (2010) Measurement of adherent cell mass and growth. PNAS 107:20691–20696. CrossRefGoogle Scholar
  38. Peeters EAG, Oomens CWJ, Bouten CVC, Bader DL, Baaijens FPT (2005) Mechanical and failure properties of single attached cells under compression. J Biomech 38:1685–1693. CrossRefGoogle Scholar
  39. Rodriguez ML, McGarry PJ, Sniadecki NJ (2013) Review on cell mechanics: experimental and modeling approaches. Appl Mech Rev 65:060801CrossRefGoogle Scholar
  40. Sajeesh P, Raj A, Doble M, Sen AK (2016) Characterization and sorting of cells based on stiffness contrast in a microfluidic channel. RSC Adv 6:74704–74714. CrossRefGoogle Scholar
  41. Soloukhin VA, Brokken-Zijp JCM, van Asselen OLJ, de With G (2003) Physical aging of polycarbonate: elastic modulus, hardness, creep, endothermic peak, molecular weight distribution, and infrared data. Macromolecules 36:7585–7597. CrossRefGoogle Scholar
  42. Tang Y, Shi J, Li S, Wang L, Cayre YE, Chen Y (2014) Microfluidic device with integrated microfilter of conical-shaped holes for high efficiency and high purity capture of circulating tumor cells. Sci Rep 4:6052. CrossRefGoogle Scholar
  43. Vaidyanathan R, Soon RH, Zhang P, Jiang K, Lim CT (2019) Cancer diagnosis: from tumor to liquid biopsy and beyond. Lab Chip 19:11–34. CrossRefGoogle Scholar
  44. Vona G et al (2000) Isolation by size of epithelial tumor cells: a new method for the immunomorphological and molecular characterization of circulating tumor cells. Am J Pathol 156:57–63CrossRefGoogle Scholar
  45. White FM, Corfield I (2006) Viscous fluid flow, vol 3. McGraw-Hill, New YorkGoogle Scholar
  46. Wicha M, Hayes D (2011) Circulating tumor cells: not all detected cells are bad and not all bad cells are detected. J Clin Oncol 29:1508–1511CrossRefGoogle Scholar
  47. Xu G, Shao J-Y (2008) Human neutrophil surface protrusion under a point load: location independence and viscoelasticity. Am J Physiol Cell Physiol 295:C1434–C1444. CrossRefGoogle Scholar
  48. Ye S, Ng Y, Tan J, Leo H, Kim S (2014) Two-dimensional strain-hardening membrane model for large deformation behavior of multiple red blood cells in high shear conditions. Theor Biol Med Model 11:19CrossRefGoogle Scholar
  49. Zhang Z, Xu J, Hong B, Chen X (2014) The effects of 3D channel geometry on CTC passing pressure—towards deformability-based cancer cell separation. Lab Chip. CrossRefGoogle Scholar
  50. Zhang Z, Chen X, Xu J (2015) Entry effects of droplet in a micro confinement: implications for deformation-based circulating tumor cell microfiltration. Biomicrofluidics 9:024108. CrossRefGoogle Scholar
  51. Zheng S, Lin H, Liu JQ, Balic M, Datar R, Cote RJ, Tai YC (2007) Membrane microfilter device for selective capture, electrolysis and genomic analysis of human circulating tumor cells. J Chromatogr A 1162:154–161CrossRefGoogle Scholar
  52. Zhou EH, Lim CT, Quek ST (2005) Finite element simulation of the micropipette aspiration of a living cell undergoing large viscoelastic deformation. Mech Adv Mater Struct 12:501–512. CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mechanical and Aerospace EngineeringThe Hong Kong University of Science and Technology (HKUST)Hong KongChina
  2. 2.College of Civil Engineering and MechanicsXiangtan UniversityXiangtanChina
  3. 3.Guangzhou First People’s HospitalGuangzhouChina
  4. 4.Sun Yat-sen University Cancer CenterGuangzhouChina
  5. 5.Department of Aerospace and Mechanical EngineeringUniversity of ArizonaTucsonUSA

Personalised recommendations