Skip to main content
SpringerLink
Log in

Biomechanical parameter estimation using untethered nonprehensile magnetic microrobot

  • Research
  • Published:
Journal of Micro and Bio Robotics Aims and scope Submit manuscript

Abstract

Cell biomechanical parameters, such as modulus of elasticity, are crucial biomarkers for indicating their physiological and pathological states. Traditionally, tethered techniques like atomic force microscopy (AFM), micropipette aspiration, and microinjection are used for the estimation of cell biomechanical parameters. These techniques being tethered are restricted by the direction of approach and require skilled manual interventions. This paper presents an untethered approach based on magnetic microrobot for estimating biomechanical parameters. We use spherical ferromagnetic particles as microrobots which when actuated by a global magnetic field produced by electromagnetic coils placed in quadrupole configuration, deform the target zebrafish embryos. The deformation is estimated using an image-based approach while the actuating magnetic force is determined using multiphysics simulations. We then employ a two-parameter Mooney-Rivlin model to estimate the biomechanical parameters. The developed approach is untethered and hence can be used for performing measurements from various directions, unlike the traditional tethered approaches. Furthermore, our approach can be used for studying large cells and their agglomerates without causing photodamage and oxidative stress that are associated with the conventional untethered approaches using optical and acoustic tweezers, respectively.

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

Fig. 1
Algorithm 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

Availability of data and materials

Available on reasonable request.

References

  1. Shen Y, Nakajima M, Yang Z, Tajima H, Najdovski Z, Homma M, Fukuda T (2013) Single cell stiffness measurement at various humidity conditions by nanomanipulation of a nano-needle. Nanotechnology 24(14):145703

    Article  Google Scholar 

  2. Pu H, Liu N, Yu J, Yang Y, Sun Y, Peng Y, Xie S, Luo J, Dong L, Chen H et al (2019) Micropipette aspiration of single cells for both mechanical and electrical characterization. IEEE Trans Biomed Eng 66(11):3185–3191

    Article  Google Scholar 

  3. Suresh S (2007) Biomechanics and biophysics of cancer cells. Acta Biomater 3(4):413–438

    Article  Google Scholar 

  4. Rianna C, Radmacher M (2016) Cell mechanics as a marker for diseases: Biomedical applications of AFM. AIP Conf Proc 1760(1):020057. https://pubs.aip.org/aip/acp/article-pdf/doi/10.1063/1.4960276/12828775/020057_1_online.pdf

  5. Maciaszek JL, Lykotrafitis G (2011) Sickle cell trait human erythrocytes are significantly stiffer than normal. J Biomech 44(4):657–661

    Article  Google Scholar 

  6. Zemła J, Bobrowska J, Kubiak A, Zieliński T, Pabijan J, Pogoda K, Bobrowski P, Lekka M (2020) Indenting soft samples (hydrogels and cells) with cantilevers possessing various shapes of probing tip. Eur Biophys J 49(6):485–495

    Article  Google Scholar 

  7. Tan Y, Sun D, Huang W, Cheng SH (2008) Mechanical modeling of biological cells in microinjection. IEEE Trans Nanobioscience 7(4):257–266

    Article  Google Scholar 

  8. Khangai N, Kojima M, Horade M, Kamiyama K, Sakai S, Mae Y, Arai T (2014) Cell stiffness measurement using two-fingered micro-hand equipped with plate-shaped end effector. In: 2014 11th international conference on ubiquitous robots and ambient intelligence (URAI), pp. 517–521. IEEE

  9. Yousafzai MS, Ndoye F, Coceano G, Niemela J, Bonin S, Scoles G, Cojoc D (2016) Substrate-dependent cell elasticity measured by optical tweezers indentation. Opt Lasers Eng 76:27–33

    Article  Google Scholar 

  10. Aermes C, Hayn A, Fischer T, Mierke CT (2020) Environmentally controlled magnetic nano-tweezer for living cells and extracellular matrices. Sci Rep 10(1):1–16

    Article  Google Scholar 

  11. Lim HG, Liu H-C, Yoon CW, Jung H, Kim MG, Yoon C, Kim HH, Shung KK (2020) Investigation of cell mechanics using single-beam acoustic tweezers as a versatile tool for the diagnosis and treatment of highly invasive breast cancer cell lines: an in vitro study. Microsyst Nanoeng 6(1):1–12

    Article  Google Scholar 

  12. Luo Y, Chen D, Zhao Y, Wei C, Zhao X, Yue W, Long R, Wang J, Chen J (2014) A constriction channel based microfluidic system enabling continuous characterization of cellular instantaneous young’s modulus. Sens. Actuators B Chem 202:1183–1189

    Article  Google Scholar 

  13. Adam G, Hakim M, Solorio L, Cappelleri DJ (2020) Stiffness characterization and micromanipulation for biomedical applications using the vision-based force-sensing magnetic mobile microrobot. In: 2020 international conference on manipulation, automation and robotics at small scales (MARSS), pp. 1–6. IEEE

  14. Zhang H, Liu K-K (2008) Optical tweezers for single cells. J R Soc Interface 5(24):671–690

    Article  Google Scholar 

  15. Wang X, Ho C, Tsatskis Y, Law J, Zhang Z, Zhu M, Dai C, Wang F, Tan M, Hopyan S et al (2019) Intracellular manipulation and measurement with multipole magnetic tweezers. Sci Robot 4(28):6180

    Article  Google Scholar 

  16. Li M, Dang D, Liu L, Xi N, Wang Y (2017) Atomic force microscopy in characterizing cell mechanics for biomedical applications: A review. IEEE Trans Nanobioscience 16(6):523–540

    Article  Google Scholar 

  17. Wang X, Law J, Luo M, Gong Z, Yu J, Tang W, Zhang Z, Mei X, Huang Z, You L et al (2020) Magnetic measurement and stimulation of cellular and intracellular structures. ACS Nano 14(4):3805–3821

    Article  Google Scholar 

  18. Zeng D, Juzkiw T, Read AT, Chan DW-H, Glucksberg MR, Ethier CR, Johnson M (2010) Young’s modulus of elasticity of schlemm’s canal endothelial cells. Biomech Model Mechanobiol 9(1):19–33

    Article  Google Scholar 

  19. Bausch AR, Möller W, Sackmann E (1999) Measurement of local viscoelasticity and forces in living cells by magnetic tweezers. Biophys J 76(1):573–579

    Article  Google Scholar 

  20. Kawahara T, Sugita M, Hagiwara M, Arai F, Kawano H, Shihira-Ishikawa I, Miyawaki A (2013) On-chip microrobot for investigating the response of aquatic microorganisms to mechanical stimulation. Lab Chip 13(6):1070–1078

    Article  Google Scholar 

  21. Hochmuth RM (2000) Micropipette aspiration of living cells. J Biomech 33(1):15–22. https://doi.org/10.1016/S0021-9290(99)00175-X

    Article  MathSciNet  Google Scholar 

  22. Pors S, Nikiforov D, Cadenas J, Ghezelayagh Z, Wakimoto Y, Jara L, Cheng J, Dueholm M, Macklon K, Flachs E et al (2022) Oocyte diameter predicts the maturation rate of human immature oocytes collected ex vivo. J Assist Reprod Genet 39(10):2209–2214

    Article  Google Scholar 

  23. Chen J, Niu N, Zhang J, Qi L, Shen W, Donkena KV, Feng Z, Liu J (2019) Polyploid giant cancer cells (pgccs): the evil roots of cancer. Curr Cancer Drug Targets 19(5):360–367

    Article  Google Scholar 

  24. Tang X, Liu X, Li P, Liu D, Kojima M, Huang Q, Arai T (2021) Efficient single-cell mechanical measurement by integrating a cell arraying microfluidic device with magnetic tweezer. IEEE Robot Autom Lett 6(2):2978–2984

    Article  Google Scholar 

  25. Nakajima M, Ahmad MR, Kojima S, Homma M, Fukuda T (2009) Local stiffness measurements of c. elegans by buckling nanoprobes inside an environmental sem. In: 2009 IEEE/RSJ international conference on intelligent robots and systems, pp. 4695–4700. IEEE

  26. Wang X, Zhang X (2019) Biomechanical study on elastic and viscoelastic properties of osteoblasts using atomic force microscopy. In: 2019 IEEE international conference on mechatronics and automation (ICMA), pp. 1377–1381. https://doi.org/10.1109/ICMA.2019.8816579

  27. Nam JH, Chen PC, Lu Z, Luo H, Ge R, Lin W (2010) Mechanoinduction of reduction in the stiffness of zebrafish chorion. In: 2010 11th international conference on control automation robotics & Vision, pp. 1024–1028. IEEE

  28. Kim D-H, Hwang CN, Sun Y, Lee SH, Kim B, Nelson BJ (2006) Mechanical analysis of chorion softening in prehatching stages of zebrafish embryos. IEEE Trans Nanobioscience 5(2):89–94

    Article  Google Scholar 

  29. Liu F, Wu D, Chen K (2014) A zebrafish embryo behaves both as a “cortical shell- liquid core” structure and a homogeneous solid when experiencing mechanical forces. Microsc Microanal 20(6):1841–1847

  30. Schoetz E-M (2007) Dynamics and mechanics of zebrafish embryonic tissues. PhD thesis, Dresden, Techn. Univ., Diss., 2007

  31. Agarwal D, Thakur AD, Thakur A (2022) Magnetic microbot-based micromanipulation of surrogate biological objects in fluidic channels. J Microbio Robot 1–15

  32. Lee H, Lee D, Jeon S (2022) A two-dimensional manipulation method for a magnetic microrobot with a large region of interest using a triad of electromagnetic coils. Micromachines 13(3). https://doi.org/10.3390/mi13030416

  33. Agarwal D, Thakur AD, Thakur A (2019) A robotic tool for magnetic micromanipulation of cells in the presence of an ambient fluid flow. In: International design engineering technical conferences and computers and information in engineering conference, vol. 59223, pp. 004–08017. American Society of Mechanical Engineers

  34. Agarwal D, Thakur AD, Thakur A (2022) A feedback-based manoeuvre planner for nonprehensile magnetic micromanipulation of large microscopic biological objects. Robot Auton Syst 148:103941

    Article  Google Scholar 

  35. Amokrane W, Belharet K, Souissi M, Grayeli AB, Ferreira A (2018) Macro-micromanipulation platform for inner ear drug delivery. Robot Auton Syst 107:10–19

    Article  Google Scholar 

  36. Yesin KB, Vollmers K, Nelson BJ (2006) Modeling and control of untethered biomicrorobots in a fluidic environment using electromagnetic fields. Int J Rob Res 25(5–6):527–536

    Article  Google Scholar 

  37. Yasukuni R, Minamino D, Iino T, Araki T, Takao K, Yamada S, Bessho Y, Matsui T, Hosokawa Y (2021) Pulsed laser activated impulse response encoder (plaire): sensitive evaluation of surface cellular stiffness on zebrafish embryos. Biomed Opt Express 12(3):1366–1374

    Article  Google Scholar 

  38. Tomizawa Y, Dixit K, Daggett D, Hoshino K (2019) Biocompatible cantilevers for mechanical characterization of zebrafish embryos using image analysis. Sensors 19(7):1506

    Article  Google Scholar 

  39. Wu P-H, Aroush DR-B, Asnacios A, Chen W-C, Dokukin ME, Doss BL, Durand-Smet P, Ekpenyong A, Guck J, Guz NV et al (2018) A comparison of methods to assess cell mechanical properties. Nat Methods 15:491–498

    Article  Google Scholar 

  40. Kontomaris SV, Stylianou A, Georgakopoulos A, Malamou A (2023) Is it mathematically correct to fit afm data (obtained on biological materials) to equations arising from hertzian mechanics? Micron 164:103384. https://doi.org/10.1016/j.micron.2022.103384

    Article  Google Scholar 

  41. Rawson D, Zhang T, Kalicharan D, Jongebloed W (2000) Field emission scanning electron microscopy studies of the chorion, plasma membrane and syncytial layers of the gastrula-stage embryo of the zebrafish brachydanio rerio. Aquac Res 31:325–336. https://doi.org/10.1046/j.1365-2109.2000.00401.x

    Article  Google Scholar 

  42. Kummer MP, Abbott JJ, Kratochvil BE, Borer R, Sengul A, Nelson BJ (2010) Octomag: An electromagnetic system for 5-dof wireless micromanipulation. IEEE Trans Robot 26(6):1006–1017. https://doi.org/10.1109/TRO.2010.2073030

    Article  Google Scholar 

  43. Zhou H, Mayorga-Martinez CC, Pané S, Zhang L, Pumera M (2021) Magnetically driven micro and nanorobots. Chem Rev 121(8):4999–5041

  44. Beicker K, O’Brien E, Falvo M, Superfine R (2018) Vertical light sheet enhanced side-view imaging for afm cell mechanics studies. Sci Rep 8. https://doi.org/10.1038/s41598-018-19791-3

  45. Ren Y, Keshavarz M, Anastasova S, Hatami G, Lo B, Zhang D (2022) Machine learning-based real-time localization and automatic trapping of multiple microrobots in optical tweezer. In: 2022 international conference on manipulation, automation and robotics at small scales (MARSS), pp. 1–6. https://doi.org/10.1109/MARSS55884.2022.9870467

  46. Cui G, Zhang P, Liu X, Xie L, Huang W, Pan P, Qu J, Fan Q (2023) Novel coil array design and modeling for independent control of multiple magnetic microrobots. IEEE Trans Ind Electron 70(10):10302–10311. https://doi.org/10.1109/TIE.2022.3222626

    Article  Google Scholar 

  47. Chowdhury S, Jing W, Cappelleri DJ (2015) Controlling multiple microrobots: recent progress and future challenges. J Microbio Robot 10(1):1–11

    Google Scholar 

Download references

Acknowledgements

This work was supported by the Indian Institute of Technology Patna, Patna, Bihar, India. We express our sincere gratitude to Dr. Deepak Kumar Sinha, Associate Professor, School of Biological Sciences, Indian Association for the Cultivation of Science, Kolkata, India, for his assistance with zebrafish embryos.

Author information

Author notes

  1. Dharmveer Agarwal and Yuvaraj Kamble contributed equally to this work.

Authors and Affiliations

  1. Department of Mechanical Engineering, Indian Institute of Technology Patna, Bihta, Patna, 801106, Bihar, India

    Dharmveer Agarwal, Yuvaraj Kamble, Abhishek Raj & Atul Thakur

  2. Department of Physics, Indian Institute of Technology Patna, Bihta, Patna, 801106, Bihar, India

    Ajay D. Thakur

Authors
  1. Dharmveer Agarwal
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yuvaraj Kamble
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Abhishek Raj
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ajay D. Thakur
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Atul Thakur
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Conceptualization: A.T., A.D.T., and A.R. Investigation, Formal analysis, and Writing: D.A., and Y.K. contributed equally. Supervision and Draft Revision: A.T.

Corresponding author

Correspondence to Atul Thakur.

Ethics declarations

Conflict of interest/Competing interests

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Competing interests

The authors declare no competing interests.

Additional information

Publisher's Note

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

Supplementary Information

Below is the link to the electronic supplementary material.

Supplementary file 1 (pdf 593 KB)

Supplementary file 2 (pdf 178 KB)

Supplementary file 3 (mp4 1272 KB)

Supplementary file 4 (pdf 66 KB)

Index

Index

Table 3 Index to supplementary information
Full size table

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Agarwal, D., Kamble, Y., Raj, A. et al. Biomechanical parameter estimation using untethered nonprehensile magnetic microrobot. J Micro-Bio Robot 19, 59–70 (2023). https://doi.org/10.1007/s12213-023-00164-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12213-023-00164-7

Keywords

Search

Navigation