Advertisement

Formal Analysis of Robotic Cell Injection Systems Using Theorem Proving

  • Adnan RashidEmail author
  • Osman Hasan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11267)

Abstract

Cell injection is an approach used for the delivery of small sample substances into a biological cell and is widely used in drug development, gene injection, intracytoplasmic sperm injection (ICSI) and in-virto fertilization (IVF). Robotic cell injection systems provide the automation of the process as opposed to the manual and semi-automated cell injection systems, which require expert operators and involve time consuming processes and also have lower success rates. The automation of the cell injection process is achieved by controlling the injection force and planning the motion of the injection pipette. Traditionally, these systems are analyzed using paper-and-pencil proof and computer simulation methods. However, the former is human-error prone and the later is based on the numerical algorithms, where the approximation of the mathematical expressions introduces inaccuracies in the analysis. Formal methods can overcome these limitations and thus provide an accurate analysis of the cell injection systems. Model checking, i.e., a state-based formal method, has been recently proposed for the analysis of these systems. However, it involves the discretization of the differential equations that are used for modeling the dynamics of the system and thus compromises on the completeness of the analysis of these safety-critical systems. In this paper, we propose to use higher-order-logic theorem proving, a deductive-reasoning based formal method, for the modeling and analysis of the dynamical behaviour of the robotic cell injection systems. The proposed analysis, based on the HOL Light theorem prover, enabled us to identify some discrepancies in the simulation and model checking based analysis of the same robotic cell injection system.

Keywords

Robotic cell injection system Higher-order logic Theorem proving 

References

  1. 1.
    Formal Analysis of Robotic Cell Injection Systems using Theorem Proving (2018). http://save.seecs.nust.edu.pk/projects/farcistp/
  2. 2.
  3. 3.
    HOL Light Multivariate Calculus (2018). https://github.com/jrh13/hol-light/blob/master/Multivariate
  4. 4.
  5. 5.
  6. 6.
  7. 7.
    Clarke, E.M., Grumberg, O., Peled, D.: Model Checking. MIT Press, Cambridge (1999)Google Scholar
  8. 8.
    Clarke, E.M., Klieber, W., Nováček, M., Zuliani, P.: Model checking and the state explosion problem. In: Meyer, B., Nordio, M. (eds.) LASER 2011. LNCS, vol. 7682, pp. 1–30. Springer, Heidelberg (2012).  https://doi.org/10.1007/978-3-642-35746-6_1CrossRefGoogle Scholar
  9. 9.
    Durán, A.J., Pérez, M., Varona, J.L.: The Misfortunes of a Mathematicians’ Trio using Computer Algebra Systems: Can We Trust? CoRR abs/1312.3270 (2013)Google Scholar
  10. 10.
    Faroque, M., Nizam, S.: Virtual Reality Training for Micro-robotic Cell Injection. Deakin University, Australia, Technical report (2016)Google Scholar
  11. 11.
    Harisson, J.: HOL Light Transcendental Theory (2018). https://github.com/jrh13/hol-light/blob/master/Multivariate/transcendentals.ml
  12. 12.
    Harrison, J.: HOL light: a tutorial introduction. In: Srivas, M., Camilleri, A. (eds.) FMCAD 1996. LNCS, vol. 1166, pp. 265–269. Springer, Heidelberg (1996).  https://doi.org/10.1007/BFb0031814CrossRefGoogle Scholar
  13. 13.
    Harrison, J.: Handbook of Practical Logic and Automated Reasoning. Cambridge University Press, New York (2009)CrossRefGoogle Scholar
  14. 14.
    Harrison, J.: The HOL light theory of euclidean space. J. Autom. Reasoning 50(2), 173–190 (2013)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Harrison, J., et al.: Formalized Mathematics. Turku Centre for Computer Science, Turku (1996)Google Scholar
  16. 16.
    Hasan, O., Tahar, S.: Formal Verification Methods. Encyclopedia of Information Science and Technology, pp. 7162–7170. IGI Global Pub. (2015)Google Scholar
  17. 17.
    Huang, H., Sun, D., Mills, J.K., Li, W.J.: A visual impedance force control of a robotic cell injection system. In: Robotics and Biomimetics, pp. 233–238. IEEE (2006)Google Scholar
  18. 18.
    Huang, H., Sun, D., Mills, J.K., Li, W.J., Cheng, S.H.: Visual-based impedance control of out-of-plane cell injection systems. Trans. Autom. Sci. Eng. 6(3), 565–571 (2009)CrossRefGoogle Scholar
  19. 19.
    Kuncova, J., Kallio, P.: Challenges in capillary pressure microinjection. In: Engineering in Medicine and Biology Society, vol. 2, pp. 4998–5001. IEEE (2004)Google Scholar
  20. 20.
  21. 21.
    Nakayama, T., Fujiwara, H., Tastumi, K., Fujita, K., Higuchi, T., Mori, T.: A new assisted hatching technique using a piezo-micromanipulator. Fertil. Steril. 69(4), 784–788 (1998)CrossRefGoogle Scholar
  22. 22.
    Nethery, J.F., Spong, M.W.: Robotica: a mathematica package for robot analysis. IEEE Robot. Autom. Mag. 1(1), 13–20 (1994)CrossRefGoogle Scholar
  23. 23.
    Paulson, L.C.: ML for the Working Programmer. Cambridge University Press, Cambridge (1996)CrossRefGoogle Scholar
  24. 24.
    Sardar, M.U., Hasan, O.: Towards probabilistic formal modeling of robotic cell injection systems. In: Models for Formal Analysis of Real Systems, pp. 271–282 (2017)CrossRefGoogle Scholar
  25. 25.
    Sun, D., Liu, Y.: Modeling and impedance control of a two-manipulator system handling a flexible beam. In: Proceedings of the 1997 IEEE International Conference on Robotics and Automation, vol. 2, pp. 1787–1792. IEEE (1997)Google Scholar
  26. 26.
    Sun, Y., Nelson, B.J.: Biological cell injection using an autonomous microrobotic system. Robot. Res. 21(10–11), 861–868 (2002)CrossRefGoogle Scholar
  27. 27.
    Yanagida, K., Katayose, H., Yazawa, H., Kimura, Y., Konnai, K., Sato, A.: The usefulness of a piezo-micromanipulator in intracytoplasmic sperm injection in humans. Hum. Reprod. 14(2), 448–453 (1999)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of Electrical Engineering and Computer Science (SEECS)National University of Sciences and Technology (NUST)IslamabadPakistan

Personalised recommendations