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The Simulation the Contact Interaction of the Needle and Brain Tissue

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Part of the Lecture Notes in Mechanical Engineering book series (LNME)


The needle is modeled as an elastic hollow cylindrical flexible rod, partially immersed into a viscoelastic material that simulates brain tissue. The controlled force and moment are applied at the end of the rod. The insertion of the needle is modeled as sliding with friction along a channel whose walls compress the needle. The compression force varies along the axis of the embedded part of the needle and changes in time. The magnitude of the compression forces is determined from the solution of the initial-boundary-value problem. The compression stiffness of the rod is assumed to be infinite, i.e. its deformation is reduced only to bending. Along the axis, the rod moves like an absolutely rigid body. The interaction of a viscoelastic material and a needle is modeled in the linear Winkler approximation as a dynamic system “beam-viscoelastic base” with a time-variable interaction zone length.


  • Contact interaction
  • Brain tissue
  • Immersion
  • Elastic needle
  • Viscoelastic media
  • Analytical solution
  • Non self-conjugate operators

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The study was partially supported by the Russian Government program (contract # AAAA–A20–120011690132–4) and partially supported by RFBR (grant No. 19–58–52004 and grant No. 18–29–03228).

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Lycheva, T., Lychev, S. (2022). The Simulation the Contact Interaction of the Needle and Brain Tissue. In: Indeitsev, D.A., Krivtsov, A.M. (eds) Advanced Problem in Mechanics II. APM 2020. Lecture Notes in Mechanical Engineering. Springer, Cham.

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-92143-9

  • Online ISBN: 978-3-030-92144-6

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