  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.
