Towards Probabilistic Formal Modeling of Robotic Cell Injection Systems

Abstract

Cell injection is a technique in the domain of biological cell micro-manipulation for the delivery of small volumes of samples into the suspended or adherent cells. It has been widely applied in various areas, such as gene injection, in-vitro fertilization (IVF), intracytoplasmic sperm injection (ISCI) and drug development. However, the existing manual and semi-automated cell injection systems require lengthy training and suffer from high probability of contamination and low success rate. In the recently introduced fully automated cell injection systems, the injection force plays a vital role in the success of the process since even a tiny excessive force can destroy the membrane or tissue of the biological cell. Traditionally, the force control algorithms are analyzed using simulation, which is inherently non-exhaustive and incomplete in terms of detecting system failures. Moreover, the uncertainties in the system are generally ignored in the analysis. To overcome these limitations, we present a formal analysis methodology based on probabilistic model checking to analyze a robotic cell injection system utilizing the impedance force control algorithm. The proposed methodology, developed using the PRISM model checker, allowed to find a discrepancy in the algorithm, which was not found by any of the previous analysis using the traditional methods.

Formal Analysis of Robotic Cell Injection Systems Using Theorem Proving

“…where M , N and T in the above equation denote the inertia, positioning table and transformation matrices. The above equation was wrongly presented in simulations [17] and model checking [24] based analysis as follows:…”

“…Primarily, these techniques involve the development of a mathematical model of a system and verification of its properties using computer-based mathematical reasoning. Sardar et al [24] recently used probabilistic modeling checking [7], i.e., a state-based formal method, to formally analyze the robotic cell injection systems. However, their methodology involves the discretization of the differential equations that model the dynamics of these systems, which compromises the accuracy of the corresponding analysis.…”

“…In Equation (7) (used in the simulations based analysis [17]), the transformation matrix (T) is missing, which includes the amount of applied force and the angles at which the injection pipette is pierced into the cell and its absence can lead to disastrous consequences, i.e., excess substance injection, damaging cell tissues etc. Similarly, in Equation (8) (used in the model checking based analysis [24]), f ed is wrongly interpreted as f e , i.e., the desired force, is taken equal to the applied force, which can never happen in a real-world system. We caught these wrong interpretations of Equation (6) in the simulations and model checking based analyses during the verification of the implication relationship between force control and torque controller.…”

“…The distinguishing feature of our formal analysis is that all the verified theorems are universally quantified and can thus be specialized to the required values based on the requirement of the analysis of the cell injection systems. Moreover, our approach allows us to model the dynamics of the cell injection systems involving differential and derivative (Equations (1), (3), ( 5)) in their true form, whereas, in their model checking based analysis [24], they are discretized and modeled using a state-transition system, which may compromise the accuracy and completeness of the corresponding analysis.…”