“Duffing-type” Motion Models Powered by “System Effect” Based Prediction of Cutting Force Evolution in Minimally Invasive Surgeries

• Applicant: Kostyantyn Malukhin, Ph.D.
• Subject Area: Mechanics
• Term: since 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 439145569

The main objective of this DFG project is to expand and verify the previously developed advanced fundamental theoretical modelling method, aimed at predicting the cutting process responses occurring during various minimally invasive surgical interventions (e.g., biopsy, breast or prostate brachytherapy, laparoscopy, ventriculostomy, etc.) between a soft biological tissue and a cutting edge of a medical cutting instrument (here - a bevel tip needle). The previous study was performed in the frame of a DFG project as well. The predicted cutting process responses are the main deliverables of the project. They represent the total cutting force (the process “force signature”), acting on the needle, the tissue dynamic fracture force, the needle/tissue dynamic friction force, the dynamic cutting process damping and the tissue “strain rate function” as a constitutive law. The previously developed surgical cutting process modelling approach is based on the basic Kirchhoff’s laws and basic conservation laws, written in the form of the corresponding force balances or motion equations. The motion equations are derived using the newly suggested velocity-controlled formulation employed to describe the needle motion inside the tissue and the corresponding tissue response during a surgical intervention. The novel analytical tissue fracture force model for the bevel tip needle is derived using the newly developed generic universal derivative-based fracture force model, adopted from classical metal cutting mechanics, fracture mechanics and oblique cutting theory. The novel dynamic friction force model is derived using the feedback forces from the cutting instrument and the tissue response, expanded into the corresponding force balances. The tissue “strain rate function” represents the reformulated tissue constitutive law in terms of strain rate/stress constitutive correlation, whose usage was suggested by the predominantly visco-elastic nature of soft biological tissues. Due to the highly non-linear nature of the soft biological tissue cutting process (e.g., the Mullin’s tissue softening effect, tissue fracture toughness variation, or other) the additional non-linear “Duffing-type” force terms (e.g., the cubic stiffness, cubic damping term, etc.) and, tentatively, other non-linear terms (e.g., fractional, fractal, trigonometric ones, etc.), as well as the so-called “floppy” tissue model will be added to expand the main cutting process model. All of the above mentioned models will be united by the common “system effect” based approach, manifested in the maximally possible usage of the basic conservation laws and the lowest possible number of conventional constitutive laws, leading to the minimal error of the method and the highest accuracy of predicting the cutting process responses. The non-linear advanced tissue cutting process model will be verified experimentally, using artificial phantom tissues and/or numerically, using available commercial FEM software.

• DFG Programme: Research Grants
• International Connection: USA
• Cooperation Partners: Professor Dr. Kornel F. Ehmann; Professor Michael Verta, Ph.D.
• Co-Investigator: Professor Dr.-Ing. Timon Rabczuk, Ph.D.