Reliable surgical simulators remain elusive. Computer-based simulators could allow surgeons to practice surgical operations without any danger to the patients, to plan difficult interventions and could also help guide surgeons during the operations themselves. This could lead to major improvements in surgical training, decrease risks and ultimately raise ethical standards in surgery. The central stumbling block in surgical simulation is the need to simulate in real-time the interaction of the surgeon with a model of the body. Any numerical model of cutting is as adequate and realistic as the fundamental (phenomenological) models of the underlying physical phenomena that occur during the biological tissue cutting process. The importance of having relevant phenomenological process models of cutting is a motivation for this research. These models will also be able to account for the tissue constitutive behavior. The majority of existing FEM simply ignore the existence of the cutting forces, assuming that the instrument ‘always’ cuts the tissue, thus moving away from the reality of the true physical situation and making force feedback impossible. The FEM models are likely to be physically incorrect (due to the computational necessity), while the existing energy balance based models can be physically correct, but with a very limited application usage. Thus, creating a feasible synergy between the FEM and the analytical energy methods is another important goal of this research.
The major aim of this research is to create feasible analytical models of dynamics and mechanics of soft tissue cutting process and experimentally verify those models. Another goal is to be able to connect the suggested cutting process models with the corresponding FEM models.
(a) Derivation of the cutting process dynamics model. The 1-D cutting process dynamics model will be based on a conventional spring/mass/damping type approach to model the needle/tissue system by means of the ‘lumped’ parameters, derived using a novel velocity-controlled formulation. The usage of energy methods will allow to simulate virtually any cutting instrument (geometry, stiffness, etc.), and any biological tissue interaction process (law). The dynamics model will be able to capture, for example, the system effects related to the cutting equipment, needle motion controller, varying cutting conditions, possible chatter vibrations that can affect the penetration force and can be difficult to separate from the actual cutting process-related parameter oscillations (e.g., stick-slip friction, etc.). The model will be powered by an additional tissue constitutive model in the form of either a strain rate function derived from the corresponding constitutive equation (e.g., Mooney-Rivlin model or other) or by introduction of an additional dynamics equation that characterize the tissue properties (from the corresponding needle insertion tests).
(b) Objective 2: Derivation of the cutting process mechanics model. We aim to derive a unique mechanics model of the tissue/cutting instrument interaction based on a conventional metal cutting mechanics approach. This will be the first attempt to combine the universal model of the effective rake angle of an infinitesimal cutting edge of a needle tip active cutting edge, derived using a novel derivative based approach from the metal cutting mechanics and the conventional fracture force model (for a single-point cutting tool), applied to describe the needle tip cutting edge in this research. The novelty of the suggested analytical model lies in the fact that this model is more comprehensive, that is, it can be applied to any needle tip cutting edge geometry (e.g., bevel, conical, cylindrical, helicoidal, etc.) due to the usage of the derivative based approach.
(c) Verification of the suggested tissue cutting process models. An experimental verification of both proposed models will be carried out by means of a series of needle insertion tests into an artificial (phantom) tissue (silicon gel or candle gel) .
We would like to underline that the experimentation tissues will not be human nor animal ones.
(a) Derive the process model that simulates only penetration force without non-linear friction, and plastic deformation effects considered. The model will take advantage of classic spring/mass/damper type modelling approach formulated in a velocity-controlled form. The model will also contain a tissue constitutive model in the form of an additional strain rate function in the cutting process dynamics equation. Perform testing of the model, using a commercially available software, e.g., Matlab/Simulink, under various cutting conditions. Upgrade the cutting process model with linear semi-experimental stiffness, linear damping, and friction models, based on experimental tissue cutting data available.
(b) Derive the corresponding fracture force model for an infinitesimal cutting edge and for the whole active cutting edge of a needle. The cutting edge is represented by a single point cutting tool characterized by an effective rake angle. Afterwards, derive a corresponding fracture force model for the whole active cutting edge, being a distribution of the infinitesimal cutting edges. A tissue fracture toughness will be obtained from the corresponding needle insertion experiments on an artificial tissue of constant thickness and properties.
(c) A typical experimental test case will consist of a needle being inserted inside and retracted from a phantom tissue at various insertion speeds (1…10 mm/s). During this insertion, a feedback force from the needle will be measured by means of the force sensor. The measured data will be recorded using the LabVIEW. During these experiments, different needle tip geometries and various artificial tissue types will be tested under various cutting conditions.
(a) The deliverable of the 1-D dynamics model will be a cutting force ‘signature’ model of the cutting process in question (i.e., needle insertion).
(b) The deliverable of the mechanics model will be an analytical fracture force expression.
(c) The deliverable will be a series of needle insertion verification tests providing us with experimental cutting force ‘signatures’ to verify the suggested mechanics and dynamics models .
The future work will aim to answer the following questions:
1) Does the 1-D model, resulting in 1-DOF process description, adequately describe the tissue cutting or must extra DOFs be added? What are the plausible process effects to be considered significant in the process model: e.g., friction, damping, chatter, etc.?
2) How well does the derivative based metal cutting mechanics approach describe the needle edge geometry? Does the fracture force mostly depend on the needle tip’s cutting edge geometry?
3) How to create a feasible synergy between the analytical and FEM soft tissue cutting process models?
Eventually, we will integrate the obtained force ‘signature’ with the available FEM models of the tissue cutting processes.
INRIA (France), Northwestern University (USA)