Needle Steering Force Model and Trajectory Planning

1. Needle Steering Force Model and Trajectory Planning Reporter : Pan Li Supervisors: Prof. ZhiyongYang, A.P. Shan Jiang

2. Future Works 3 1 2 Content Needle Insertion Force Model Trajectory Planning for insertion needle

3. Experimental design Fig.2 The devices for force measuring experiments High speed camera Fig.1 Visual image acquisition hardware and software systems Force sensor

4. Experimental procedure The force acting on a needle is written as: C 3 Deformation 1 2 Extraction Insertion B Friction Force Friction and Cutting Force A D Stiffness Force Material Relaxation and Friction Fig.4 Insertion force-deep profile Fig.3 Insertion force-time profile 1) Deformation phase (from A to B): Tissue deformation occurs. 2) Insertion phase (from B to C): The needle penetrates into the soft tissue. 3) Extraction phase (from C to D): The needle is exacted from the soft tissue.

5. Needle Insertion Force Model • Stiffness Force The stiffness force corresponds to viscoelasticinteraction and can be described as prepuncture force. Fig.6 Error comparison between polynomial and exponential model Fig.8 Stiffness model schematic diagram Fig.7 Comparison between stiffness model and experimental data Fig.5 Five experiments of force curve profile polynomial model: exponential function model:

6. Stiffness Force Strain energy density expression: Stiffness force： Deformation tenser invariant: Equivalent modulus: Parameter acquisition: Mooney-Rivlin model experiment: Fig.9 Parameter acquisition experiment diagram of insertion needle mm mm Geometry of needle : Optimization toolbox by ANSYS: Moment of inertia: = 116KPa Deflection equation: • =14.1±1.6GPa Five experiment result:

7. Friction Force The friction force occurs along the length of the needle inside the tissue and is due to Coulomb friction, tissue adhesion and damping. Measurement of friction force: (a) Impale the soft tissue (c) Two consecutive insertions (b) Withdrawing of the needle Fig.10 Measurement of friction force

8. Friction Force Fig.11 Modified Winker foundation model sketch diagram Normal force: Contact area: Fig.12 Comparison between force model and experimental data Coulomb friction Foundation modulus: Friction force model:

9. Cutting Force Constant The cutting force ranges from 0.04N to 0.1N periodically, and the fluctuation can disappear when the insertion speed is equal to 3mm/s and the insertion forces of two consecutive insertions are parallel to each other.

10. Complete force model The overall shape of the model is coherent to the experimental results, although the fluctuations in the insertion phase make a perfect match impossible. Comparison: • (1) : • (2) : • (3) :

11. Pelvis Bladder Tumor Prostate Rectum Urethra • Trajectory Planning for insertion needle • Key technology ： • Avoiding vital tissues; • Implanting into tumor accurately; • Shorten trajectory path; • Reducing implant errors.

12. G O P Relationship of force and potential value: Repulsive potential value and force: Attractive potential value and force: 3D trajectory planning result of the spiral pipe model 3D trajectory planning result of the concave curved surface model 3D trajectory planning result of local minimum • Artificial potential field • Local minimum in concave curved surface model

13. APF ICGA Improved conjugate gradient method Escaping from Local minimum Optimization of trajectory planning • (a) , is selected as search direction angle • (b) , is selected as search direction angle • Judgment

14. Future works • Modeling interactive forces during needle insertion and experiment validation. • Modeling and simulation of tissue deformation. • Modeling needle deflection during insertion. • Trajectory planning considering tissue deformation and needle deflection. • Needle guidance and steering with experiment validation.

15. Fig.1 Accurate robotic needle steering requires a model that predicts needle motion within the tissue. Both a stochastic motion planner (used pre- and/or intra-operatively) and an image-guided model-based feedback controller can use the mechanics-based model Modeling interactive forces Mechanics model and insertion model Trajectory planning Insertion model Tissue deformation and needle deflection Needle guidance and steering

16. Modeling interactive forces during needle insertion • Stiffness force: To symmetric needle tip: Surface shape function : Stiffness force: (a) Symmetric needle tip Simplified into: Whereas: To asymmetric needle tip: Surface shape function: ? (b) Asymmetric (bevel) needle tip Deduction: Fig.2 Asymmetry of the bevel tip produces a resultant transverse load which causes a flexible needle to naturally bend

17. Friction force: Coulomb friction { Evolutionary: Elastic deformation phase Fig.3 Overall slip model Friction force： Partial slip phase Friction force： Entire slip phase Fig.4 Partial slip model

18. Friction force: • Stribeck friction model: • LuGre friction model: Where v is the contact velocity of each differential element and L is the incision length; and • Karnopp friction model: Fig.5 Stribeck model Fig.6 LuGre friction model :stiffness coefficient of the microscopic deformations : the damping coefficient associated with : the viscous relative damping and are the normalized coulomb and stiction Fig.7 Karnopp model

19. Modeling needle deflection during insertion • Modeling and simulation of needle insertion into soft tissue Rayleigh-Ritz: energy Sum of energy: Fig.8 Distributed compressive load acting on a needle shaft as it interacts with an elastic medium. Needle-tissue interaction energy: Insertion force work: Transverse tip load: Axial tip load: Fig.9 Free-body diagram of the forces acting on the needle tip as it interacts with the elastic medium. Rupture the elastic medium:

20. Trajectory planning considering tissue deformation and needle deflection • Trajectory planning considering tissue deformation • and needle deflection • Considering needle deflection • Neglecting tissue deformation Fig.10 Artificial potential field (c)needle deflection and local changes in needle orientation. (a)Tissue deformation (b) trajectory changes • mathematic(al) model • physiological anatomical model Fig.12 Inverse Kinematics solution Fig.11 Numerical analysis method

21. Needle guidance and steering with experiment validation • Needle guidance and steering with experiment • validation Input constraints: State constraints: (a) Basic concept Model predictive control: Discrete control inputs Linearized tracking error model Fig. 14. The reference flexible probe, the measured real flexible probe, and their local coordinates. (b)Subdivided sampling time for higher update rate of the MPC-based feedback controller. Fig.13. Concept diagram of a model predictive controller.

22. Thank you