Introduction
Research Objectives:
• Develop tissue cutting mechanics theoretical foundation to describe geometry and cutting forces of a needle, penetrating inside a tissue
• Develop an analytical model that describes geometry of a needle tip in terms of its characteristic angles
• Develop tissue cutting dynamics theoretical foundation to describe needle motion during its penetration inside a tissue
Approach:
• Use conventional metal cutting mechanics theory and represent the needle cutting edge as a distribution of infinitesimal cutting edges described by 4 characteristic angles: inclination, velocity, normal and effective rake angles. • Combine the metal cutting mechanics approach and the fracture mechanics
method to formulate the fracture force model for the needle active cutting edge • Use a velocity controlled formulation of the equation of motion of a needle and
Needle/Tissue FEM model
Applications and challenges
•
Model Major Output: “force signature” (insertion force vs. insertion time)
•
Model Applications: usage of the “force signature” to accelerate performance of the
haptic loops of the virtual surgical simulators; as a validation tool of FEM models of
tissue cutting processes (brachytherapy, biopsy, etc.); as a new theoretical basis for
the tissue cutting mechanics; and others;
•
Model Challenges: prediction of abnormal cutting force (“force signature”)
General Analytical Model for Any Rake and Inclination Angles
Given vectors: (cylindrical surface), (rake surface) , , , .NF1
2 F N NX Y N NZ i γ γn Pr Pp Pn i Aγ η = i γe Pe T 1 2 1' 2' 3 4 5 K R VC A N' B N Aα NL L X Y' Z, Z' A P R φ Vc O, O' X' Y Aγ NF1 Vc NF2 φ F1 F2 T F1' NZ NY NX
Oblique cutting model: (a) single-point cutting tool, (b) needle tip cutting edge
Cylindrical Tip Needle
Solid models of the needle tips and their characteristic angles (UNIGRAPHICS NX 6)
T
Bevel Tip Needle
Needle Types
Analytical Model of a Normal Rake Angle Distribution
X Y' P R φ O, O' X' Y Aγ Z, Z' T Vc Pp 4 1' Nz NF2 Pn i + γn K 3 2' L NY NX1 ∂ ∂ + ∂ ∂ ∂ ∂ − = 2 2 2 2 2 tan y F z F x F a nγ
Needle tip cutting edge
Fn Ft Mt Tissue Needle Cut tissue
Cutting Dynamics
+ + + − + + + + − = − − 5 4 2 2 tan 2 tan 2 tan 5 1 2 tan 2 tan 2 tan 4 cot 2 cot cot 0 1 4 2 3 0 1 4 2 0 ψ ψ ψ ϕ ϕ ϕ ϕ ϕ ϕ ξ µ φ ξ µ c b a c b a R R FCaveFracture force of a bevel tip needle Needle/Tissue system conceptual schematic
Cutting Dynamics
( )
t
V
F
M
F
C
F
K
n−1
n+
n−1 n+
n−1∫
n=
n( )
( )
t t t t tK
s
C
s
M
s
x
s
F
+
+
=
2Simulink/Matlab needle/tissue interaction model Equations of motion of the needle/tissue:
Mechanics and Dynamics of Needle Insertion Into
Tissue Simulation Example
Fn Ft Mt Tissue Needle Cut tissue γV P Fn α T K Tissue Tissue layer removed Needle Needle rake face Needle cutting edge γV α=0 Fn µK µP K P Needle outside surface h b T Infinitesimal cutting edge Simulink model Force signature Ins er tio n Fo rc e ( N)
Insertion Time (sec)
Lum ped pa ra m et ers needl e ins ert io n m odel O utput Model layout Virtual Simulator Haptic Loop Strain rate function model Transfer function model Fracture force model Pre-fracture, Coulomb, stick-slip friction models Variable fracture toughnes s model Poynting effect model Velocity-controlled motion model (“force signature”) Poro-elastic medium fracture model or Variable friction coefficien t model Into Virtual Simulator Model Schematic
Simulink/Matlab results of needle/tissue interaction model: needle insertion velocity (V) controlled solutions
0 2 4 6 8 10 12 14 0 1 2 3 4 5 6 7 8 In se rt io n F or ce (N )
Insertion Time (sec)
V=var
V=const
Force Signature
Example of the Model Application
Haptics Loop of a Virtual Surgical Simulator (curtesy of Dr. Hadrien Courtecuisse, INRIA, France)
a “force signature” can be used in order to accelerate the haptics loop of a virtual surgical simulator”
