Biological Tissue Cutting Mechanics and Dynamics
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 combine it with the developed cutting mechanics model
• Experimentally verify the developed needle motion model
Needle/Tissue FEM model
Needle/Tissue Interaction Simulation (ANSYS 12 FEM)
Applications and challenges
• Model Major Output: “force signature” (insertion force vs. insertion time)
• Model Applications: usage of the “force signature” to accelerate performance of thehaptic loops of the virtual surgical simulators; as a validation tool of FEM models oftissue cutting processes (brachytherapy, biopsy, etc.); as a new theoretical basis forthe tissue cutting mechanics; and others;
• Model Challenges: prediction of abnormal cutting force (“force signature”)oscillations during the needle/tissue interaction process, such as: oscillations due tothe variable tissue fracture toughness; oscillations due to the needle/tissue systemdynamics effects (needle motion controller induced instability, etc.); oscillations dueto the Poynting effect; oscillations due to the stick-slip friction; oscillations due tothe tissue springback effect and others.
General Analytical Model for Any Rake and Inclination Angles
Given vectors: (cylindrical surface), (rake surface) , , , .1FN
2FN
XN
YN
ZN
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
LX
Y'
Z, Z'
A
P
R φ
Vc
O, O'
X'
Y
AγNF1
Vc
NF2
φF1
F2
T
F1'
NZ
NY NX
Oblique cutting model: (a) single-point cutting tool, (b) needle tip cutting edge
(a) (b)
Cylindrical Tip Needle
Solid models of the needle tips and their characteristic angles(UNIGRAPHICS NX 6)
T
Bevel Tip Needle
Needle Types
T
Analytical Model of a Normal Rake Angle Distribution
X
Y'
P
R φO, O' X'
Y
Aγ
Z, Z'
T
Vc
Pp
41'
Nz
NF2Pn
i+
γnK
3 2'
L
NYNX1
∂∂
+
∂∂
∂∂
−=2
22
2
2
tan
yF
zF
xF
anγ
Needle tip cutting edge
Normal rake angle model
FnFt
Mt
Tissue
Needle
Cut tissue
Cutting Dynamics
+
++−
+++
+−=
−−
542
2tan
2tan
2tan
51
2tan
2tan
2tan4
cot
2cotcot
0
1423
0
142
0
ψψ
ψ
ϕϕϕϕϕϕξµ
φξµ
cbacbaR
RF aveC
Fracture force of a bevel tip needle
Needle/Tissue system conceptual schematic
MnMt
Ct Cn
KnKt
Ft Fn
Fp
NeedleTissue
Cutting Dynamics
( )tVFMFCFK nnnnnnn =++ ∫−−− 111 ( )( ) tttt
t KsCsMsxsF
++= 2
Simulink/Matlab needle/tissue interaction model
Equations of motion of the needle/tissue:
- needle
- tissue
( )∑∫∑∑∑ =++ −−•
− tVFMFCFKiiii nnnnnnn
111or
Output“forcesignature”
Mechanics and Dynamics of Needle Insertion Into Tissue Simulation Example
FnFt
Mt
Tissue
Needle
Cut tissue
γVP Fn
αT
K
Tissue
Tissue layerremoved
Needle
Needle rakeface
Needle cuttingedge
γV α=0
Fn
µK
µP
K
P
Needleoutsidesurface
h
b
T
Infinitesimalcutting edge
Simulink model
Force signatureIn
sert
ion
Forc
e (N
)
Insertion Time (sec)
Lum
ped
para
met
ers
need
le in
sert
ion
mod
el
Out
put
Model layout
Virtual Simulator
Haptic Loop
Strain rate
function model
Transfer function model
Fracture force
modelPre-fracture, Coulomb, stick-slip friction models
Variable fracture
toughness model
Poyntingeffect model
Velocity-controlled
motion model (“force
signature”)
Poro-elastic
medium fracture model
or
Variable friction
coefficient model
Into Virtual Simulator
Model Schematic
Simulink/Matlab needle/tissue interaction model as a part of a haptics loop ofa virtual surgical simulator
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
Inse
rtio
n Fo
rce
(N)
Insertion Time (sec)
V=var
V=const
Force Signature
Mechanics and Dynamics of Needle Insertion Into Tissue Simulation Example
Example of the Model Application
Haptics Loop of a Virtual Surgical Simulator (curtesy of Dr. Hadrien Courtecuisse, INRIA,France)
a “force signature” can beused in order to acceleratethe haptics loop of a virtualsurgical simulator”
needle
operator haptics loop
Thank you!
Biological Tissue Cutting Mechanics and DynamicsSlide Number 2Slide Number 3Slide Number 4Slide Number 5Slide Number 6Slide Number 7Slide Number 8Slide Number 9Slide Number 10Slide Number 11Slide Number 12Thank you!