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!