This document summarizes a study on developing a fracture mechanics model to predict the insertion force of needles cutting through tissue. Experimental tests were conducted to determine the fracture toughness, shear modulus, frictional force, and crack length for different size needles inserted at various speeds into porcine skin. A force model was developed incorporating these parameters and validated against experimental force measurements, with errors less than 0.2 N. The model accurately predicts insertion forces and shows that 61% of the force comes from creating a crack in the tissue, while 21% is from friction and 18% from spreading the tissue. Increasing insertion speed was found to not reduce force for porcine skin.

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FRACTURE MECHANICS MODEL OF
NEEDLE CUTTING TISSUE
SUBMITTED BY
NAME: NEHEM TUDU
ROLL NO.: M150360ME
MANUFACTURING TECHNOLOGY

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CONTENTS
Introduction
Needle Manufacturing Process
Needle Insertion Mechanics
Experimental Procedures
Results and Discussion
Force Model and Validation
Conclusions
Reference

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INTRODUCTION
 Needles are a commonly used instrument
in medicine
 Low insertion force is critical in these
procedures for two reasons:
1. Reduce pain felt in patients
2. Allows for more accurate needle tip
placement
Fig. 2 Simulated needle intercept of a small target embedded within elastic tissue.

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 Insertion force of needle can be reduce by altering tip & reducing the
gauge size
 But microneedle cannot be used in all procedure
 Force can be reduced by applying vibratory actuator & can be
controlled precisely
How to reduce insertion force ?
Fig.4 Graph of skin penetration force from excized animal tissue showing a
greater than 70% reduction in insertion force using the vibratory actuator
Fig. 3 Different needle tips

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 Increasing the insertion speed of the needle, the force needed to puncture
the tissue is reduced & followed by reduction in tissue deflection in
porcine heart, porcine liver samples, & turkey breast
 In case of skin it is found that the insertion force increases by increasing
the insertion speed
 Model incorporates parameters including fracture toughness & shear
modulus of tissue
 Because of the viscoelastic properties of tissue, these factors are strain rate
dependent, causing speed of insertion to vary insertion force
Fig. 5. Mean peak rupture force versus velocity for pig heart insertion.
Error bars denote standard deviation.
Figure 6. Insertion force–displacement curves of 30G needles in 3%
agarose gel with polyurethane foil at different speeds.

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NEEDLE MANUFACTURING PROCESS
Rolling of metal sheet Drawing process of needle
Cutting of needle
Grinding of needle
Fixed to needle hub

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NEEDLE INSERTION MECHANICS
 As the needle inserts through a
4mm section of porcine tissue with
no backing, there are three phases
1. Tissue deflects & the force gradually
rises
2. Tissue is cut
3. Needle continues to pass through tissue
 The maximum cutting force is
reached in phase 2 & is defined as
total cutting force, P
 The three forces:
 Tearing force (Pt)
 Spreading force (PS)
 Friction force (PF)
Fig. 7 Force profile
of needle passing
through porcine skin
Fig. 8 Forces that compose total cutting force

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FRACTURE MECHANICS MODEL
 The model is formed dependent on
1. Needle diameter
2. Insertion speed
 As the needle inserts into tissue, work is performed equal to Pδl, where P is
force exerted & δl is a differential insertion length
 Needle then creates a crack in tissue & spreads tissue apart to accommodate
the width of needle
 Kinetic energy was neglected in development of model
Fig. 9 Different mode of fracture

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 Crack around the needle is not completely circular because of this, a non-
dimensional contact factor f(d) needs to be added into the δ termɅ
 Goal of this work is to be able to describe maximum insertion force of
needle into tissue
 Friction occurring at maximum insertion force is puncture friction force PFP
 Where μ is the shear modulus

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EXPERIMENTAL PROCEDURES
 Two experimental procedures were carried out to determine the
parameters utilized in the model
 In procedure 1 fracture toughness, frictional force, & crack length were
found by inserting a needle into tissue
 In procedure 2, shear modulus was determined by stretching the porcine
skin at four different strain rates (0.25, 1, 10, & 25% mm/mm s)

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NEEDLE INSERTION EXPERIMENT
Fig. 10 (a)
Experimental
setup for needle
insertion and
(b) porcine
skin mounting
Fig. 11 (a) Graph of first and
second needle insertion and
(b) graph of fracture work
performed to determine JIC
Fig. 12 Measured needle crack length in porcine skin

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TISSUE TENSION EXPERIMENT
 Results of this experiment were analyzed with
an Ogden model
 Porcine skin is viscoelastic and anisotropic
 Young’s modulus of the tissue is low to begin
because the collagen fibers are moving about
each other
 At higher strains, the fibers become aligned and
the tissue stiffens
 where is the strain energy density, μ is theϕ
shear modulus, α is the strain hardening, λiare
the principle stretch ratios, σz is the stress & λz is
stretch ratio in the pull direction
Fig. 13 Experimental setup for stretching porcine skin to determine
shear modulus
Fig. 14 Stress–strain curve of the porcine skin parallel, at a 45 deg angle,
and perpendicular (including Ogden Fit) to the Langer lines

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RESULT
Needle
insertion
experiment
Tissue
tension
experiment
Contact
factor
Shear
Modulus
Fracture
toughness
Frictional
force
Crack
length

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FRACTURE TOUGHNESS
 A third-degree multivariable (d & v)
polynomial was fit to the data with an R2
value of 0.95
 Hypodermic needles have three angles
that define their geometry ξ1, ξ2 & β
Fig. 16 Definition of the three angles that define hypodermic needle
geometry
Fig. 15 Fracture toughness of varying gauge needles from 1 to 80 mm/s

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FRICTION FORCE
 A two-dimensional fit was
applied to the data with an R2
value of 0.90
 Frictional force increases with
increasing speed
 Puncture friction force also
increases with increasing
needle diameter
Fig. 17 Two-dimensional fit of friction data where the points are
the experimental data and the surface is the best fit

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CRACK LENGTH
 The crack size occurs smaller than needle diameter occurs
 Crack does not run & keep enlarging
Fig. 18 Tissue crack length results with linear fit

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SHEAR MODULUS
 Where μ is in MPa, and έ is the strain
rate of insertion in mm/mm s
 The shear modulus decreased as the
strain rate increased, confirming that
the porcine skin shows shear
thinning
 It was assumed that the tissue
strained perpendicular to the
insertion direction
 Where β is the major bevel angle of
the needle, & RS is the radius of the
hole in the back plate holding the
skin
Fig. 19 Measured shear modulus compared to strain rate

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CONTACT FACTOR
 Contact factor f was found by fitting insertion force model, to
experimental force results
 Contact factor was found for each needle gauge size separately using a
best fit least-squares regression
Fig. 20 Contact factor f compared to needle outer diameter

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FORCE MODEL AND VALIDATION
 Completed force model, with the values of JIC(d,v), & PFP(d,v) is formed
 Model for each needle gauge is within one standard deviation of the
experimental data with largest error being 0.2 N
 Tearing force is given by JIC(d,v)a(d), spreading force is given by
μ(v)R2
f(d), & puncture friction force is PFP
 On average across four needle sizes, tearing force accounts for 61% of total
insertion force, spreading force accounts for 18%, & friction force accounts
for remaining 21%
Fig. 21 Completed force model (lines) plotted against
experimental needle insertion force results (points)

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 To validate force model, a 27
gauge hypodermic needle was
tested with outer diameter is
0.41mm
 Overprediction of model is
caused by complex third-degree
fit of fracture toughness
overestimating fracture
toughness outside range of
needles tested
 The model is still within one
standard deviation for each data
point with all the errors less than
the 0.2 N maximum error of the
trials used to create the model
Fig. 22 Completed force model (line) plotted against
experimental needle insertion force result (point) for 27
gauge needle

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CONCLUSION
 A dynamic physics-based model was constructed & shown to accurately
predict insertion forces upon needle insertion into porcine skin for four
different gauge hypodermic needles
 Model shows that on average 61% of the total insertion force comes from
creating the crack, friction contributes 21% of the total force & the
spreading of the tissue contributes 18% of the force
 For porcine skin, increasing the insertion speed did not lower the insertion
force
 Fracture toughness is relatively constant across different insertion speeds
 Increasing insertion speed increases the frictional force on the needle
 Increasing speeds were shown to benefit in reducing the spreading force
of the tissue to accommodate the needle

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REFERENCE
 Dimaio, S. P., and Salcudean, S. E., 2003, “Needle Insertion Modeling and
Simulation,” IEEE Trans. Rob. Autom., 19(5), pp. 864–875.
 Ehmann, K., and Malukhin, K., 2012, “A Generalized Analytical Model of the
Cutting Angles of a Biopsy Needle Tip,” ASME J. Manuf. Sci. Eng., 134(6), p.
061001.
 Yang, M., and Zahn, J. D., 2004, “Microneedle Insertion Force Reduction Using
Vibratory Actuation,” Biomed. Microdevices, 6(3), pp. 177–182.
 Mahvash, M., and Dupont, P. E., 2010, “Mechanics of Dynamic Needle Insertion
into a Biological Material,” IEEE Trans. Biomed. Eng., 57(4), pp. 934–943.
 Ogden, R. W., Saccomandi, G., and Sgura, I., 2004, “Fitting Hyperelastic Models
to Experimental Data,” Comput. Mech., 34(6), pp. 484–502.
 Koelmans, W., Krishnamoorthy, G., Heskamp, A., Wissink, J., Misra, S., and
Tas, N., 2013, “Microneedle Characterization Using a Double-Layer Skin
Simulant,” Mech. Eng. Res., 3(2), pp. 51–63.
 Cuppoletti, J., 2011, Nanocomposites with Unique Properties and
Applications in Medicine and Industry, InTech, CC BY-NC-SA 3.0 license

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THANK YOU