Deflection Detection on Needles in an MRI Environment using Optical Fiber Bragg Gratings

1
Deflection Detection on Needles in an MRI
Environment using Optical Fiber Bragg Gratings

• April 14, 2008
• Yong-Lae Park

2
Model Construction
d2
d1
F2
F1
Sensor 2
Sensor 1
Tip Deflection
x1
x2
3
Deflection Calculation
F2
F1
Shear Force
f1 F1F2
f2
EI
f1
f2 F2
x
Bending Moment
f1 (F1F2)x - F1d1 - F2d2
x
f2
f2 F2x - F2d2
EI
f1
1
Curvature

?
Slope
f1(EI) ½F2x2 - F2d2x - ½F1d12
x
f2
f2 (EI) ½(F1F2)x2 - (F2d2F2d2)x
f1
Deflection
f1 (EI) 1/6 (F1F2)x3 - ½(F1d1F2d2)x2
x
y
f1
f2 (EI) 1/6 F2x3 - ½F2d2x2 - ½F1d 12x 1/6
F1L13
f2
d2
d1
4
Model Estimation
Sensor 1
Sensor 2
x2
x1
1
Curvature

?
Curvature (1/ ?)
x
? radius of curvature ex strain measured by FBG
sensor d distance from neutral axis
f(x) ax2bxc
Slope
x
?
f(x) dx

Deflection
??
x
f(x) dx dx
yestimated
y
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Tip Deflection Error (E)
Tip deflection Error
x2
x2
x1
x1
x1 Location of 1st Sensor X2 Location of 2nd
Sensor
E ytruexd2 - yestimated xd2
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Sensitivity Test (x1)
Sensitivity of x1
x2
x2
x1
x1
Sensitivity for x1 ?E / ?x1 E Tip deflection
error
x1 Location of 1st Sensor X2 Location of 2nd
Sensor
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Sensitivity Test (x2)
Sensitivity of x2
x2
x2
x1
x1
Sensitivity for x2 ?E / ?x2 E Tip deflection
error
x1 Location of 1st Sensor X2 Location of 2nd
Sensor
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Simulation Result
Sensor 1
Sensor 2
x2
x1
x2
x1

• Optimum Locations for Sensor Placement
• - Minimum error
• - Minimum sensitivity

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Example
D2 150
d1 75
1
0.5
Sensor 2
Sensor 1
Tip Deflection
X1 25
X2 82
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Test 1

• One Point Bending
• Single Mode

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One Point Bending
X1 25
X2 82
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Deflection -5 mm, Error 0.1334 mm
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Deflection -10 mm, Error 1.7827 mm
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Deflection -15 mm, Error 0.2896 mm
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Deflection -20 mm, Error 1.3272 mm
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Deflection -25 mm, Error 0.3676 mm
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Deflection -30 mm, Error 0.0457 mm
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Test 2

• Two Point Bending
• Modes of 2 (S-curve)

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Two Point Bending (S-curve)
X1 25
X2 82
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Deflection 10 mm, Error 0.0903 mm
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Deflection 5 mm, Error 0.5611 mm
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Deflection 0 mm, Error 1.4089 mm
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Deflection -5 mm, Error 1.4433 mm
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Deflection -10 mm, Error 0.2661 mm
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Deflection -15 mm, Error 0.0102 mm
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Deflection -20 mm, Error 0.1840 mm