Second Sight Presentation

William Yang, Second Sight Summer Intern 2016
Supervisor: Dr. David Zhou
1

Motivation and Purpose
 Understand how stimulation strategies
and electrode spacing relate to the
shape of voltage distributions and
electric fields in order to inform and
improve future innovations
3

Voltage and Electric Field
 𝐸 = −𝛻𝑉
 𝐸𝑥, 𝐸𝑦, 𝐸𝑧 = −
𝑑𝑉
𝑑𝑥
,
𝑑𝑉
𝑑𝑦
,
𝑑𝑉
𝑑𝑧
 The strength of the electric field must take into
account all components of the electric field
𝑬
𝐸𝑥 𝑖 = −dV/dx
𝐸𝑦 𝑗 = −dV/dy
+x
+y
4

Voltage/Electric Field and
Activating Function (AF)
 The activating function is the second derivative
of voltage in the direction of the neuron fiber
(Rattay 1986, Litvak 2007, Falcone 2011)
V-pp
Neuron
AF =
𝑑2 𝑉𝑝𝑝
𝑑𝑥2
+x
+y
5

More on Activating Function
 If the electrodes are simplified to point
electrodes, the activating function can be
modeled by the following equation, for a
given point electrode at point (u,v,w):
Using this equation, one can obtain the discrete AF in space by
plugging in a discrete spatial voltage distribution for each
electrode and summing the AF’s
𝐴𝐹 𝑥, 𝑦, 𝑧 = 𝑉 𝑥, 𝑦, 𝑧
3𝑧
2((𝑥 − 𝑢)2+(𝑦 − 𝑣)2+(𝑧 − 𝑤)2)2
−
1
(𝑥 − 𝑢)2+(𝑦 − 𝑣)2+(𝑧 − 𝑤)2
6

Derivation of AF using
equations from Falcone 2011:
Equation 1: 𝐴𝐹 𝑥, 𝑦, 𝑧, 𝐼 =
ρ𝐼
4π
3𝑧
2(𝑥2+𝑦2+𝑧2)5/2 −
1
(𝑥2+𝑦2+𝑧2)3/2
Equation 2: 𝑉 𝑥, 𝑦, 𝑧, 𝐼 =
ρ𝐼
4π 𝑥2+𝑦2+𝑧2
Equation 1 can be factored to obtain:
𝐴𝐹 𝑥, 𝑦, 𝑧, 𝐼 =
ρ𝐼
4π 𝑥2 + 𝑦2 + 𝑧2
3𝑧
2(𝑥2 + 𝑦2 + 𝑧2)2
−
1
𝑥2 + 𝑦2 + 𝑧2
The factored expression can be replaced by V(x,y,z,I) from Equation 2:
𝐴𝐹 𝑥, 𝑦, 𝑧 = 𝑉 𝑥, 𝑦, 𝑧
3𝑧
2(𝑥2 + 𝑦2 + 𝑧2)2
−
1
𝑥2 + 𝑦2 + 𝑧2
Where ρ is resisitivity, 𝐼 is current, and x, y, and z define the location of
a point relative to a point electrode at (0,0,0)
7

Experimental Setup
Stimulator
Coil
PC Running
ADAQA
VPU
External
Coil
Oscilloscope
Measuring
Voltage
Stimulation Electrode Array
Return Electrode
Petri Dish w/ 10 mM PBS
PC moving
stepper motor
and recording
voltage
measurements
Wireless RF Link
Micro-Probe
Stepper
Motor
9

Experimental Setup
10
Micro-Probe
Stepper Motor
Test Array
Array surface and tip of probe submerged in PBS Solution
+z
+y
+x

Experimental Setup
11
Micro-Probe
Stepper Motor
Test Array
+z
+y
+x

Experimental Setup
12
Micro-Probe
Stepper Motor
Test Array
+z
+y
+x

Data Acquisition Software
 Previous acquisition software
 WinCommander to manually control the microprobe
stepper motor
 LabVIEW software to record voltage measurements
 Phantom to automate mouse clicking of
WinCommander controls and record-voltage push
buttons in LabVIEW
 New acquisition software uses only one
LabVIEW program that automates stepper
motor movement and voltage recording
 Enables automated 1D, 2D and 3D scans
 Saves time, easier to use
13

Electrode Array Numbering
1234
8
9
13
765
1112
1516
10
14+x
+y
15

Data Processing for 2D XZ
Scans
 % Initialize Vpp before running the script. Vpp contains the scan of
Vpp
 % values. The script rearranges the Vpp data ready to be plotted in 3
 % Space. It also gives the x and z components of the electric field

 % Initialize the matrix that will contain the Vpp data. It will be
called
 % "VppGrid"
 x = 0:.02:4;
 z=0:.05:.5;
 [X,Z] = meshgrid(x,z);

 % Insert Vpp data into VppGrid
 VppGrid = X';
 VppGrid(1:end) = Vpp(1:end);
 VppGrid = VppGrid';

 % Take the gradient to find the X and Z components of the electric
field
 [Ex,Ez] = gradient(VppGrid,X',Z);
 Ex = -1*Ex;
 Ez = -1*Ez;
16

Resulting Vpp Matrix for XZ
Scans
+x
+z
17

AF
…
E1, (u1,v1,w1)
E2, (u2,v2,w2)
E3, (u3,v3,w3)
Ei, (ui,vi,wi)
19

Data Processing for 3D
Scans
 x = xLim(1):xStep:xLim(2);
 y = yLim(1):yStep:yLim(2);
 z = zLim(1):zStep:zLim(2);

 [X,Y,Z] = meshgrid(x,y,z);

 gridDimensions = size(X);

 VppGrid =
zeros(gridDimensions(2),gridDimensions(1),gridDimensions(3));
 VppGrid(1:end) = Vpp(1:end);
 VppGrid = permute(VppGrid, [2,1,3]);

 [Ex,Ey,Ez] = gradient(VppGrid, xStep, yStep, zStep);
 Ex = -1*Ex;
 Ez = -1*Ez;
 Ey = -1*Ey;
20

Data Processing Cont’d
 Peak-to-peak voltages corresponding to
biphasic pulses beginning with the
cathodic phase were assigned as “+”
 Anodic phase-leading signals were
assigned as “-”
+Vpp -Vpp
21
*All current pulses in the experiments have pulse widths of .5ms at 120 Hz

Voltage Distribution, Electric
Fields, and AF Shapes
 The voltage, electric field, and activating function follow the
same shape given a stimulation pattern
 Since the E Field and AF follow the same shape as the
Vpp distribution, we can use any one of the 3 to
visualize the shape of the stimulation signal
26

Voltage Sum
0
0.005
0.01
0.015
0.02
0.025
-2 -1 0 1 2
Vpp(V)
X Distance (mm)
Monopolar Vpp Distribution
Vpp at Z = 100 um
E6: 50 uA, Cathodic
Pulse First
E11: 0 uA
0
0.005
0.01
0.015
0.02
0.025
-2 -1 0 1 2
Vpp(V)
X Distance (mm)
Monopolar Vpp Distribution
Vpp at Z = 100um
E6: 0 uA
E11: 50 uA, Cathodic
Pulse First
0.015
0.02
0.025
0.03
0.035
0.04
0.045
-2 -1 0 1 2
Vpp(V)
X Distance (mm)
Sum of Monopolar Vpp Distributions
Vpp at Z = 100 um
E6: 50uA, Cathodic Pulse
First
E11: 50uA, Cathodic Pulse
First
27

0.015
0.02
0.025
0.03
0.035
0.04
0.045
0.05
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
Vpp(V)
X Distance (mm)
Calculated (Summed) Monopolar Vpp Distribution
Vpp at Z = 100 um
E6: 50uA, Cathodic Pulse First
E11: 50uA, Cathodic Pulse First
28

0.015
0.02
0.025
0.03
0.035
0.04
0.045
0.05
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
Vpp(V)
X Distance (mm)
Measured Monopolar Vpp Distribution
Vpp at Z = 100um
E6, 50uA, Cathodic Pulse First
E11, 50 uA, Cathodic Pulse First
29

Summing Voltages
 When multiple electrodes are on, the resulting
voltage distribution in space is equal to the sum of
the voltages coming from each electrode
0.015
0.02
0.025
0.03
0.035
0.04
0.045
0.05
-2 -1 0 1 2
Vpp(V)
X Distance (mm)
Measured Monopolar Vpp
Distribution
0.015
0.02
0.025
0.03
0.035
0.04
0.045
0.05
-2 -1 0 1 2
Vpp(V)
X Distance (mm)
Calculated Monopolar Vpp
Distribution
30Raw Data

Focusing Stimulation
Patterns
Monopolar Control
Control 1: 50 uA Amplitude
+x
+y
32

Patterns
Tripolar Focusing
Middle Electrode: 100uA Amplitude
Side Electrodes: 50uA Amplitude
+x
+y
33

Patterns
Tripolar Focusing
+x
+y
34

Patterns
Pentapolar Focusing
+x
+y
35

Patterns
Pentapolar Focusing
+x
+y
36

Quantifying Peak Width and
Height
V-pp
Peak Width
75% of peak Vpp
37
Peak Height
0 V

Relative Vpp Peak Widths
Mean Stdev (n = 3)
Monopolar 1 0
Tripolar 0.25 0.028
Pentapolar 0.41 0.031
Relative Peak Width in X Direction
Mean Stdev (n = 3)
Monopolar 1 0
Tripolar 0.33 0.036
Pentapolar 0.37 0.053
Relative Peak Width in Y Direction
38Spreadsheet Data

Relative Vpp Peak Heights
Mean Relative
Height Stdev (n = 3)
Monopolar (100 uA) 1 0
Monopolar (50 uA) 0.51 0.0057
Monopolar (20 uA) 0.20 0.0093
Tripolar (50 uA ↓, 100 uA ↑, 50 uA ↓) 0.20 0.0077
Pentapolar (100 uA ↑, 25 uA ↓ 4x) 0.20 0.0093
Tripolar (100 uA ↓, 200 uA ↑, 100 uA ↓) 0.43 0.0048
Pentapolar (200 uA ↑, 50 uA ↓ 4x) 0.48 0.014
39Spreadsheet Data

Spread and Peak
Comments
 Tripolar and Pentapolar stimulation focus current
in the X and Y directions
 Tripolar focuses the current better than Pentapolar
in the X direction
 Tripolar and Pentapolar have similar current
spread in the Y direction, but these results may be
due to experimental error
 Tripolar and Pentapolar have peaks that are ~20%
of the monopolar
40

Steering Strategy #1
50 uA Amplitude, 120 Hz, .5 ms PW
+x
+y
42

43
+.05 mm

44
+.05mm

45
+ .05 mm

Comments
 The E Field and AF follow the same
shape as Vpp
 None of the signals peak in the space
between the electrodes given the test
conditions
 The signal can peak in the middle if the
electrodes are close enough
46

120 Hz, .5 ms PW
Left Electrode: 75uA Amplitude
Right Electrode: 25uA Amplitude
+x
+y
47

48Spreadsheet Data
-0.01
-0.005
0
0.005
0.01
0.015
-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5
Vpp(V)
X Distance (mm)
Asymetric Tripolar Vpp Curve
Asymetric Tripolar Vpp, Probe Height = 50um
E6 25uA Anodic Pulse First
E11 100uA Cathodic Pulse First
E15 25uA Anodic Pulse First
0.015
0.02
0.025
0.03
0.035
0.04
0.045
-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5
Vpp(V)
X Distance (mm)
Monopolar Vpp Curve
Asymetric Tripolar Vpp, Probe Height = 50um
E6 0uA
E11 100uA Cathodic Pulse First
E15 0uA
Peak occurs at x = .04 mm
Peak occurs at x = -0.02 mm

50 uA Amplitude, 120 Hz, .5 ms PW
+x
+y
49

0
0.005
0.01
0.015
0.02
0.025
-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5
Vpp(V)
X Distance (mm)
Monopolar Vpp Distribution Vpp at Z = 100um
E6: 0 uA
E11: 50 uA, Cathodic Pulse First
-0.006
-0.004
-0.002
0
0.002
0.004
0.006
0.008
-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5
Vpp(V)
X Distance (mm)
Observed Bipolar Vpp Distribution Vpp at Z = 100um
E6, 50uA, Anodic Pulse First
E11, 50 uA, Cathodic Pulse
First+Sheet1!$A$3
Peak occurs at
x = .08 mm
Peak occurs at
x = .01 mm
50Spreadsheet Data

Current Steering Comments
 Current is not necessarily “steered”
additively. This is possible only when the
electrodes are close (i.e. Strategy 1)
 May be possible through subtractive
strategies (i.e. Strategies 2 and 3)
 Limited current steering effects
 Unclear how much the peak height is affected
 The extent to which the current is steered for
strategies 2 and 3 is inconclusive without
repeated experiments
51

Peak Fusion
 At various heights above the array,
determine the spacing between two
electrodes at which the peaks fuse
50
uA
50
uA
L
120 Hz, .5 ms PW
53

Peak Fusion
V-pp 1 V-pp 2
L
54

Peak Fusion
V-pp 1 V-pp 2
L
55

Peak Fusion
Critical L
V-pp 1 + 2
56

“Critical L” vs. Height Above
Array
y = 0.0028x + 0.0587
R² = 0.9897
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 100 200 300 400 500 600 700
ElectrodeCenter-to-CenterSpacingatWhichPeaksFuse
(mm)
Z Distance Away from Electrode Surface (um)
50 uA
100 uA
150 uA
200 uA
Linear (100 uA)
57Spreadsheet Data

Distinguishable Peaks
 At various heights above the array, determine
the spacing between two electrodes at which
the signals become two peaks
L
V-pp 1 + 2
60

V-pp 1 V-pp 2
L
61

V-pp 1 V-pp 2
Critical L
h1
h2
ℎ1 − ℎ2 ≥ 2𝑚𝑉
62

Distinguishable Peaks Example
63
h2
h1
h1-h2 = 2mV

Critical L for Distinguishable
Peaks vs. Z Distance
64
y = 8.04x + 0.248
R² = 0.9977
0
0.5
1
1.5
2
2.5
0 0.05 0.1 0.15 0.2 0.25 0.3
CriticalL(mm)
Z Distance Above Electrode Surface (mm)
50 uA
Linear (50 uA)
Spreadsheet Data

y = 4.98x + 0.2403
R² = 0.994
0
0.5
1
1.5
2
2.5
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
CriticalL(mm)
100 uA
Linear (100 uA)
65Spreadsheet Data

66
y = 4.8971x + 0.2898
R² = 0.9933
0
0.5
1
1.5
2
2.5
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
CriticalL(mm)
200 uA
Linear (200 uA)
Spreadsheet Data

Fused Critical L’s and
Distinguishable Critical L’s
67
y = 0.0028x + 0.0587
R² = 0.9897
y = 0.008x + 0.248
R² = 0.9977
y = 0.0051x + 0.185
R² = 0.9912
0
0.5
1
1.5
2
2.5
0 100 200 300 400 500 600 700
ElectrodeCenter-toCentersSpacingat(mm)
Z Distance Away from Electrode Surface (um)
50 uA Fused
100 uA Fused
150 uA Fused
200 uA Fused
50 uA Distinguishable
Linear (100 uA Fused)
Linear (50 uA Distinguishable)
Linear (100 uA Distinguishable)
Fused Region
Distinguishable
Peaks Region
Spreadsheet Data
In-Between
Fused and
Distinguishable

Tripolar Focusing Electrode
Spacing
 Determine the relationship between electrode spacing and
peak width in tripolar focusing
 Determine the relationship between electrode spacing and
peak height in tripolar focusing
 Peak heights and widths are normalized to the Voltage
distribution of monopolar current pulses
50
uA
100
uA
50
uA 120 Hz, .5 ms PW
68

Spacing
V-pp
L L
Peak Width
75% of peak Vpp
69

Spacing
V-pp
L L
70

Spacing
V-pp
L L
71

Spacing: Peak Height vs. L
y = -0.0849x2 + 0.3423x - 0.0175
R² = 0.9995
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
NormalizedPeakHeight
Electrode Center to Center Spacing (mm)
Series1
Poly. (Series1)
72Spreadsheet Data Raw Data

Spacing: Peak Width vs. L
y = -0.063x2 + 0.2526x + 0.0232
R² = 0.9936
0
0.05
0.1
0.15
0.2
0.25
0.3
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
NormalizedPeakWidth
Electrode Center to Center Spacing (mm)
Series1
Poly. (Series1)
73Spreadsheet Data Raw Data

Summary of Results
 Tripolar stimulation focuses the current better than
pentapolar and monopolar
 All multipolar focusing requires more current
 Current steering is not possible with the given array
design, but can be achieved if electrodes are close
enough
 Current steering could be achieved subtractively, but
the extent is not clear
 Electrode spacing is linearly related to the peak
separation when two electrodes are stimulated
 Electrode spacing is linearly related to peak width
 Electrode spacing has a polynomial relationship with
the tipolar-focused Vpp peak
74

Limitations and Sources of
Error
 AF oversimplifies electrode geometry
 Overestimates the steepness and sharpness of AF
distributions
 Arbitrarily assigning +/- Vpp values creates noise
through human error
 Qualitative nature of determining “peak fusion”
 Surface/array tilt
 Inherent noise within each scan especially when
measured Vpp < 10mV
 Quality of micro-probe tip
 Variability across measurements that aren’t conducted
on the same day
 Varying concentration of PBS
76

Future Studies
 Repeated asymmetric current steering
trials
 Other stimulation patterns
 Running all future experiments with
higher stimulation amplitudes
 Computational tissue models
 Approximate the direction of neuron
fibers so the second derivative of
voltage can be taken to find AF
77

Second Sight Presentation

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