1. Rod-Cone Convergence
In The Retina
PhD Thesis Presentation
12th
January 2014
Presented By:
Kendi Muchungi
Supervised By:
Dr. Matthew Casey
Dr. André Grüning

2. How does one see?
2Source:
University of Utah; Webvision, 2011

3. The Retina: Participating Neurons (i)
3
- Light Sensitive Neurons (Photoreceptors)
- Rods
- Cones
- Horizontal Cells (HCs) [Lateral Neurons]
- Bipolar Cells (BCs)
- Amacrine (AII) [Lateral Neurons]
- Retinal Ganglion Cells (RGCs)

4. The Retina: Participating Neurons (ii)
4
1
2
CONE
3
2
4
3
Light
OuterPlexiformLayerInnerPlexiformLayer
ROD
HC
RNB CNB
AII
CFB
CNG
CFG
HC – Horizontal Cell
RNB – Rod ON Bipolar Cell
CNB – Cone On Bipolar Cell
CFB – Cone Off Bipolar Cell
AII – Amacrine Cell
CNG – Cone On Ganglion Cell
CFG – Cone Off Ganglion Cell
1 - Electric Gap Junction (Coupling)
2 - Sign Reversing Symbol
3 - Synapse
4 - Sign Conserving Symbol
Source:
Muchungi & Casey, 2012

5. A little by the way …..
5
Source:
Deakin University, 2014

6. How clearly can one see?
 What can you see at 20 feet?
 Visual Acuity
=> Optical and Neural Factors
 Focus within the eye
 State and function of the Retina
 Faculty of the brain
6

7. For this Presentation
- Motivation
- Functions
- Existing Models
- Research Question
- Our Model
- Significance of Our Model
- Conclusion
- Application
- Future Work
7

8. Initial Motivation
Retinal degeneration is the cause of about 50%
of the existing cases of total blindness . (Graf et
al., 2007)
Sadly, no medical treatment exists that can help
with the regeneration of the affected retina
tissue/neurons.
Retinal prosthetics: Computational simulations
inform their design and development.
8

9. Hence ……..
Our research
–Biologically inspired model of the retina
Because
1) The retina outperforms existing man-made image
acquisition devices.
2)Inform and motivate the design and development
of retinal implants/prosthesis.
9

10. The Retina: Her Functionality
 Light adaptation
Allows for visual perception even when there is a dynamic
range of light intensity
 Contrast Gain Control
Allows for the perception of the presence of contrast, however
subtle; manages sensitivity to the presence of contrast
 Spike Generation
Generates action potential [ON/OFF]
10

11. Existing Retina Models: Light Adaptation
Computer Retina
(Shah & Levine,
1996)
Neural Model
(Wilson, 1996)
Silicon Retina
(Zaghloul &
Boahen, 2006)
Virtual Retina
(Wohrer &
Kornprobost, 2009)
Aspects of
Light
Adaptation
1. Phototransduction
2. Cone--Cone Coupling
3. HC feedback
1. Phototransduction
2. Cone-Cone Coupling
3. HC feedback
1. Phototransduction
2. Cone--Cone Coupling
3. HC feedback
1. Phototransduction
2. Cone-Cone Coupling
3. HC feedback
How they
captured
these aspects
1. Low-pass temporal filter
2. Gaussian Operator
3. Difference of Gaussians
(D-o-G)
4. Michaelis-Menten
function
1. Low-pass temporal
filter
2. Gaussian Operator
3. D-o-G
4. Michaelis-Menten
function
1. nMOS transistors
2. Synaptic strengths
adjusted
3. Subtractive HC
feedback
1. Low-pass filters
2. Difference of Dirac
3. D-o-G
4. Gaussian Operator
Comments 1. 1st
to model dynamic
adaptation
2. Use a visual acuity
function for cone-cone
coupling
1. Single nonlinear
differential equation
for each retina neuron
2. Temporal mapping
only
1. Captured all aspects of
light adaptation and
fabricated a retina
using silicon chips
1. Linear filters throughout
model
2. Adapted for large-scale
simulations
11

12. Existing Retina Models: Contrast Gain Control
Computer Retina
(Shah & Levine,
1996)
Neural Model
(Wilson, 1996)
Silicon Retina
(Zaghloul &
Boahen, 2006)
Virtual Retina
(Wohrer &
Kornprobost, 2009)
Aspects of
Contrast Gain
Control
1. ON pathways
2. Midget and Diffuse
BCs
3. Antagonistic
morphology of retina
neurons in the IPL
and Ganglion Layer
1. ON and OFF pathways
2. Midget and Diffuse
BCs
3. Antagonistic
morphology of retina
neurons in the IPL
and Ganglion Layer
1. ON and OFF pathways
2. BCs
3. Narrow and Wide
Amacrine
1. ON and OFF pathways
2. Diffuse BCs
3. Antagonistic morphology
of retina neurons in the
IPL and Ganglion Layer
How they
captured these
aspects
1. Low-pass filters
2. Gaussian Operators
3. D-o-G
4. Arctangent Function
1. Non-linear differential
equation
2. Divisive feedback from
Amacrine Cells (A+)
1. Transistors
(Increase/Decrease
Voltage for
excitation/inhibition)
1. Low-pass filters
2. Gaussian Operators
3. D-o-G
4. Non-linear divisive
feedback loop
Comments 1. No involvement of
Amacrine cells
1. Incorporates Amacrine
cells
1. Switch between ON
and OFF pathways (not
very parallel)
2. Divisive feedback from
Narrow and Wide
Amacrine
1. Allow the level of
luminance to influence
CGC
12

13. Existing Models: Biological Aspects Established
13
Light Adaptation Contrast Gain Control
Participating Neurons and Pathways
1) Cone Specific
2) No Rod Influence
1) ON & OFF Pathways
2) Midget & Diffuse Bipolar
Cells
Biological Processes Involved
1) Phototransduction
2) Cone-cone coupling
3) Negative Feedback
1) Concentric Morphology
2) Divisive Feedback

14. Existing Models: Mathematical Approximations
14
1. Low-pass filter
1. Gaussian Operator
1. Difference of Gaussians (D-o-G)
1. Michaelis-Menten Function
Kτ t;τ( ) =
e
−t
τ
τ
Gσ x, y( ) =
1
2πσ 2
e
−( x2+y2 )
2σ 2
CS x,y,t( ) = αCK t;τC( ) G x,y;σ C( ) −αSK t − d;τ S( ) G x, y;σ S( )
P I( ) =
In
In
+
kr
kb
A +kr





÷
n









÷
÷
÷
÷
÷
Pmax

15. What is New?
Recent research (Thoreson, 2007; Trumpler, 2008;
Pang, 2010; Schiller, 2010) point to the importance
of the connections between our Rod and Cone
pathways.
1) Rods and Cones do have electrical connections
between them; Gap junctions [Rod-Cone Coupling]
2) By the use of lateral neurons; Horizontal Cells and
Amacrine cells
15

16. Research Questions
1. What effect does rod-cone convergence have
on retina functionality; light adaptation and
contrast gain control?
2. How might this convergence be exploited?
16

17. Our Retina Model: Biological Aspects
17
Light Adaptation Contrast Gain Control
Participating Neurons and Pathways
1) Cone Specific
2) With Rod Influence
1) ON & OFF Pathways
2) Diffuse Bipolar Cells
3) Rod ON Bipolar Cells
4) Amacrine Cells
Biological Processes Involved
1) Phototransduction
2) Cone-cone Coupling
3) Rod-cone Coupling
4) Negative Feedback
1) Concentric Morphology
2) Divisive Feedback

18. Schematic Representation: Light Adaptation
18
CONE CONE
BasicROD
or
BioROD
S(x,y,t)T(x,y,t)
HC
H(x,y,t)
- +
I(x,y,t)
coneResponse(x,y,t)
rodResponse(x,y,t)
Temporal Extent Spatial Extent

19. Spatial Extent: Light Adaptation
Incorporated Rod model developed by Lamb
and Pugh in 1992
Integration
1.Rod output gives us our spatial extent
2.Is a 10th
of the driving ambient intensity within
the OPL
19

20. Biological Evaluation: Light Adaptation (i)
Using Threshold vs Intensity (tvi) function
To steady background intensity, flash intensities given by 10×2p
td, where p is an
integer in 0 ≤ p ≤ 5 (Hood, 1998).
20
Source:
Schnapf et al., 1990

21. Biological Evaluation:
Light Adaptation (ii)
To attain results comparable to biology
-It took evaluating four variations of our model
-Determined the need for a ‘rod input factor’
(rif)
- rif is dynamic
- Pegged to existing level of light intensity
- Allowed for close replication of input intensity
- Response to the tvi function closely replicating
biology
21

22. Schematic Representation: Contrast Gain Control
22

23. Spatial Extent: Contrast Gain Control
Incorporated
1.Rod ONBC model developed by Shapley & Enroth-
Cugell in 1973 (Cat)
2.Amacrine (AII) model by using Michaelis-Menten
Function and low-pass filter (tau = 80ms)
Integration
1.Rod ONBC output gives the spatial extent
2.Is a 10th
of the divisive feedback Spatio-temporal
intensity.
23

24. Biological Evaluation: Contrast Gain Control (i)
24Source:
Baccus & Meister, 2002

25. Biological Evaluation:
Contrast Gain Control (ii)
25
- No obvious value was attributed to Rod ONBC time constant
- Determined a range
- Lower bound 0.05ms [Wohrer & Kornprobst, 2009]
- Upper bound 140ms [Wilson, 1997]
- To allow for ease of testing we narrowed down the range
- Lower bound 1ms
- Upper bound 10ms
- At 4 different time steps
- We then carried out 40 tests
- We then concluded on a time constant of 7ms

26. Rod Influence Significance (i)
26
 Quantitative Approach
 Signal-to-Noise Ratio (SNR)
Why?
Point to SNR being improved by Rod-Cone
Convergence [Thoreson, and by Trümpler et. al]
 Compare
- Unsharp Mask [USM]
Contrast Enhancement Algorithm
- With rod influence [BioRod] [CGC]
- No rod influence [NoRod] [CGCNoRod]

27. Rod Influence Significance (ii)
27
To facilitate this analysis, we adapted the brightness of a
segment of input stimuli
1)Obtain Mean
2)Subtract Mean
1)Add back a fraction of the Mean
I ' x, y( ) = I x, y( ) −µ 1+α( )
µ =
I x, y( )
n
0.00 1.00 2.00 3.00 4.00 5.00
Lena

28. Significance of Analysis: Implications
28
SNR 
LA CGC
Contrast is
perceived in spite
of varying
luminance levels
High sensitivity
to subtle
presence of
contrast
SD 
LA CGC
Visual
Perceptual
Consistency
Contrast
Perceptual
Consistency
Signal-to-Noise Ratio (SNR) Standard Deviation (SD)

29. Implications for Light Adaptation (i)
29
0.00 2.00 3.00 4.00 5.001.00
Unsharp
Mask
Original Image
BioRod
0.00
5.00
10.00
15.00
20.00
25.00
0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
2.25
2.50
2.75
3.00
3.25
3.50
3.75
4.00
4.25
4.50
4.75
5.00
Signal-to-NoiseRatio(SNR)
Factors of Luminance (LF)
USM
BioRod
No Rod Input

30. Implications for Light Adaptation (ii)
30
USM BioRod NoRod
0.00 11.24 3.42 3.42
0.25 13.19 3.42 3.42
0.50 15.86 3.42 3.42
0.75 19.81 14.72 3.42
1.00 23.15 12.99 3.42
1.25 19.07 14.14 3.42
1.50 14.67 15.15 3.42
1.75 11.55 15.77 3.42
2.00 9.23 15.94 3.42
2.25 7.47 15.60 3.42
2.50 6.15 14.95 3.42
2.75 5.20 14.00 3.42
3.00 4.52 13.05 3.42
3.25 4.00 13.31 3.42
3.50 3.63 13.73 3.42
3.75 3.47 14.04 3.42
4.00 3.43 14.34 3.42
4.25 3.42 14.63 3.42
4.50 3.42 14.90 3.42
4.75 3.42 15.23 3.42
5.00 3.42 15.44 3.42

31. Implications for Contrast Gain Control (i)
31
USM CGC CGCNoRod USM CGC CGCNoRod
0.00 17.70 0.00 0.00
0.10 16.38 65.54 0.12 2.60 1.29 49.32 1.82
0.20 15.15 64.14 0.17 2.70 1.10 49.14 1.91
0.30 14.05 62.89 0.22 2.80 0.93 48.95 2.00
0.40 13.05 61.75 0.27 2.90 0.79 48.80 2.09
0.50 12.11 60.83 0.32 3.00 0.66 48.66 2.17
0.60 11.24 59.86 0.37 3.10 0.54 48.55 2.25
0.70 10.43 58.95 0.43 3.20 0.43 48.43 2.34
0.80 9.65 58.10 0.48 3.30 0.33 48.33 2.42
0.90 8.92 57.38 0.53 3.40 0.25 48.25 2.49
1.00 8.23 56.62 0.58 3.50 0.18 48.18 2.57
1.10 7.58 55.91 0.63 3.60 0.13 48.17 2.65
1.20 6.97 55.31 0.68 3.70 0.10 48.16 2.72
1.30 6.38 54.68 0.73 3.80 0.09 48.16 2.79
1.40 5.84 54.09 0.79 3.90 0.08 48.16 2.86
1.50 5.32 53.53 0.86 4.00 0.07 48.16 2.93
1.60 4.82 53.06 0.94 4.10 0.07 48.16 3.00
1.70 4.35 52.56 1.02 4.20 0.07 48.16 3.06
1.80 3.91 52.08 1.10 4.30 0.07 48.16 3.13
1.90 3.48 51.62 1.19 4.40 0.07 48.16 3.19
2.00 3.08 51.24 1.28 4.50 0.07 48.16 3.25
2.10 2.71 50.83 1.37 4.60 0.07 48.16 3.31
2.20 2.37 50.46 1.46 4.70 0.07 48.16 3.38
2.30 2.06 50.16 1.55 4.80 0.07 48.16 3.43
2.40 1.77 49.85 1.64 4.90 0.07 48.16 3.50
2.50 1.52 49.57 1.73 5.00 0.07 48.16 3.56

32. Implications for Contrast Gain Control (ii)
32

33. Implications for Contrast Gain Control (iii)
33

34. Implications for Contrast Gain Control (iv)
34
0.00 1.00 2.00 3.00 4.00 5.00
LenaUSM
CGC
ONBC
CGC
OFFBC
CGCNoRod
ONBC
CGCNoRod
OFFBC

35. Conclusion
Rod-Cone Convergence
a.Improves SNR
-Better perception of contrast [Light Adaptation]
-Increases sensitivity to contrast [Contrast Gain Control]
b.Reduces SD thereby increasing
-Visual perceptual constancy [Light Adaptation]
-Contrast perceptual constancy [Contrast Gain Control]
Rod-Cone convergence improves visual acuity.
35

36. Thesis Contributions
Posters, Papers and Publications
a. Bernstein Conference 2014: Poster presentation
b. ICANN 2012: Paper publication
c. Computing Department PhD Conference 2012:
Paper presentation
d. University of Surrey PhD Conference 2012: Paper
presentation
e. Computing Department PhD Conference 2011:
Poster presentation
36

37. Thesis Contributions
Model Contributions
a. Biologically viable model of the cone pathway: OPL
level with rod-cone integration via rod-cone coupling
b. Biologically viable model of the cone pathway: IPL
level with rod-cone integration via rod Bipolar Cells
and Amacrine Cells
c. Unique method of evaluating model performance.
d. Demonstrated the importance of rod-cone
convergence to visual acuity. 37

38. Applicability
1) Obstacle avoidance in mobile robots
Ryad Benosman and his lab developed an asynchronous
neuromorphic visual sensor.
- Bio-inspired
Incorporates parallel processing (Schiller,2010)
2) Improve visual acuity
Daniel Palanker’s Hensen Lab [Stanford University] made
a major breakthrough in the restoration of sight
- Bio-inspired
Introducing stimulation at the IPL
38

39. Future Work
- Motion
- Colour
- Intrinsically photosensitive
Retina Ganglion Cells (ipRGCs)
39

40. References
40
University of Utah; Webvision, October 8th
2011. The Organization of the Retina and
Visual System: Simple Anatomy of the Retina by Helga Kolb
Deakin University, 2014. Eye Fun; Online Eye Tests. Retrieved from
http://www.deakin.edu.au
K. Muchungi and M. Casey, 2012. Simulating light adaptation in the retina with rod-
cone coupling. ICANN 339-346, Berlin, Heidelberg, Springer-Verlag.
J. L. Schnapf, B. J. Nunn, and D. A. Baylor, 1990. Visual Transduction In Cones of
the Monkey Macaca Fascicularis. 427(1):681-713.
S. A. Baccus and Markus Meister, 2002. Fast and slow contrast adaptation in retinal
circuitry. Neuron, 36(5):909-919.

41. Rod-Cone Convergence
In The Retina
PhD Thesis Presentation
12th
January 2014
Presented By:
Kendi Muchungi || k.muchungi@surrey.ac.uk
Thank You!

42. Parallel Pathways in the Retina
42
 Cone and Rod Pathways
Cones
- Processes lightness
- Processes colour
Rods
- Processes darkness
- Monochromatic
 ON and OFF Pathways
ON
- Respond to light increment
OFF
- Respond to light decrement
 Midget and Diffuse Pathways
Midget
- Colour selective
Diffuse
- Respond to changes in contrast
- Monochromatic

43. 43

44. Michaelis-Menten Function
44
T x, y,t( ) =
I(x, y,t)n
I(x, y,t)n
+
krK t;τCone( )
kb
+ kr





÷
n









÷
÷
÷
÷
÷
Tmax
K(t;τCone ) =
e
−t
τCone
τCone
Input Intensity at position (x,y) at time t
Steepness of response curve
Half-pigment bleach constant
(103td)
Half-saturation constant
(833td)
Maximum
Input Intensity
Receptive Field Time Constant
= 1ms

45. Spatio-Temporal Intensity
Summation of Temporal Intensity with the Spatial Intensity
45
A x, y,t( ) = αTT x, y,t( ) +αSS x, y,t( )
Weighting of Temporal Intensity
= 0.9
Weighting of Spatial Intensity
= 1 - αT

46. Testing for rif (i)
46
50.00
55.00
60.00
65.00
70.00
75.00
80.00
BioRod rif 0.5 rif 1.0 rif 1.5 rif 2.0 rif 2.5 rif 3.0 rif 3.5 rif 4.0 rif 4.5 rif 5.0
Signal-to-NoiseRatio
BioRod and RIF Impact on HC Feedback
Q1
Min
Median
Max
Q3

47. Testing for rif (ii)
47
BasicRod, 12.29
BioRod (rif = 1.0),
7.031
BioRod (rif = 2.5),
17.19
0
2
4
6
8
10
12
14
16
18
20
22
0 1 2 3 4 5
Signal-to-NoiseRatio(SNR)

48. Testing for Rod ONBC Time Constant
48
0
1
2
3
4
5
6
7
8
1 2 3 4 5 6 7 8 9 10 11 12
RodONBCResponse
Time (ms)
Tau 1
TS 1
TS 2
TS 3
TS 4
0
2
4
6
8
1 2 3 4 5 6 7 8 9 10 11 12
RodONBCResponse
Time (ms)
Tau 2
0
2
4
6
8
1 2 3 4 5 6 7 8 9 10 11 12
RodONBCResponse
Time (ms)
Tau 3
0
2
4
6
8
1 2 3 4 5 6 7 8 9 10 11 12
RodONBCResponse
Time (ms)
Tau 4
6
8
esponse
Tau 5
0
2
4
6
8
1 2 3 4 5 6 7 8 9 10 11 12
RodONBCResponse
Time (ms)
Tau 6
0
2
4
6
8
10
1 2 3 4 5 6 7 8 9 10 11 12
RodONBCResponse
Time (ms)
Tau 7
0
2
4
6
8
1 2 3 4 5 6 7 8 9 10 11 12
RodONBCResponse
Time (ms)
Tau 8
0
1
2
3
4
5
6
7
1 2 3 4 5 6 7 8 9 10 11 12
RodONBCResponse
Time (ms)
Tau 9
5
6
7
esponse
Tau 10

49. TTP: Spatial Intensity
Rod Input – Constituting Rod-Cone Coupling
49
S x, y,t( ) = I x, y,t( ) *σS x, y,t( ) K(t;τRod )
σS = αRod I(x, y,t)
Convolution
Weighting of Rod Temporal Intensity
= 100 (Baylor, 1996)
Temporal Latency
Receptive Field Time Constant
= 4ms
(Yau, 1994)

50. Cone-Cone Coupling
The Visual Acuity Function (Shah & Levine,1996)
50
CCoupling x, y,t( ) =
3
2
A(x, y,t)nA
+Qo
nA
A(x, y,t)nA
+δnA





÷
= 0.5
= 65td
= 0.01Number of Coupling Cones

51. Cone Output:
Convolving Spatio-Temporal Intensity with Intensity from adjust Cones
Difference-of-Gaussians to generate final Cone output (with HC feedback)
51
CNoHC x, y,t( ) = A(x, y,t)∗CCoupling (x, y,t)K(t;τCone )
CResponse x, y,t( ) = CNoHC x, y,t( ) −αHC HResponse x, y,t( )
HResponse x, y,t( ) = αHCCNoHC x, y,t( ) K(t;τHC )
CResponse x, y,t( ) = CNoHC x, y,t( ) 1−αHCK(t;τHC )( )

52. The Transduction Process:
The Underlying Biology
52

53. 53
CONE CONE
ST(x,y,t)
HC
H(x,y,t)
- +
I(x,y,t)
coneResponse(x,y,t)
Spatio-Temporal
Extent

54. 54
CONE CONE
ST(x,y,t)
HC
H(x,y,t)
- +
I(x,y,t)
coneResponse(x,y,t)
ConeBC
coneBCResponse(x,y,t)
Spatio-Temporal
Extent