1. Computational Modeling of the Auditory Periphery:
From Soundfiles to Spiketrains
Marcos Cantu
Center for Computational Neuroscience and Neural Technology (CompNet)
Graduate Program for Neuroscience (GPN)
Boston University
Figure 11. Circuit model of the DCN that includes all the effects described above. Shaded neurons are the primarily auditory neurons described in Fig. 6. The granule cell and cartwheel cell of the superficial layer and a GABAergic neuron of unknown identity have been added. The relative size of synaptic terminals corresponds roughly to the relative synaptic strength needed to account for the effects described above. (Redrawn from Davis and Young 2000 with permission.)
MCN 2013

2. - Model Sensory Transduction at the Auditory Periphery
Project Aims:
- Model Sensory Transduction at the Auditory Periphery
- Use Natural Ethologically Relevant Stimuli (i.e. Vocalizations)
- Create Large Scale Spiking Network with several Cell Types
I want to see how the circuit reacts to natural sound.

3. Basilar Membrane model (Bank of Bandpass Filters)
Acoustic Stimulus
Basilar Membrane model
(Bank of Bandpass Filters)
Meddis Hair Cell Model
Auditory Nerve Fiber
Spiketrains

4. Patterson-Holdsworth ERB Filter Bank  
Acoustic Stimulus
Auditory Toolbox
by Malcolm Slaney
Basilar Membrane model
(Bank of Bandpass Filters)
Patterson-Holdsworth
ERB Filter Bank  
Auditory Toolbox
by Malcolm Slaney
Ray Meddis,
1986 and 1990 
Meddis Hair Cell Model 
Auditory Nerve Fiber
Spiketrains
Eugene Izhikevich
Spiking Neuron
(2003)

5. From Soundfiles to Spiketrains
 .WAV audiofile
 Gammatone Filterbank
Getting TO the cochlear nucleus.
Before I get to the cochlear nucleus, I should talk about how I got to the cochlear nucleus. That is, how I created the input vector for each timestep of the network.
From sound to spiketrain…
 Meddis Hair Cell Model
 Spiking Izhikevich Neurons

6. Sound to spiketrain Meddis Hair Cell Model
(actually Sound to Probability)
Inner hair cell
Auditory nerve fiber
K is driven by filter respone at frequency
q = free transmitter pool 
c = transmitter at synaptic cleft 
output:
prob(event) = hc(t) dt
w = reprocessed transmitter 
The higher the stimulus,
the higher the permeability (k)

7. Auditory Nerve Fibers (ANFs)
Spiking neurons were modeled with the system of ordinary differential equations developed by Eugene M. Izhikevich :
v’ = 0.04v2 + 5v u + I
u’ = a(bv - u)
with the auxiliary after-spike resetting:
if v >= 30 mV then v  c and u  u + d
“v” corresponds to the membrane potential of the neuron
“u” represents a membrane recovery variable
a, b, c and d are dimensionless parameters
a time scale of recovery,
b the sensitivity of recovery,
c the after-spike reset value of the membrane potential
d the after-spike reset of the recovery variable.
K is driven by filter respone at frequency
Izhikevich, EM: Simple model of spiking neurons.
IEEE Transactions on Neural Networks 2003,
14(6): (2003)

8. From Soundfiles to Spiketrains
 .WAV audiofile
 Gammatone Filterbank
Getting TO the cochlear nucleus.
Before I get to the cochlear nucleus, I should talk about how I got to the cochlear nucleus. That is, how I created the input vector for each timestep of the network.
From sound to spiketrain…
 Meddis Hair Cell Model
 Spiking Izhikevich Neurons

9. Spiking Neuron Model of Dorsal Cochlear Nucleus (DCN): 4 cell types
2 excitatory: Auditory Nerve Fiber (Input to DCN)
Type IV cell (Output Cell of DCN)
2 inhibitory: Type II cell (Low to High Frequency Inhibition)
WBI cell (Wide Band Inhibition)
the responses to sound of DCN neurons display substantial inhibitory influences
the responses to sound of DCN neurons display substantial inhibitory influences

10. Wiring Diagram of Principal Cell Types in the Dorsal Cochlear Nucleus:
ou
This is the circuitry in functional space,
not in physical space.
 Output Cell
Figure 11. Circuit model of the DCN that includes all the effects described above. Shaded neurons are the primarily auditory neurons described in Fig. 6. The granule cell and cartwheel cell of the superficial layer and a GABAergic neuron of unknown identity have been added. The relative size of synaptic terminals corresponds roughly to the relative synaptic strength needed to account for the effects described above. (Redrawn from Davis and Young 2000 with permission.)
This is the circuitry in functional space, not in physical space. 
All three cell types receive feedforward input from frequency tuned Auditory Nerve Fibers (ANFs)
Young and Davis 2001

11. Figure 11. Circuit model of the DCN that includes all the effects described above. Shaded neurons are the primarily auditory neurons described in Fig. 6. The granule cell and cartwheel cell of the superficial layer and a GABAergic neuron of unknown identity have been added. The relative size of synaptic terminals corresponds roughly to the relative synaptic strength needed to account for the effects described above. (Redrawn from Davis and Young 2000 with permission.)

12. Recovering the “Missing Fundamental” with a Feedforward Network
Spiking Network (1000 frequency tuned neurons in each layer)

13. Recovering the “Missing Fundamental” with a Feedforward Network
Spiking Network (1000 frequency tuned neurons in each layer)

14. Feed-Forward Connectivity Matrices
Projection to 1st Population
1st  2nd
2nd  3rd
3rd  4th

15. Spike Timing Dependent Plasticity (STDP)
Connectivity Matrix (previous work)

16. Feed-Forward Connectivity Matrices
1st  2nd
2nd  3rd
3rd  4th

17. Fundamental Frequency (500Hz) Absent in Input Spectrum
Larger Spiking Network (4000 frequency tuned neurons in each layer)

18. Fundamental Frequency (500Hz) Present in Input Spectrum
Larger Spiking Network (4000 frequency tuned neurons in each layer)

19. Future Directions:
Adding Various Forms of Inhibition to Network
Adding “Top-Down” Recurrent Connectivity
Adding Plasticity and Training the Network on Natural Sound