Differential effects of stimulus strength and volitional control ondominance durations in bistable perception

James Rankin1 and John Rinzel1,21Center for Neural Science, New York University

2Courant Institute of Mathematical Sciences, New York University Center for Neural ScienceCNSNYU/

Poster summary: Bistable perception has been widely studied in the visual system and, morerecently, in the auditory system where ambiguity in sensory information leads to spontaneous shifts inperception. Common dynamical characteristics have been found across different sensory cues anddifferent sensory modalities, however, the different way in which stimulus strength manipulations andvolitional control affect dynamics are not fully understand. We study this aspect of perceptualbistability with reduced rate models.

Motivation and previous results

Input strength modulation: visual bistable stimuli

Stimulus strength manipulations about equidominance behave consistently across three different visualcues [1]:

Generalised LeveltsII: The meandominance durationof the strongerpercept changesmore than that ofthe weaker percept

Volitional control: visual plaids and auditory streaming

Bistability between an integrated/grouped and a segregated/split percept share common characteristicsfor visual plaids and auditory streaming (exclusivity, randomness, inevitability) [2].

I Study also looked at the affect of volitional control (e.g.“attend integrated”)

I Not accounted for by adjusting input strengths.

I Mean dominance duration of the unattendedpercept changes more than that of theattended percept

Auditory streaming paradigm

A widely studied psychoacoustics stimulus (van Noorden 1975, Denham et al 2010, [2]):

Neural correlates of initial transition from Integrated to Segregated [4]:

I Single unit recordings in awake rhesusmonkey A1

I Initially integrated, later, segregated.

I Observations are consistent withhuman psychoacoustics.

Our goals

1) Propose a new mechanism to account for the difference between input strength manipulations and theeffect of volition.

2) Develop a model for the auditory streaming case where the inputs are periodic.

3) First test the mechanism in a canonical rivalry model, then in our auditory streaming model.

Models and parameter study

Rivalry model with mutual inhibition, slow adaptation and normalised inputs

Introduce normalisation of inputs [1] to standard, widely-studied model:

Model equations are given by

τuu1 = −u1 + Sf

(−βu2d1 − γa1 + I1

),

τuu2 = −u2 + Sf

(−βu1d2 − γa2 + I2

),

τaa1 = (−a1 + u1),

τaa2 = (−a2 + u2),

where Sf is a sigmoidal firing rate function.

Bifurcation diagram (see [3] and others) for symmetric input I0 and no volition ψ = 0:

0 1 2 30

0.2

0.4

0.6

0.8

1

Activity(u

1)

I0 0 1 2 30.5

1

1.5

2

Period(s)

I0 0 0.5 1 1.5 20

0.2

0.4

0.6

0.8

1

Activity

u1u2a1a2

With a bias to pop. #2 (ψ > 0), inputs given by:

Iv = ψSv(u2), I1 = I0

(I1 + Iv

I1 + I2 + Iv

), I1 = I0

(I2

I1 + I2 + Iv

).

Auditory streaming model with recurrent excitation

Each of three populations receives a different proportion of input dependent on the frequency separation φbetween two tones A and B.

Periodic ABA- sequence input:

0 200 4000

0.2

0.4

0.6

t(s)

Amplitude

IAIB

τuu =− u + Sf(βuuru − βvu(v1 + v2)

− γau + Sφ(IA + IB)),

τaau =(−au + u), τrru = (−ru + u),

τuv1 =− v1 + Sf (βuur1 − βuvu− γa1 + IA) ,

τaa1 =(−a1 + v1), τrr1 = (−r1 + u),

τuv2 =− v2 + Sf (βuur2 − βuvu− γa2 + IB) ,

τaa2 =(−a2 + v2), τrr2 = (−r2 + u).

I Input IA to the “A” population v1 and IB to the“B” population v2

I For increasing φ, less input to the “AB”population u as controlled by a sigmoid functionSφ

I A recurrent ndma excitation r keeps activityup when input is low or silent.

I Bifurcation study with constant IA = IB = Ibase,

I Simulations with Ibase = 0 and periodic input shown above:

0 0.2 0.4 0.60

0.2

0.4

0.6

0.8

1

Activity

Ibase

βuu = 0

0 0.5 1 1.5 20

0.2

0.4

0.6

0.8

1

Activity

0 0.2 0.4 0.60

0.2

0.4

0.6

0.8

1

Activity

Ibase

βuu = 0.5

0 1 2 3 40

0.2

0.4

0.6

0.8

1

t(s)

Activity

Recurrent excitation allows for a sustained response with “AB” (integrated) or “A” + “B” (segregated)dominant populations.

Numerical methods

I Constant-input cases studied directly with AUTO07p.

I Periodic-input cases using Matlab’s ode23t with reduced RelTol and MaxStep.

Differential effects of stimulus strength and volitional control Hy

Set parameters in both models for equidominance

As in [1] and [2] we tune the parameters in both models for equidominance:

I between u1 and u2 in the canonical model (T1 = T2)

I between the integrated and segregated states in the auditory model (Tint = Tseg)

0 1 2 3 4 50

0.2

0.4

0.6

0.8

1

Activity

t(s)

u1u2a1a2

0 2 4 6 8 10 12 140

0.2

0.4

0.6

0.8

1

t(s)

Activity

Input and control manipulations for the canonical rivalry model

For stimulus strength manipulations the dominantstate is affected the most, as in [1].

Increase input to pop. #1: I1/I2 > 1

0.9 1 1.10

0.5

1

1.5

Dom.durations(s)

I1/I2

T1T2

0 1 20

0.5

1

Activity

t(s)

u1u2a1a2

With volitional bias towards one state, the otherduration is affected the most, as in [2].

Attend to state #1: ψ > 0

−0.2 0 0.20

0.5

1

1.5

Dom.durations(s)

ψ

T1T2

0 1 20

0.5

1

Activity

t(s)

u1u2a1a2Iv

Input and control manipulations for the auditory streaming model

With a bias to integrated the inputs to the u-, v1-, and v2-equations become

Iu = (1 + ψSv ([v1 + v2]/2)Sφ(IA + IB), Iv1 = IA, Iv2 = IB.

Increase input to integrated: φ > 40

35 40 450

1

2

3

4

5

Do

m.

du

ratio

ns (

s)

φ

TsegTint

4 5 6 7 80

0.2

0.4

0.6

0.8

1

t(s)

Activity

Attend to integrated: ψ > 0

−5 0 50

1

2

3

4

5

Do

m.

du

ratio

ns (

s)

ψ

TsegTint

4 5 6 70

0.2

0.4

0.6

0.8

1

t(s)

Activity

Same result holds for the auditory model.

Key results:I The proposed volitional mechanism with state-dependent inputs resolves the apparent conflict by

accounting for differences between direct input strength manipulations and top-down attention.

I A three-population model with periodic inputs for the auditory case has been presented, to which ourgeneral result extends.

I Our modeling results can explain important differences between input strength andattention that generalize across sensory modalities.

[1] Moreno-Bote R, Shpiro A, Rinzel J and Rubin N, Alternation rate in perceptual bistability ismaximal at and symmetric around equi-dominance. J. Vision 2010[2] Pressnitzer D, and Hupe, JM, Temporal dynamics of auditory and visual bistability revealcommon principles of perceptual organization. Current Biology 2006[3] Shpiro A, Curtu R, Rinzel J and Rubin N, Dynamical characteristics common to neuronalcompetition models. J. Neurophys 2007[4] Micheyl, C, Tian B, Carlyon RP and Rauschecker JP, Perceptual organization of tonesequences in the auditory cortex of awake macaques, Neuron 2005

e-mail: james.rankin@nyu.edu web: http://www-sop.inria.fr/members/James.Rankin/