Interaction between spatial perception and temporal perception enables preservation of cause-effect relationship: Visual psychophysics and neuronal dynamics

Pratik Purohit; Prasun K. Roy; Pratik Purohit; Prasun K. Roy

doi:10.3934/mbe.2023400

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 5: 9101-9134. doi: 10.3934/mbe.2023400

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Research article Special Issues

Interaction between spatial perception and temporal perception enables preservation of cause-effect relationship: Visual psychophysics and neuronal dynamics

Pratik Purohit ¹,
Prasun K. Roy ^{1,2
,
,}

1.
School of Biomedical Engineering, Indian Institute of Technology (BHU), Varanasi 221005, India
2.
Department of Life Sciences, Shiv Nadar University (SNU), Delhi NCR, Dadri 201314, India

Academic Editor: Domenico Tegolo

Received: 02 December 2022 Revised: 20 February 2023 Accepted: 21 February 2023 Published: 13 March 2023

Introduction
Visual perception of moving objects is integral to our day-to-day life, integrating visual spatial and temporal perception. Most research studies have focused on finding the brain regions activated during motion perception. However, an empirically validated general mathematical model is required to understand the modulation of the motion perception. Here, we develop a mathematical formulation of the modulation of the perception of a moving object due to a change in speed, under the formulation of the invariance of causality.

Methods
We formulated the perception of a moving object as the coordinate transformation from a retinotopic space onto perceptual space and derived a quantitative relationship between spatiotemporal coordinates. To validate our model, we undertook the analysis of two experiments: (i) the perceived length of the moving arc, and (ii) the perceived time while observing moving stimuli. We performed a magnetic resonance imaging (MRI) tractography investigation of subjects to demarcate the anatomical correlation of the modulation of the perception of moving objects.

Results
Our theoretical model shows that the interaction between visual-spatial and temporal perception, during the perception of moving object is described by coupled linear equations; and experimental observations validate our model. We observed that cerebral area V5 may be an anatomical correlate for this interaction. The physiological basis of interaction is shown by a Lotka-Volterra system delineating interplay between acetylcholine and dopamine neurotransmitters, whose concentrations vary periodically with the orthogonal phase shift between them, occurring at the axodendritic synapse of complex cells at area V5.

Conclusion
Under the invariance of causality in the representation of events in retinotopic space and perceptual space, the speed modulates the perception of a moving object. This modulation may be due to variations of the tuning properties of complex cells at area V5 due to the dynamic interaction between acetylcholine and dopamine. Our analysis is the first significant study, to our knowledge, that establishes a mathematical linkage between motion perception and causality invariance.
- space perception,
- time perception,
- visual psychophysics,
- retinotopic map,
- area MT/V5,
- acetylcholine,
- dopamine,
- MRI tractography,
- dendritic synapse,
- Lotka-Volterra equation
Citation: Pratik Purohit, Prasun K. Roy. Interaction between spatial perception and temporal perception enables preservation of cause-effect relationship: Visual psychophysics and neuronal dynamics[J]. Mathematical Biosciences and Engineering, 2023, 20(5): 9101-9134. doi: 10.3934/mbe.2023400

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Abstract

Introduction

Visual perception of moving objects is integral to our day-to-day life, integrating visual spatial and temporal perception. Most research studies have focused on finding the brain regions activated during motion perception. However, an empirically validated general mathematical model is required to understand the modulation of the motion perception. Here, we develop a mathematical formulation of the modulation of the perception of a moving object due to a change in speed, under the formulation of the invariance of causality.

Methods

We formulated the perception of a moving object as the coordinate transformation from a retinotopic space onto perceptual space and derived a quantitative relationship between spatiotemporal coordinates. To validate our model, we undertook the analysis of two experiments: (i) the perceived length of the moving arc, and (ii) the perceived time while observing moving stimuli. We performed a magnetic resonance imaging (MRI) tractography investigation of subjects to demarcate the anatomical correlation of the modulation of the perception of moving objects.

Results

Our theoretical model shows that the interaction between visual-spatial and temporal perception, during the perception of moving object is described by coupled linear equations; and experimental observations validate our model. We observed that cerebral area V5 may be an anatomical correlate for this interaction. The physiological basis of interaction is shown by a Lotka-Volterra system delineating interplay between acetylcholine and dopamine neurotransmitters, whose concentrations vary periodically with the orthogonal phase shift between them, occurring at the axodendritic synapse of complex cells at area V5.

Conclusion

Under the invariance of causality in the representation of events in retinotopic space and perceptual space, the speed modulates the perception of a moving object. This modulation may be due to variations of the tuning properties of complex cells at area V5 due to the dynamic interaction between acetylcholine and dopamine. Our analysis is the first significant study, to our knowledge, that establishes a mathematical linkage between motion perception and causality invariance.

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