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<abstract> <sec><title>Introduction</title><p>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.</p> </sec> <sec><title>Methods</title><p>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.</p> </sec> <sec><title>Results</title><p>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.</p> </sec> <sec><title>Conclusion</title><p>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.</p> </sec> </abstract>

Introduction:Alzheimer's disease(AD) displays progressive neurodegenerative atrophy, causing neuronal lossaffecting cognitive skills and memory. As precuneus is associated with episodic memory and is the reflexive self-awareness hub node, we consider precuneus as region-of-interest(ROI) for analysing AD.Objective:The main objective is find AD-caused alteration in nerve fibres, using diffusion tensor imaging(DTI) parameters like Mean Diffusivity(MD), Fractional Anisotropy(FA), and Nerve-tract Parameters, as number, length, volume, density, and thus, analyse the effect on precuneus by AD [when compared to normal subjects(CN)].Materials/Methods:Normals and Alzheimer’s subjects (n=50 each) were scanned with Siemens 3-tesla MRI-scanner. DTI parameters were estimated by DSI-FSL procedure, with statistical analysis usingt-test/ANOVA.Results:While ageing-process occurs in both AD and CN subjects, there is no change in “macro-structural” nerve fibre characteristics (e.g. Tract Indices: Number, density, volume, length). Contrastingly, there is significant alteration in “micro-structural” fibre characteristics, as increase in Mean Diffusivity(p=0.0006) and decrease in Fractional Anisotropy(p=0.0009) in Alzheimer's disease, when compared with normal subjects. Furthermore, comparing left-versus-right brain, Alzheimer’s patients (but not Normal subjects) show diminution in macro-structural nerve characteristics in left precuneus (compared to right precuneus): namely Tract’s number(p=0.0010), length(p=0.0107), volume(p=0.0225), density(p=0.0340).Conclusion:Under neurodegeneration, change in “micro-structural” nerve-fibre characteristics (Tract Indices), as opposed to “macro structural” fibre indices, can be hallmark for AD. Moreover, right precuneus is more protected in AD. Conversely, left precuneus has more neurodegeneration since its blood-flow is supplied by left common-carotid artery (unlike right common-carotid artery), this left artery arises directly from high-pressure aortic flow, transmitting turbulent hemodynamic stress to left precuneus.