From Observed Viability to Internal Predictive Approximation: A Single-Subject Latent-Space Analysis of Gait Dynamics Under Occlusal Constraint

Q: What is the main goal of Level 5 in this study?

Level 5 tests whether observed longitudinal centroid displacement between M1 and M2 can be internally approximated using a supervised model within the same single-subject dataset.

Q: How were gait measurements collected under different occlusal probes?

Gait data were recorded with instrumented insoles during six occlusal observational probes, and measurements were repeated in two sessions spaced eleven weeks apart while undergoing a structured sensorimotor intervention.

Q: What computational representation is used to model M1–M2 transformations?

A common PCA representation is used to describe the observed M1–M2 transformations in the selected PC1–PC2 coordinate system, and a simplified feed-forward neural network approximates these transformations directly in that coordinate space.

Jul 16, 2026

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The study addresses how to distinguish observable performance, static multivariate representation, longitudinal displacement, and whether observed representational change can be approximated. Building on earlier Level 3 and Level 4 findings that occlusal observational probes cannot be uniquely resolved by aggregate scores or static embeddings, it introduces Level 5: internal predictive approximation of longitudinal centroid displacement. In a Parkinson’s disease participant, gait is recorded with instrumented insoles across six occlusal probes over two sessions, using a PCA coordinate system and a supervised feed-forward neural network with internal test protocols.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages29

Reading Time1 h 13 min

Abstract

Keywords

Introduction

Methodological Framework (Level 3–Level 5)

PCA coordinate representation of M1–M2 transformations

Feed-forward neural network approximation

Internal testing within the single-subject dataset

Findings and Displacement Hierarchy

Core Level 4-aligned model results

Extended six-probe analysis

Limitations and Scope

arXiv :2605 . 15862v2 [ cs .LG] 13 Jul 2026 From Observed Viability to Internal Predictive Approximation: A Single-Subject Latent-Space Analysis of Gait Dynamics Under Occlusal Constraint Jacques Raynal 1,∗ , Pierre Slangen2 , Elsa Raynal3 , Jacques Margerit4 1Laboratory of Bioengineering and Nanosciences (LBN), University of Montpellier, France 2EuroMov Digital Health in Motion, University of Montpellier, IMT Mines Alès, Alès, France 3 Certified Sophrologist and Dental Assistant, Sensorimotor Practice, Montpellier, France 4Emeritus Professor, University of Montpellier, France ∗ Corresponding author: [raynal.cab@gmail.com](raynal.cab@gmail.com) Abstract Understanding adaptive biomechanical systems requires distinguishing between observable performance, static multivariate representation, longitudinal displacement, and the possibility of approximating observed representational change. The preceding Level 3 study showed that neither an aggregated scalar score nor a static exploratory embedding uniquely resolved the occlusal observational probes. The subsequent Level 4 study therefore shifted the analysis from static representational non-identifiability to longitudinal centroid displacement within a common PCA representation. In that selected projection, OC3 showed the lowest M1–M2 centroid displacement, ONL occupied an intermediate position, and OC2.5 showed the highest displacement. The present study introduces a fifth analytical level centered on internal predictive approximation of this observed longitudinal displacement. The term predictive is used here in a restricted methodological sense: it refers to approximation of observed M1–M2 transformations within the same single-subject dataset, not to prospective clinical prediction, patient-level forecasting, or generalization to unseen individuals. Using an exploratory single-subject design in a participant with Parkinson’s disease, gait data were recorded with instrumented insoles under six occlusal observational probes: neutral natural occlusion (ONL), wide open-mouth disengagement without dental contact (OBL), strong voluntary clenching (OSL), a nominal 2.5-degree increase in vertical dimension of occlusion in centric relation (OC2.5), a nominal 3-degree increase in vertical dimension of occlusion in centric relation (OC3), and a nominal 3-degree increase combined with mandibular protrusion and hinge-axis displacement (OC3P) . Two measurement sessions were conducted eleven weeks apart, during which the participant underwent a structured sensorimotor intervention. A common PCA representation was used to describe the observed M1–M2 transformations. A simplified feed-forward neural network was then trained to approximate these transformations directly in the selected PC1–PC2 coordinate system. Occlusal configurations were treated as observational probes applied during measurement, not as continuous causal drivers of longitudinal evolution. Within the core Level 4-aligned analysis, the model approximated the observed centroid displacements and preserved the previously reported Euclidean displacement hierarchy: dOC3 < dONL < dOC2 .5. Within the extended six-probe analysis, the model also approximated condition-level displacementsand preserved the broad structure of the exploratory ordering. Held-out M2 and leave-condition-out analyses were used as internal tests within the same single-subject dataset. A complementary withinsession analysis compared the relative positions of the six probes with respect to the ONL centroid at M1 and M2 . This work remains exploratory, retrospective, representation-dependent, and non-causal. It does not establish clinical predictive validity, causal occlusal effects, validated viability thresholds, therapeutic superiority, or generalizable patient-level prediction. Its contribution is methodological: it examines whether observed longitudinal centroid displacement can be internally approximated within a simplified

FAQs

What is the main goal of Level 5 in this study?

Level 5 tests whether observed longitudinal centroid displacement between M1 and M2 can be internally approximated using a supervised model within the same single-subject dataset.

How were gait measurements collected under different occlusal probes?

Gait data were recorded with instrumented insoles during six occlusal observational probes, and measurements were repeated in two sessions spaced eleven weeks apart while undergoing a structured sensorimotor intervention.

What computational representation is used to model M1–M2 transformations?

A common PCA representation is used to describe the observed M1–M2 transformations in the selected PC1–PC2 coordinate system, and a simplified feed-forward neural network approximates these transformations directly in that coordinate space.

Jul 16, 2026

Upload by Patrick