Hypothesis

Serial multi-omic trajectories (proteomics, metabolomics, and flow cytometry immunophenotyping) sampled every 2–4 weeks in ANCA-associated vasculitis (AAV) patients in remission encode topological features — persistent homology barcodes and Betti numbers — that identify hidden dynamical attractors. Patients whose trajectories converge toward a specific attractor basin will relapse within 8–16 weeks, detectable 6–10 weeks before clinical manifestation (BVAS ≥ 1).

Background and Rationale

AAV relapses remain unpredictable. ANCA titers alone have poor positive predictive value (~30–50%), and no single biomarker reliably forecasts flare timing. The immune system in AAV behaves as a high-dimensional nonlinear dynamical system: cytokine networks, neutrophil activation cascades, and B-cell reconstitution interact through feedback loops that resist linear modeling.

Topological Data Analysis (TDA) — specifically persistent homology — captures the shape of data manifolds without requiring linearity or distributional assumptions. In dynamical systems theory, attractors represent stable states toward which trajectories converge. We hypothesize that the pre-relapse immune state constitutes a distinct attractor basin distinguishable from stable remission via TDA applied to time-delay embeddings of multi-omic panels.

Proposed Methodology

1. Cohort: n ≥ 80 AAV patients (GPA + MPA) in clinical remission (BVAS = 0, prednisone ≤ 5 mg/day), followed prospectively for 12 months with sampling every 2 weeks.
2. Multi-omic panel: 92-plex Olink proteomics (inflammation panel), targeted metabolomics (tryptophan-kynurenine pathway, lipid mediators), and 12-color flow cytometry (B-cell subsets, NETs markers, Treg frequency).
3. Time-delay embedding: Construct Takens embeddings (τ = 2–4 weeks, dimension d = 3–5 via false nearest neighbors) for each patient trajectory in the combined feature space (after UMAP reduction to 15–20 dimensions).
4. TDA pipeline: Compute Vietoris-Rips persistent homology (H₀, H₁, H₂) on sliding windows of 6 consecutive timepoints. Extract persistence landscapes and Betti curves as features.
5. Attractor identification: Apply DBSCAN clustering on persistence landscape space to identify distinct trajectory classes. Define "relapse attractor" as the cluster enriched in pre-relapse trajectories (≤16 weeks before BVAS ≥ 1).
6. Prediction model: Train a Bayesian logistic regression (with horseshoe prior for sparsity) on TDA features + clinical covariates (ANCA type, prior relapses, maintenance regimen). Evaluate via leave-one-out cross-validation with calibration plots.

Testable Predictions

• P1: Pre-relapse trajectories will show significantly higher H₁ persistence (indicating cyclic immune oscillations) compared to stable remission (Wilcoxon rank-sum, Bonferroni-corrected p < 0.01).
• P2: The relapse attractor will be identifiable ≥6 weeks before clinical relapse with sensitivity ≥ 0.75 and specificity ≥ 0.80 (PPV ≥ 0.60, NPV ≥ 0.90).
• P3: TDA-based prediction will outperform ANCA titer change alone (ΔAUC ≥ 0.15, DeLong test p < 0.05).
• P4: The dominant H₁ cycle in pre-relapse attractors will correlate with oscillatory dynamics in the kynurenine/tryptophan ratio and CD19+CD27⁻ naïve B-cell reconstitution rate.

Limitations

• Sample size: 80 patients with ~30% expected relapse rate yields ~24 events — adequate for TDA feature extraction but limits the complexity of the prediction model. External validation cohort essential.
• Sampling frequency: Every 2 weeks may miss rapid transitions; continuous wearable inflammatory biomarkers (e.g., CRP via microfluidic patches) could improve temporal resolution in future iterations.
• Takens embedding assumptions: Requires sufficient dimensionality and stationarity within sliding windows — violated during acute transitions. Sensitivity analysis with varying τ and d is mandatory.
• Confounders: Immunosuppressive regimen changes, infections, and vaccinations could perturb trajectories. Propensity-adjusted subgroup analysis required.
• Computational cost: Persistent homology on high-dimensional time series is O(n³) per window; approximate methods (e.g., Ripser) needed for scalability.

Clinical Significance

If validated, TDA-based attractor monitoring could enable preemptive immunosuppression escalation 6–10 weeks before clinical relapse, reducing organ damage (estimated 40–60% reduction in relapse-associated GFR decline based on RAVE trial kinetics). This shifts AAV management from reactive to anticipatory — a paradigm aligned with precision rheumatology. The framework generalizes to any chronic relapsing autoimmune disease modeled as a nonlinear dynamical system.

RheumaAI Research • rheumai.xyz • DeSci Rheumatology