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Practical Geometric and Quantum Kernel Methods for Predicting Skeletal Muscle Outcomes in chronic obstructive pulmonary disease

Azadeh Alavi, Hamidreza Khalili, Stanley H. Chan, Fatemeh Kouchmeshki, Ross Vlahos

TL;DR

This work tackles predicting COPD-associated skeletal muscle outcomes from a compact, biomarker-based dataset. It benchmarks tuned classical baselines, geometry-aware SPD representations, and quantum kernel approaches to model three muscle endpoints: TA weight, specific force, and a muscle quality index. Quantum kernel ridge regression shows the strongest gains on weight (RMSE ≈ 4.41 mg, $R^2$ ≈ 0.605), with clustered quantum kernel features offering robust screening performance (ROC-AUC up to ≈0.90) under a fixed feature budget; SPD descriptors provide consistent but smaller improvements. The findings suggest that non-Euclidean representations and quantum feature lifts can enhance prediction in low-data biomedical problems while preserving interpretability, though repeated-split validation and external data are needed for broader generalization.

Abstract

Skeletal muscle dysfunction is a clinically relevant extra-pulmonary manifestation of chronic obstructive pulmonary disease (COPD) and is closely linked to systemic and airway inflammation. This motivates predictive modelling of muscle outcomes from minimally invasive biomarkers that can be acquired longitudinally. We study a small-sample preclinical dataset comprising 213 animals across two conditions (Sham versus cigarette-smoke exposure), with blood and bronchoalveolar lavage fluid measurements and three continuous targets: tibialis anterior muscle weight (milligram: mg), specific force (millinewton: mN), and a derived muscle quality index (mN per mg). We benchmark tuned classical baselines, geometry-aware symmetric positive definite (SPD) descriptors with Stein divergence, and quantum kernel models designed for low-dimensional tabular data. In the muscle-weight setting, quantum kernel ridge regression using four interpretable inputs (blood C-reactive protein, neutrophil count, bronchoalveolar lavage cellularity, and condition) attains a test root mean squared error of 4.41 mg and coefficient of determination of 0.605, improving over a matched ridge baseline on the same feature set (4.70 mg and 0.553). Geometry-informed Stein-divergence prototype distances yield a smaller but consistent gain in the biomarker-only setting (4.55 mg versus 4.79 mg). Screening-style evaluation, obtained by thresholding the continuous outcome at 0.8 times the training Sham mean, achieves an area under the receiver operating characteristic curve (ROC-AUC) of up to 0.90 for detecting low muscle weight. These results indicate that geometric and quantum kernel lifts can provide measurable benefits in low-data, low-feature biomedical prediction problems, while preserving interpretability and transparent model selection.

Practical Geometric and Quantum Kernel Methods for Predicting Skeletal Muscle Outcomes in chronic obstructive pulmonary disease

TL;DR

This work tackles predicting COPD-associated skeletal muscle outcomes from a compact, biomarker-based dataset. It benchmarks tuned classical baselines, geometry-aware SPD representations, and quantum kernel approaches to model three muscle endpoints: TA weight, specific force, and a muscle quality index. Quantum kernel ridge regression shows the strongest gains on weight (RMSE ≈ 4.41 mg, ≈ 0.605), with clustered quantum kernel features offering robust screening performance (ROC-AUC up to ≈0.90) under a fixed feature budget; SPD descriptors provide consistent but smaller improvements. The findings suggest that non-Euclidean representations and quantum feature lifts can enhance prediction in low-data biomedical problems while preserving interpretability, though repeated-split validation and external data are needed for broader generalization.

Abstract

Skeletal muscle dysfunction is a clinically relevant extra-pulmonary manifestation of chronic obstructive pulmonary disease (COPD) and is closely linked to systemic and airway inflammation. This motivates predictive modelling of muscle outcomes from minimally invasive biomarkers that can be acquired longitudinally. We study a small-sample preclinical dataset comprising 213 animals across two conditions (Sham versus cigarette-smoke exposure), with blood and bronchoalveolar lavage fluid measurements and three continuous targets: tibialis anterior muscle weight (milligram: mg), specific force (millinewton: mN), and a derived muscle quality index (mN per mg). We benchmark tuned classical baselines, geometry-aware symmetric positive definite (SPD) descriptors with Stein divergence, and quantum kernel models designed for low-dimensional tabular data. In the muscle-weight setting, quantum kernel ridge regression using four interpretable inputs (blood C-reactive protein, neutrophil count, bronchoalveolar lavage cellularity, and condition) attains a test root mean squared error of 4.41 mg and coefficient of determination of 0.605, improving over a matched ridge baseline on the same feature set (4.70 mg and 0.553). Geometry-informed Stein-divergence prototype distances yield a smaller but consistent gain in the biomarker-only setting (4.55 mg versus 4.79 mg). Screening-style evaluation, obtained by thresholding the continuous outcome at 0.8 times the training Sham mean, achieves an area under the receiver operating characteristic curve (ROC-AUC) of up to 0.90 for detecting low muscle weight. These results indicate that geometric and quantum kernel lifts can provide measurable benefits in low-data, low-feature biomedical prediction problems, while preserving interpretability and transparent model selection.
Paper Structure (60 sections, 36 equations, 4 figures, 4 tables)

This paper contains 60 sections, 36 equations, 4 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Background and Related Work
  3. COPD as a systemic disease and the motivation for earlier risk stratification
  4. Skeletal muscle dysfunction in COPD: mass, strength, and muscle quality
  5. Inflammation and oxidative stress as mechanistic drivers of muscle impairment
  6. Biomarker discovery: from candidate markers to multivariate signatures
  7. Machine learning for COPD biomarker modelling and the importance of leakage-safe evaluation
  8. Geometry-aware representations with symmetric positive definite matrices
  9. Quantum kernels and variational quantum regression
  10. Materials and Methods
  11. Problem formulation and notation
  12. Dataset and predictors
  13. Train/test protocol
  14. Feature preprocessing
  15. Condition encoding
  16. ...and 45 more sections

Figures (4)

  • Figure 1: Proposed mechanisms of skeletal muscle wasting in COPD. Oxidative stress and inflammation contribute to muscle wasting, leading to reduced strength/endurance and functional decline. These changes can reinforce systemic inflammation and inactivity, creating a vicious cycle that accelerates disease progression. Created with BioRender.com.
  • Figure 2: ROC-AUC comparison for tibialis anterior muscle weight.
  • Figure 3: ROC-AUC comparison for specific force.
  • Figure 4: ROC-AUC comparison for muscle quality index.