# Clinical validation of perfusion imaging with pulmonary function test data using Voronoi-based discretization

## TL;DR

This paper introduces a new method using Voronoi diagrams to better analyze lung perfusion images and link them to standard lung function tests.

## Contribution

The novel contribution is a Voronoi-based framework that improves the correlation between perfusion imaging and pulmonary function tests.

## Key findings

- Voronoi discretization yields stronger Spearman correlations (0.636–0.843) between perfusion maps and PFT measures.
- The method reliably distinguishes normal from abnormal lung function with AUC values of 0.865–0.937.
- It preserves local spatial variability, enabling meaningful comparisons between SPECT and CT-P maps.

## Abstract

Objective. Accurate lung function assessment is essential for diagnosing and managing diseases like chronic obstructive pulmonary disorder, pulmonary emboli, and lung cancer. Single-photon emission computed tomography (SPECT) provides valuable 3D functional imaging of ventilation and perfusion, but is limited by low spatial resolution, availability, additional radiation, and cost. Alternative methods, including CT-based perfusion (CT-P) and deep learning models, require large datasets to validate results that are often scarce. Pulmonary function tests (PFTs) offer rapid and noninvasive global lung function measures and are clinically widely used. While ventilation correlates well with PFTs, perfusion imaging presents challenges due to complex blood flow and difficulty summarizing 3D data into one value. Additionally, commonly employed percentile scaling removes absolute quantitative information, complicating interpretation. Approach. We propose a framework leveraging lung discretizations based on Voronoi diagrams to capture local spatial information from raw-valued and percentile-scaled perfusion maps (SPECT and CT-P). We compute hierarchical descriptive statistics at 3 levels (intra-subvolume, inter-subvolume, left-right lungs) to derive one global value per patient. Main results. Across PFT measures of diffusing capacity of lungs for carbon monoxide, forced expiratory volume after one second (FEV1), and FEV1/forced vital capacity, we find that discretizing perfusion maps into Voronoi subvolumes always yields stronger Spearman correlations than not discretizing. Specifically, our approach demonstrates strong correlations of \documentclass[12pt]{minimal}
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$0.636 \unicode{x2A7D} \rho \unicode{x2A7D} 0.843$\end{document}0.636⩽ρ⩽0.843 (P < 0.005) for raw-valued (SPECT and CT-P) maps, \documentclass[12pt]{minimal}
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$0.590 \unicode{x2A7D} \rho \unicode{x2A7D} 0.789$\end{document}0.590⩽ρ⩽0.789 (P < 0.005) for percentile-scaled maps, and reliably distinguishes normal from abnormal lung function via logistic regression analysis (\documentclass[12pt]{minimal}
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$0.865 \unicode{x2A7D} \mathrm{AUC} \unicode{x2A7D} 0.937$\end{document}0.865⩽AUC⩽0.937 for raw-valued maps, \documentclass[12pt]{minimal}
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$0.877 \unicode{x2A7D} \mathrm{AUC} \unicode{x2A7D} 0.933$\end{document}0.877⩽AUC⩽0.933 for percentile-scaled maps). Significance. This framework bridges regional perfusion imaging and global pulmonary function assessment, enabling meaningful quantitative comparisons between SPECT and CT-P maps. By preserving local spatial variability, the method offers a noninvasive tool for integrating imaging and physiological data, paving the way toward broader clinical and AI-driven applications in lung function evaluation.