Physics-Informed Graph Learning for Spatially Contiguous and Capacity-Constrained Hospital Service Area Delineation

Area of Science:

• Health Geography
• Computational Social Science
• Network Science

Background:

• Accurate delineation of Hospital Service Areas (HSAs) is crucial for effective healthcare resource allocation and policy development.
• Existing methods for HSA delineation face challenges in simultaneously integrating patient flow, spatial contiguity, and capacity constraints.
• Traditional spatial clustering and Graph Neural Networks (GNNs) often fail to adequately capture complex network dynamics or enforce strict capacity limits.

Purpose of the Study:

• To develop a novel framework, SGCN-MST, that integrates physics-informed graph learning with constraint-based regionalization for improved HSA delineation.
• To address the limitations of existing methods in capturing patient flow, spatial contiguity, and multiple capacity constraints simultaneously.
• To provide a statistically robust and administratively practical tool for health geography research and policy.

Main Methods:

• A physics-informed GNN is employed to simulate patient flow as a spatial diffusion process, capturing interaction decay.
• An "interaction-aware" embedding is generated and utilized within a spatial Minimum Spanning Tree (MST) algorithm.
• A Depth-First Search (DFS) strategy is incorporated to dynamically balance modularity optimization with multiple capacity constraints.

Main Results:

• The SGCN-MST model reveals a nested, hierarchical spatial structure in Florida's inpatient data, reflecting functional medical hierarchies.
• Large regional referral centers and compact local communities were identified, mirroring real-world healthcare delivery patterns.
• Comparative analysis demonstrated that SGCN-MST offers a more balanced and policy-ready solution than baseline methods like ScLeiden and Region2Vec.

Conclusions:

• SGCN-MST provides a statistically robust and administratively practical tool for delineating Hospital Service Areas.
• The framework effectively balances modularity optimization with critical constraints like localization, contiguity, and capacity feasibility.
• This approach offers significant advancements for healthcare resource allocation, policy-making, and health geography.