SoS:BIO: The Shape of Suffering: Topological Tools for Aligning Biomedical Research with Clinical Need and Biological Opportunity - The promise of the U.S. biomedical enterprise is that scientific attention tracks human suffering—that research effectively addresses the reality of disease. Yet for decades, studies have shown that research effort correlates only modestly with disease burden, and this misalignment persists. A central reason is that the question has been framed too narrowly— condition by condition, treating each in isolation—even though diseases co-occur in patients, connect through shared molecular pathways, and fragment across research disciplines. Correcting misalignment requires knowing where it is: which disease relationships are neglected, which biological opportunities remain unexploited, and which gaps reflect genuine opportunities rather than dead ends. Yet few tools provide this knowledge. This project develops a Science of Science framework that makes misalignment visible and actionable, reframing alignment from a question of volume—does funding match burden?—to one of shape—does the structure of research mirror the structure of disease? We conceptualize the biomedical landscape as three layers—clinical demand (disease co-occurrence in patients), scientific response (disease co-occurrence in research), and biological opportunity (shared genes, pathways, and drug targets)—projected onto a common set of disease nodes, and use Topological Data Analysis to characterize the shape of each. Objective 1 constructs a multi-layer network over a shared disease backbone mapped to ICD-10 via the UMLS Metathesaurus: a Clinical Layer from MarketScan claims (~200M patients) and the Medical Expenditure Panel Survey; a Scientific Layer from Dimensions and PubMed; and a Mechanistic Layer integrating PrimeKG, DisGeNET, KEGG, and Reactome, with temporal snapshots to track alignment dynamics. Objective 2 applies persistent homology and adapts image persistence—largely unused in empirical work—to detect two forms of misalignment: fragmentation, where clinical clusters are disconnected in research, and hollowing, where relationships exist but integrated investigation is absent; minimal cycle representatives identify the specific diseases involved, with tools built as extensions to the Open Applied Topology library. Objective 3 validates detected misalignments through expert assessment, scientometric benchmarking, and retrospective drug-repurposing tests, examines whether gaps self-correct over time, and delivers openly available disease-network datasets, open-source software (including the first general-purpose implementation of image persistence), and an interactive dashboard that translates gaps into actionable targets for researchers and funders. Pilot analyses confirm clinical relevance: patients whose disease combinations are misaligned with research have up to 16-fold more emergency department visits.