The Role of Mathematics in Cardiovascular Clinics: Why Our Time Is Now

This talk is motivated by the conviction that mathematics is essential to societal progress, and that its impact on healthcare—particularly cardiovascular medicine—has yet to be fully realized. While technological transfer is often celebrated as the primary driver of innovation in medicine, the equally critical role of methodological transfer is frequently overlooked. Advances in clinical understanding and decision-making are ultimately grounded in models, methods, and analytical frameworks that rely on mathematical representations of complex physiological processes.

Drawing on more than three decades of research in cardiovascular mathematics, this talk highlights the fundamental contributions mathematicians have made to elucidating cardiovascular pathophysiology. Despite these advances, the translation of mathematical insight into routine clinical practice has historically been limited. The inherent complexity of cardiovascular systems, combined with cultural and structural barriers between disciplines, has constrained the clinical uptake of mathematical models and tools.

I will examine the reasons for this gap and argue that we are now at a pivotal moment. The unprecedented availability of high-quality clinical data, advances in data assimilation and uncertainty quantification, and the rapid development of artificial intelligence—when used in synergy rather than competition with mechanistic modeling and mathematical analysis—are transforming what is possible. Together, these developments open the door to clinically actionable models that can operate within realistic decision-making timelines.

A particular focus will be placed on ischemic heart disease and myocardial infarction, which currently account for approximately 400,000 deaths per year in the United States. I will argue that a substantial reduction in this number within the next five years is achievable, provided we succeed in translating existing mathematical knowledge into tools that clinicians can trust and use. This requires numerically efficient methods, grounded in strong theory, and designed explicitly for integration into clinical workflows.

The talk concludes with a forward-looking perspective: just as medical imaging revolutionized clinical practice a century ago, mathematics now has the opportunity—and responsibility—to drive the next transformation in cardiovascular care. The time is right for mathematicians to play a central role in shaping the future of clinical decision-making.