An analytical framework for managing innovation trajectories in medical technology

This paper presents a novel methodological approach for the dynamic evaluation of innovative medical devices under consideration of external stochastic risks. We develop a model based on the Hamilton–Jacobi formalism with stochastic extensions that integrates both deterministic aspects of regulatory inertia and stochastic influences such as patent disputes and market dynamics. The theoretical innovation diffusion patterns are described by coupled stochastic differential equations, whose solution is approximated using numerical methods. Particularly, the coupling of Bass diffusion models with multi-stage decision processes enables a realistic representation of the complex interactions between risk activation and market penetration. The presented methodology bridges concepts from statistical physics, thermodynamics, and innovation economics, providing both theoretical insights into the transfer of physical methods to economic questions and practical decision aids for innovators in the medical technology sector. By introducing the Non-ergodic risk functional (NERF) — based on recent advances in ergodicity economics—we establish a mathematically rigorous framework for evaluating innovation trajectories under various non-ergodic risk scenarios based on literature derived parametrizations. • Develop a decision model for optimizing innovation under regulatory and patent uncertainty. • Quantify how regulatory delays and patent erosion affect innovation outcomes. • Apply physics-inspired analytics to improve health technology decision-making. • Demonstrate the strategic benefits of dynamic pathway selection in device development. • Offer a reproducible method for optimizing high-stakes innovation decisions.