온라인강의

Mathematical Principles of Optimal Herbal Formulation: A Geometric Approach to the Efficacy-Stability Paradox
강사명Chang-Eop Kim 강의시간24분 강의개설일2025-12-10
온라인강의

강의소개

Introduction: The combination of multiple herbs into complex formulas is a foundational principle of East Asian medicine, intended to produce synergistic therapeutic actions. However, the principles governing how an increase in complexity can simultaneously enhance both mean efficacy and the stability (i.e., reliability) of the outcome remain largely unexplored. This work frames this issue as the “”efficacy-stability paradox”” and proposes a quantitative framework to resolve it. Methods: We introduce a “”Therapeutic Utility Function,”” U(h)=E[f]−λ Var(f), to formalize the trade-off between maximizing the mean therapeutic effect, E[f], and minimizing the therapeutic variance, Var(f). Pharmacological interactions are deconstructed into two key components: “”Signal Correlation,”” which governs mean efficacy, and “”Noise Correlation,”” which determines the formula’s stability. This theoretical model is then grounded in the multi layer Herb-Compound-Target-Function (H-C-T-F) cascade to provide a mechanistic basis. Results: Our analysis suggests that an optimal formula is not merely a combination of potent components, but rather one that is engineered to simultaneously exhibit strong positive signal correlation (to maximize efficacy) and non-positive, ideally negative, noise correlation (to actively suppress variance). From a geometric perspective, this framework elucidates an optimal design strategy: for a given noise environment (covariance matrix Σ h), the formula should be designed such that its therapeutic sensitivity gradient (∇g) is orthogonal to the dominant eigenvectors of the noise. This is termed the “”Principle of Noise Orthogonality””. Conclusion: This work provides a new perspective on the principles of complex herbal formulation through the lens of “”variance engineering””. The proposed framework offers a rational, quantitative language for the empirically derived art of formulation. By deconstructing pharmacological interactions into components governing efficacy (Signal Correlation) and stability (Noise Correlation), it provides a principled approach to designing formulas that balance the pursuit of potency with the critical need for therapeutic reliability. This presents a theoretical basis for transforming the art of formulation into a modern, quantitative, decision-theoretic process.

강사소개

Dr. Chang-Eop Kim is an Associate Professor in the Department of Physiology at Gachon University College of Korean Medicine, where he leads a research group at the intersection of neuroscience, artificial intelligence, and medicine. He holds a diverse educational background with a Ph.D. in Medical Science (Physiology) from Seoul National University College of Medicine, a B.S. in Korean Medicine from Dongguk University, and a B.S. in Mathematics. He is also a Certified Physician in Biomedical Informatics (CPBMI).