Mechanistic determination of tear film thinning via fitting simplified models to tear breakup

The paper defines five ODE models (E, O, F, D, M), eliminates the auxiliary variables to obtain an explicit fluorescence-intensity map I(t) for M (and hence its submodels), and fits eight FT‑TBU instances via nonlinear least squares. It reports that all eight are best fit by models with time‑dependent flow, specifically five by case M and three by case D, with the no‑flow models E and O giving worse residuals in every instance (model and intensity definitions: eqs. (2)–(6), (11)–(13); Appendix A.3; and aggregate fitting/result statements) . The candidate solution recasts the intensity via S(t)=exp[−a t+(b1/b2)(e^{−b2 t}−1)], shows that E/O imply S≡1 and strictly decreasing I(t), and uses initial‑slope/curvature and sign‑change arguments to explain why the data require time‑dependent flow. It also correctly notes that F and D are strict submodels of M, so an unrestricted M fit cannot be worse than D or F in principle, consistent with the paper’s structural definitions (eq. (13) and A.3) . Minor tensions remain: the paper’s numerics sometimes list a D residual slightly smaller than M, which likely reflects local‑minimum or tolerance issues rather than a theoretical contradiction of the nesting property. Overall, the empirical paper and the structural model explanation agree on the main conclusions; they arrive there by different means.