Code Atlas: Digital Twin Impulse Absorption

Diátaxis Type: Code Atlas Record | ID: ATLAS-ALG-003 | Owner: diabetic.ml_engine.twin

1. Mathematical Formulation

Models carbohydrate absorption rate via biphasic impulse response:

\[C(t) = \frac{t}{\tau^2} e^{-t/\tau}, \quad t \ge 0\]

\[\Delta g_{carb}(t) = \text{Carbs} \cdot S_{carb} \cdot C(t)\]

\[I(t) = \frac{S_{ins}}{\tau_2 - \tau_1} \left( e^{-t/\tau_2} - e^{-t/\tau_1} \right)\]

Time step integration defends against non-positive durations:

# ponytail: guard zero/negative duration
if dt <= 0:
    return 0.0