Code Atlas: Kovatchev Risk Transform

Diátaxis Type: Code Atlas Record | ID: ATLAS-ALG-002 | Owner: diabetic.dsp.metabolic_math

1. Mathematical Formulation

Transforms blood glucose measurements into a symmetrical risk space:

\[f(g) = 1.509 \cdot \left( \ln(g)^{1.084} - 5.381 \right)\]

\[r(g) = 10 \cdot f(g)^2\]

\[\text{LBGI} = \begin{cases} r(g) & \text{if } f(g) < 0 \\ 0 & \text{otherwise} \end{cases}\]

\[\text{HBGI} = \begin{cases} r(g) & \text{if } f(g) > 0 \\ 0 & \text{otherwise} \end{cases}\]

\[\text{RI} = \text{LBGI} + \text{HBGI}\]

Input Bound: \(g \ge 1.0 \text{ mmol/L}\) (defensive clamping prevents negative logarithms).
Target Euglycemia: When \(g \approx 6.2 \text{ mmol/L}\), \(f(g) = 0\) and \(RI = 0\).