Structural Identifiability
Structural identifiability analysis determines whether model parameters can be uniquely estimated from the available output measurements, assuming noise-free data of arbitrary quantity. For the energy metabolism model, the measured outputs are \([\text{ATP}]\), \([\text{lactate}]\) (derived from \([\text{Pyr}]\)), and VOβ (proportional to \(J_\text{CIV}\)). Using the differential algebra approach, we construct the inputβoutput equations by eliminating unmeasured state variables. Parameters appearing independently in the coefficients of these equations are structurally identifiable; parameters appearing only in combinations are structurally unidentifiable (only the combination can be estimated).
Analysis of the energy metabolism model reveals that: (1) \(V_{max, \text{CI}}\) and \(K_m^{\text{NADH}}\) are individually identifiable from VOβ data; (2) \(k_\text{ROS}\) and \(k_\text{SOD}\) are identifiable only as the ratio \(k_\text{ROS} \\/ k_\text{SOD}\) from ROS-related outputs; (3) the damage parameters \(k_D\) and \(k_\text{rep}\) are identifiable from longitudinal day-1/day-2 CPET data but not from single-time-point measurements. These identifiability results guide experimental design: measuring ROS directly (rather than inferring from downstream markers) would resolve the \(k_\text{ROS} \\/ k_\text{SOD}\) ambiguity.