Approximate linear confidence and curvature of a kinetic model of dodecanedioic acid in humans

Dicarboxylic acids with an even number of carbon atoms have been proposed as an alternate energy substrate for enteral or parenteral nutrition in the acutely ill patient, due to their water solubility and their yielding TCA cycle intermediates upon beta-oxidation. In the present work, a nonlinear compartmental model of the kinetics of dodecanedioic acid is developed, and its parameters are estimated from time concentration experimental observations obtained from six healthy volunteers undergoing a per os administration of 3 g of the substance. Although the model is linear in the transfer of the free substance from plasma to the tissues, the exchange between gut and plasma compartments is represented as a saturable function. Albumin binding is then incorporated to obtain the final model in terms of the measured total concentrations. Estimates of the model's structural parameters were computed for each experimental subject, and the usual single-subject approximate confidence regions for the parameters were derived by inversion of the Hessian at the optimum. To verify the applicability of this approximation, the nonlinearity of the expectation surface at the optimum was measured by computing the normal (intrinsic) component of curvature. Because the model curvature was excessive in all subjects, the usual approximation could not be trusted to provide acceptable approximations to the parameter confidence regions. A suitable Monte Carlo simulation yielded empirical joint parameter distributions from which the approximate parameter variances could finally be obtained.