Pharmacokinetic analysis of sparse in vivo NMR spectroscopy data using relative parameters and the population approach

NMR spectroscopy in vivo when applied to studying drugs and their metabolites usually measures relative concentration in a tissue over time. Only ratios of clearance and volume parameters can be estimated from these data. Low drug dosages (relative to the sensitivity of in vivo NMR) or rapid drug elimination create the additional problem of data sparsity where a pharmacokinetic model cannot be fitted individually. We have investigated whether relative and absolute pharmacokinetic parameters can be estimated from such data by applying a population model.The data analysed were relative concentractions of 5-fluorouracil (FU) and of the sum of its catabolits -fluoro--ureido-propanoic acid (FUPA) and -fluoro--alanine (FBAL) in te liver, as monitored in 16 cancer patients by [¹⁹F]-NMP spectroscopy during and after a 10-min intravenous infusion of 650 mg FU·m^–2. The structural part of the population model was a non-linear, two-compartment model featuring one FU compartment with volume V_FU, a saturable clearance of FU by conversion into the catabolites where CL=v_max/(k_M+C_FU), a catabolite compartment with volume V_cat, and a concentration-independent clearance of the catabolites, CL_cat. The parameters actually fitted were: , v_max, k_M·V_FU, V_cat/V_FU, and CL_cat/V_catwhere is a proportionality factor relating the NMR signal intensity of FU to the amount of FU in the body and, therefore, has no purely pharmacokinetic interpretation. All parameters were checked for random interindividual variation; and v_maxwere also tested for inter-occasion variation. The program system NONMEM was used for model fitting.The estimated mean population parameters were: v_max=121 mol·min^–1, k_M·V_FU=2590 mol, V_cat/V_FU=0.0648, CL_cat/V_cat=0.0555·min^–1. The proportionality factor was found to depend on body weight and, in addition, to have an inter-occasion random variation (within patients, between examinations). No other random variation of a kinetic parameter could be identified. The estimated v_maxis similar to a reported estimate of 2.02 mol·min^–1·kg^–1 derived from FU plasma kinetics.This study shows that sparse relative concentration data can be analysed by using relative parameters in a population model. Only one parameter has no unequivocal pharmacokinetic meaning due to the lack of absolute concentration information. Any contribution of the measuring procedure to the inter-occasion variation of in vivo NMP spectroscopy measurements should be minimized in order to allow the detection of possible inter-individual variances of the pharmacokinetic parameters.Dedicated to Prof. Dr. Rudolf Preussmann on the occasion of his 65th birthday