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Evaluation of Mathematic Models to Assess Platelet Kinetics

Biophysics Department and South African Medical Research Council Blood Platelet Research Unit, University of the Orange Free State, Bloemfontein, South Africa

Correspondence: For reprints contact: Mattheus G Lötter, Biophysics Dept., UOFS, Bloemfontein, South Africa.

ABSTRACT

Twelve mathematic methods used to calculate the mean platelet survival time were compared by determining the "goodness of fit" of the models to the platelet survival curves of 15 reference subjects and 54 patients. Platelets were labeled with [¹¹¹In]oxine. The linear (LN), exponential, weighted mean, multiple hit (MH), Dornhorst (DH), Meuleman (ML), alpha order (AO), and polynomial (PO) mathematic models were investigated. The goodness of fit for the exponential model was determined by the nonlinear least squares method (EP), and also by the linear least squares method on logarithmically transformed data (EX) as is recommended. The modified weighted mean (MWM) and the usual weighted mean method (WM) obtained with these exponential models were tested. The Dornhorst (DH10) and Meuleman (ML10) models, where the potential age-dependent platelet survival times were kept constant at 10 days, were also evaluated. The goodness of fit results, expressed as % s.d. indicated that the LN (5.2%), EX (5.0%), EP (4.4%), WM (3.7%), DH10 (3.7%), and ML10 (3.7%) models all fitted the data significantly worse than the MWM, MH, DH, ML, AO, and PO models (range 3.2–3.3%). The mean platelet survival time determined with the MH model differed significantly from the results with the DH, ML, and AO models. The results of mean platelet survival time calculated with different mathematic models cannot, therefore, be compared directly. The models that fitted the platelet survival curve well varied slightly in sensitivity to noise as is indicated by the coefficient of variation of the mean platelet survival time estimates for the reference subjects (range 7.9–12.0%). Fitting data to at least two mathematic models has definite advantages. Data on which the calculations are based are probably invalid if the following are true: (a) if the mean platelet survival time estimated with the alpha order model is shorter than that estimated with the EP, MWM, or MH models, or (b) the mean platelet survival time estimated with either the DH, ML, AO, or PO models, is longer than the LN, MWM, or MH estimate of the mean platelet survival time. We conclude that the mean platelet survival time can be reliably estimated by fitting the data to either the MWM method (if limited computing facilities are available) or the MH model. Confidence in the result will be increased if considered in conjunction with the finding obtained with one other model; in those cases where the platelet survival time is very short, the alpha order model is recommended. In other instances the results of the MWM method or MH model should be compared with that obtained with either the DH, ML, AO, or PO models.