Tackling the non-linearizeable dose-response relationship in clotting time assays of heparin

Heparin sodium was assayed by turbidimetric measurement of the clotting time of bovine citrate plasma with thromboplastin, between the moment of recalcification and the moment of maximal speed of polymerization of the fibrinogen monomer, as marked by the turning-point of the trace of the turbidimetric record. Most assays were practiced in the range of 0.2-2.0 units per test volume. The lower end of the range could be extended by decreasing the thromboplastin dose, the higher end by increasing this dose. The dose-response relationship for heparin sodium, i.e. between the nominal heparin activity x and the clotting time y, was non-linear in such a way that no uniform mathematical transformation could provide a valid linearization over the whole range. A non-linear regression in the form of a cubic fit, applied to the data pairs (x, y) of both standard and test sample, proved to be satisfactory. The two non-linear regression curves were compared at varying levels of x by computing the quotient of nominal and actual activity for equal clotting times, and by computing the quotient of the slopes (tangents) of the curves for these times. The percentual deviation of the test sample potency from the standard's potency as obtained from the former quotient was termed Za, and the deviation as computed from the latter quotient was termed Ztg, Za and Ztg as functions of x were plotted and were found to intersect invariably at critical points of Za(x) within the range of the experiment. This seems to be a theorem.(ABSTRACT TRUNCATED AT 250 WORDS)