MATHEMATICAL-ANALYSIS OF BLEEDING-TIME DATA IN PATIENTS WITH PLATELETDISORDERS AND VON WILLEBRANDS DISEASE

In a previous study the volume of blood obtained from bleeding time in cisions was measured every 30 s from normal subjects (n =1 5), patient s with thrombasthenia (TSA, n = 4), idiopathic thrombocytopenic purpur a (ITP, n = 4), von Willebrand's disease (vWD, n = 3), Bernard-Soulier syndrome (BSS, n = 2), and delta- and alpha delta-storage pool defici encies (SPD, n = 4 and 5, respectively) and the experimental results a nalyzed by empirical curve-fitting of the data. In the present investi gation, a mathematical model based on blood flow physiology was develo ped to describe the rate of blood loss over time from these same patie nts as a function of two parameters, a, which describes the magnitude of vessel contraction following transection, and beta, the rate of ves sel dilation to its nominal diameter. For the normal controls a third parameter, delta, was used to describe the rate of vessel closure due to the formation of a hemostatic plug. Optimal values for these parame ters for the normal subjects and each patient group were determined by least-squared fitting of the experimental bleeding time data. For all subjects, values for the magnitude of vessel contraction were similar (alpha = 0.65 +/- 0.02). However, values for beta were reduced in bot h TSA (beta = 0.22 +/- 0.04) and vWD (beta = 0.30 +/- 0.03) and were i ncreased relative to normal controls (beta = 0.39 +/- 0.03) in BSS (be ta = 0.50 +/- 0.01) and both delta-SPD (beta = 0.50 +/- 0.07) and alph a delta-SPD (beta = 0.50 +/- 0.05), The initial rate of blood loss was also significantly greater in patients with BSS, ITP, delta-SPD, and alpha delta-SPD than in the normal subjects, as determined by a one-wa y analysis of variance. These results suggest that: (1) the initial co ntraction of severed blood vessels does not appear to be mediated by a ny plasma or platelet compounds absent in the various bleeding disorde rs considered in this study; and (2) the increased initial bleeding ob served in SPD may reflect the absence of vasoactive agents, such as AD P or serotonin, released from platelet dense granules following platel et activation. These conclusions are consistent with those reported pr eviously on the same patients and indicate that mathematical modeling of bleeding time measurements, based on assumptions of vascular and pl atelet reactivity, can provide insights into the complex series of eve nts occurring at sites of vessel injury.