Mathematical Analysis of Bleeding Time Data in Patients with Platelet Disorders and von Willebrand's Disease

In a previous study the volume of blood obtained from bleeding time incisions was measured every 30 s from normal subjects (n = 15), patients with thrombasthenia (TSA, n=4), idiopathic thrombocytopenic purpura (ITP, n=4), von Willebrand's disease ((v)WD, n=3), Bernard-Soulier syndrome (BSS, n = 2), and δ and αδ-storage pool deficiencies (SPD, n=4 and 5, respectively) and the experimental results analyzed by empirical curve-fitting of the data. In the present investigation, a mathematical model based on blood flow physiology was developed to describe the rate of blood loss over time from these same patients as a function of two parameters, α, which describes the magnitude of vessel contraction following transection, and β, the rate of vessel dilation to its nominal diameter. For the normal controls a third parameter, δ, was used to describe the rate of vessel closure due to the formation of a hemostatic plug. Optimal values for these parameters 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 (α=0.65±0.02). However, values for β were reduced in both TSA (β=0.22±0.04) and (v)WD (β = 0.30±0.03) and were increased relative to normal controls (β=0.39±0.03) in BSS (β=0.50±0.01) and both δSPD (β=0.50±0.07) and αδSPD (β=0.50±0.05). The initial rate of blood loss was also significantly greater in patients with BSS, ITP, δ-SPD, and αδSPD than in the normal subjects, as determined by a one-way analysis of variance. These results suggest that: (1) the initial contraction of severed blood vessels does not appear to be mediated by any plasma or platelet compounds absent in the various bleeding disorders considered in this study; and (2) the increased initial bleeding observed in SPD may reflect the absence of vasoactive agents, such as ADP or serotonin, released from platelet dense granules following platelet activation. These conclusions are consistent with those reported previously on the same patients and indicate that mathematical modeling of bleeding time measurements, based on assumptions of vascular and platelet reactivity, can provide insights into the complex series of events occurring at sites of vessel injury.