A simple and novel equation to estimate the degree of bleeding in haemorrhagic shock: mathematical derivation and preliminary in vivo validation

Determining blood loss [100% – RBV (%)] is challenging in the management of haemorrhagic shock. We derived an equation estimating RBV (%) via serial haematocrits (Hct(1), Hct(2)) by fixing infused crystalloid fluid volume (N) as [0.015 × body weight (g)]. Then, we validated it in vivo. Mathematically, the following estimation equation was derived: RBV (%) = 24k / [(Hct(1) / Hct(2)) – 1]. For validation, non-ongoing haemorrhagic shock was induced in Sprague–Dawley rats by withdrawing 20.0%–60.0% of their total blood volume (TBV) in 5.0% intervals (n = 9). Hct(1) was checked after 10 min and normal saline N cc was infused over 10 min. Hct(2) was checked five minutes later. We applied a linear equation to explain RBV (%) with 1 / [(Hct(1) / Hct(2)) – 1]. Seven rats losing 30.0%–60.0% of their TBV suffered shock persistently. For them, RBV (%) was updated as 5.67 / [(Hct(1) / Hct(2)) – 1] + 32.8 (95% confidence interval [CI] of the slope: 3.14–8.21, p = 0.002, R(2) = 0.87). On a Bland-Altman plot, the difference between the estimated and actual RBV was 0.00 ± 4.03%; the 95% CIs of the limits of agreements were included within the pre-determined criterion of validation (< 20%). For rats suffering from persistent, non-ongoing haemorrhagic shock, we derived and validated a simple equation estimating RBV (%). This enables the calculation of blood loss via information on serial haematocrits under a fixed N. Clinical validation is required before utilisation for emergency care of haemorrhagic shock.