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

• Published in: The Korean journal of physiology & pharmacology Vol. 26; no. 3; pp. 195 - 205
• Main Authors: Chon, Sung-Bin, Lee, Min Ji, Oh, Won Sup, Park, Ye Jin, Kwon, Joon-Myoung, Kim, Kyuseok
• Format: Journal Article
• Language: Korean
• Published: 2022
• Subjects: Isotonic solutions; Hemorrhagic shock; Hematocrit; Blood volume determination
• ISSN: 1226-4512; 2093-3827

Determining blood loss [100% - RBV (%)] is challenging in the management of haemorrhagic shock. We derived an equation estimating RBV (%) via serial haematocrits (Hct1, Hct2) 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 / [(Hct1 / Hct2) -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). Hct1 was checked after 10 min and normal saline N cc was infused over 10 min. Hct2 was checked five minutes later. We applied a linear equation to explain RBV (%) with 1 / [(Hct1 / Hct2) -1]. Seven rats losing 30.0%-60.0% of their TBV suffered shock persistently. For them, RBV (%) was updated as 5.67 / [(Hct1 / Hct2) -1] + 32.8 (95% confidence interval [CI] of the slope: 3.14-8.21, p = 0.002, R2 = 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.