Korean J Physiol Pharmacol.  2022 May;26(3):195-205. 10.4196/kjpp.2022.26.3.195.

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

• Chon SB
• Lee M
• Oh WS
• Park YJ
• Kwon JM
• Kim K

• KMID: 2529402
• DOI: http://doi.org/10.4196/kjpp.2022.26.3.195

Abstract

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, nonongoing 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. Hct 2 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.

Keyword

Blood volume determination; Hematocrit; Hemorrhagic shock; Isotonic solutions

Figure

• 

  Fig. 1 Analogy between the change of concentration of sugar water after adding some water and that of haematocrit of blood after crystalloid fluid infusion. (A) Change of concentration of sugar water after adding some water. Once you know the initial and final concentration of sugar water and the mass of water poured into it, you can tell the initial mass of the sugar water by building a linear equation (see Supplementary Text 1A for detailed explanation). (B) Change of haematocrit of blood after crystalloid fluid infusion. Likewise, if there is no blood or fluid loss via the circulation system, residual blood volume (RBV) would be calculable with serial haematocrits (Hct1 and Hct2) and the volume of crystalloid fluid infused in-between (N). The only difference from (A) is that only a certain fraction (k, which is approximately 0.25 for men) would be distributed into the intravascular volume (See Supplementary Text 1B for detailed explanation).

• 

  Fig. 2 Study protocol. POCT, point-of-care test including arterial blood gas analysis, haematocrit, and lactate; V/S, vital signs including systolic, diastolic, and mean arterial blood pressure and heart rate. Subscripts 0, 1, and 2 denote baseline before bleeding, status just before fluid resuscitation, and status after fluid resuscitation, respectively.

• 

  Fig. 3 Vital signs at the time of baseline (time 0), before (time 1), and after (time 2) crystalloid fluid resuscitation. (A) Systolic blood pressure. (B) Diastolic blood pressure. (C) Mean arterial pressure. (D) Heart rate.

• 

  Fig. 4 Laboratory findings at the time of baseline (time 0), before (time 1), and after (time 2) crystalloid fluid resuscitation. (A) pH. (B) Partial oxygen pressure (PO2). (C) Lactate. (D) Haematocrit.

• 

  Fig. 5 Relation between actual and estimated residual blood volume (RBV) among the seven rats that showed persistent shock despite fluid resuscitation. (A) Relation between actual RBV and estimated RBV calculated as 0.272N / [(Hct1 / Hct2) – 1] + 5.64. (B) Bland-Altman plot with shades showing 95% CI of mean, upper and lower limits of agreement. Hct1, initial haematocrit; Hct2, subsequent haematocrit; LoA, limit of agreement; M.A.D., maximum allowed difference (pre-determined); N, volume of crystalloid fluid infused in-between; SD, standard deviation; CI, confidence interval.

• 

  Fig. 6 Relation between actual and estimated residual blood volume (RBV) (%) among the seven rats that showed persistent shock despite fluid resuscitation. (A) Relation between actual RBV (%) and estimated RBV (%) calculated as 6.74 / [(Hct1 / Hct2) – 1] + 32.3. (B) Bland-Altman plot with shades showing 95% CI of mean, upper and lower limits of agreement. Hct1, initial haematocrit; Hct2, subsequent haematocrit; LoA, limit of agreement; M.A.D., maximum allowed difference (pre-determined); RBV, residual blood volume; SD, standard deviation; CI, confidence interval.

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