Korean J Physiol Pharmacol 2022; 26(3): 195-205
Published online May 1, 2022 https://doi.org/10.4196/kjpp.2022.26.3.195
Copyright © Korean J Physiol Pharmacol.
Sung-Bin Chon^{1,2}, Min Ji Lee^{2}, Won Sup Oh^{3}, Ye Jin Park^{2}, Joon-Myoung Kwon^{4}, and Kyuseok Kim^{2,*}
^{1}Department of Emergency Medicine, Seoul National University College of Medicine, Seoul 03080, ^{2}Department of Emergency Medicine, CHA Bundang Medical Center, Seongnam 13496, ^{3}Department of Internal Medicine, Kangwon National University Hospital, Chuncheon 24289, ^{4}Department of Critical Care and Emergency Medicine, Mediplex Sejong Hospital, Incheon 21080, Korea
Correspondence to:Kyuseok Kim
E-mail: dremkks@cha.ac.kr
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
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, 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). 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.
Keywords: Blood volume determination, Hematocrit, Hemorrhagic shock, Isotonic solutions
Haemorrhagic shock has various etiologies, including trauma, maternal haemorrhage, peptic ulcers, perioperative haemorrhage, and ruptured aortic aneurysms [1]. This medical condition causes 1.9 million deaths annually (with trauma as the leading cause; there are 1.5 million trauma-induced haemorrhagic shock deaths annually worldwide) and affects the young disproportionately raising a socioeconomic issue [2]. When trauma-related haemorrhage deteriorates, death occurs at a median of approximately 2.6 h after initial presentation addressing the importance of initial management [3,4]. Initial management is also critical for reducing delayed mortality and repaying oxygen debt before shock becomes irreversible [5]. For clinicians, prompt and correct determination of the degree of blood loss (%) is critical.
The blood loss (%) is calculated as ‘100% – residual blood volume (RBV) (%)’. For example, when RBV (%) is 65%, blood loss (%) is 35%. RBV (%) is defined as RBV/total blood volume (TBV). TBV, the denominator, is easily estimable
The gold standard to determine RBV is a dilution method using radioactive chromium (^{51}Cr); briefly after transfusing a small, fixed quantity of ^{51}Cr-labelled red blood cells, the radioactivity of the blood is measured to calculate RBV [7]. The carbon monoxide rebreathing technique, which shows high reproducibility without using radioactive materials, is based on a fixed amount of an inspired oxygen-carbon monoxide gas mixture and traces the carboxyhaemoglobin (HbCO) difference to estimate RBV [8,9]. However, neither method is applicable to real-world haemorrhagic shock patients. Clinicians estimate RBV (%) or blood loss (%) considering multiple factors such as vital signs, haemoglobin/haematocrit, central venous or pulmonary capillary wedge pressure (CVP/PCWP), ultrasonography, and visual estimation [10-16]. However, these methods provide only rough estimations.
Previously, we mathematically derived an equation to estimate RBV for acute, non-ongoing haemorrhagic shock patients [17]. In mathematics class, middle school students are asked the following question: “There is a cup of sugar water with a concentration of 45%; 0.5 kg of water is poured into this mixture. The concentration of the sugar water changed to 40%. Can you calculate the initial mass of the sugar water?”. Once the initial and final concentration of sugar water and the mass of water poured into the mixture is known, it is possible to calculate the initial mass of the sugar water through a linear equation (Fig. 1A; see Supplementary Text 1A for a detailed mathematical explanation). We paid attention to the fact that this sugar water scenario is similar to that of initial management of haemorrhagic shock patients.
For patients presenting at the emergency department (ED) with haemorrhagic shock, clinicians control bleeding, request laboratory tests, infuse crystalloid fluid restrictively, and start transfusion as soon as materials are available [1,13,18]. Along with blood type, arterial blood gas analysis (ABGA), lactate, electrolytes, coagulation profiles, thromboelastography/thromboelastometry, and complete blood counts should be checked initially as point-of-care tests (POCT) [1]. With this standard management of haemorrhagic shock, the initial and final concentration of the blood, that is, the serial haematocrits (Hct_{1} and Hct_{2}), become available immediately. In addition, clinicians themselves determine the volume of crystalloid fluid (N), which is infused as an initial resuscitative effort. As with the sugar water story solved by a linear equation, we derived the following equation to determine the initial blood volume (RBV) at the time of ED arrival using the information on Hct_{1}, Hct_{2}, and N, which are the key elements of standard management [1,13] (Fig. 1B; see Supplementary Text 1B for a detailed mathematical explanation):
(
The only difference between this approach and the sugar water example is
Clinicians prefer to know blood loss (%) or RBV (%) rather than RBV itself. In this study, we mathematically derived an equation to determine the RBV (%) (and thus the blood loss [%]) by modifying the above equation and then validated it
This study was approved by the Institutional Animal Care and Use Committee (approval number: IACUC210053) and we observed the Animal Research: Reporting of
By definition, RBV (%) is calculated as ‘RBV/TBV’. Incorporating this relationship into the original equation estimating RBV, we derive that:
Among the components, N / TBV can be substituted with a constant as follows.
In this study, we fixed N as 0.015 × body weight (g) (cc) [13,21]. We calculated TBV as 0.06 × body weight (g) + 0.77 (cc) as reported by Lee and Blaufox (
Incorporating this information, the equation to estimate the RBV (%) becomes far simpler:
This indicates that the RBV (%) can be determined solely by information on serial haematocrits when N is fixed.
The above equation we aimed to evaluate is a type of linear equation explaining RBV (%), the dependent variable, with 1 / [(Hct_{1} / Hct_{2}) – 1] as the independent variable and 24
Using this updated equation, we estimated the RBV (%) for each rat and compared it with the ‘actual’ RBV (%). We could determine the ‘actual’ RBV (%) by pre-determining the blood loss (%), which is 100% – RBV (%), in each experiment.
We performed a correlation analysis between the actual and estimated RBVs (%) by drawing a calibration plot. Finally, drawing a Bland-Altman plot, we compared the estimated RBV (%) with the actual RBV (%) [24,25]. We expected the mean and standard deviation of their difference to be 0.0% of the TBV (0.0 cc) and 4.0% of the TBV (around 1.6 cc), respectively. In this preliminary, concept-validation study with a small sample size, we set the absolute maximum allowed difference as 20.0% of the TBV (4.0 cc). When the 95% confidence interval (CI) of the upper and lower limits of agreement were included in these maximum-allowed differences, the equation was considered validated.
We validated the original equation, RBV =
Male Sprague-Dawley rats weighing 280–350 g were used in this study. They were housed in a controlled environment with free access to food and water for one week prior to the experiments.
A very strong correlation was defined as
Considering the sample size, we simulated a 30.0% loss of TBV as well as increased blood loss in 5.0% increments (35.0%, 40.0%, and so on) within each experiment. When a rat died at a certain degree of blood loss (for example, 65.0% of TBV), we performed the same experiment again with another rat. If the next rat died, we designated the previous degree of blood loss (60.0% of TBV) as the upper limit of blood loss. We then decreased blood loss by 5.0% (25.0%, 20.0%, and so on). Similarly, when two consecutive rats failed to show signs of shock (mean arterial pressure ≤ 65 mmHg or lactate ≥ 2 mmol/L) given a certain degree of haemorrhage (e.g., 15.0% of the TBV), we designated the previous degree (e.g., 20.0% of the TBV) as the lower limit of blood loss. We expected that rats bleeding at the level of 20.0%–60.0% of TBV would be included in the current investigation, fulfilling the minimum sample size of n = 9 [11,27].
We divided the experiments into five sections, modifying a previously published model [28]. These study components were (1) preparation (baseline), (2) induction of haemorrhagic shock, (3) observation without further treatment, (4) restricted crystalloid fluid resuscitation, and (5) follow-up testing (Fig. 2). We used the subscripts _{0}, _{1}, and _{2} to denote baseline before bleeding, initial ED presentation after bleeding and before fluid resuscitation, and post-fluid resuscitation status, respectively, throughout the study description.
During the study preparation phase (baseline), we injected intramuscular anesthesia into the Sprague-Dawley rats: zoletil (50 mg/kg; Virbac, Carros, France) and xylazine (10 mg/kg; Bayer, Seoul, Korea). Endotracheal intubation was performed with a 14-gauge catheter (BD Insyte, Autoguard, NJ, USA) [29]. To avoid hypoxemia and maintain normo-ventilation [13], a mechanical ventilator (Harvard rodent ventilator model 645; Harvard Apparatus, Holliston, MA, USA) was applied with a tidal volume of 2.5 ml, a respiratory rate of 50 breaths/min, and 0.21 as the fraction of inspired oxygen. A 24-gauge catheter (BD Insyte) was introduced into the left femoral artery after sterile cut-down procedure to withdraw blood, replace/infuse fluid, and monitor heart rate (HR) and systolic, diastolic, and mean arterial blood pressure (SBP, DBP, and MAP). After administering anesthesia, the procedure itself took ≤ 5 min. After the disposal of 0.2 cc within the arterial line, we performed a baseline POCT_{0} (ABL90 FLEX PLUS; Radiometer Medical, Copenhagen, Denmark) with the next 0.2 cc of blood to check ABGA_{0}, lactate_{0}, haemoglobin_{0}, and Hct_{0} levels. Following this, 0.2 cc of normal saline was replaced to avoid intra-catheter clotting. Guided by ABGA_{0}, tidal volume was adjusted to a target pH level of 7.35–7.45 and a PaCO_{2} level of 35–45 mmHg. Vital signs_{0} (SBP_{0}, DBP_{0}, MAP_{0}, and HR_{0}) were recorded throughout the procedure.
For the second phase of the study, we induced haemorrhagic shock after pre-determining the target blood loss volume as TBV × target blood loss (%). We split this target volume to lose into three. Each third was shed slowly every 2.5 min; 0.6 cc of blood had already been shed during the preparation phase (specifically, 0.2 cc of blood was used for filling the catheter hub during initial catheterisation and subsequently discarded, and 0.4 cc was used to check POCT_{0} levels). We compensated for this loss by subtracting 0.6 cc from the first third of blood loss volume. After each blood withdrawal, 0.1 cc of normal saline was replaced to prevent intra-catheter clotting.
Phase (3) of the study comprised observation without further treatment over the course of 10 min, simulating the prehospital situation in which a ‘scoop-and-run’ treatment approach is preferred to a ‘stay-and-play’ approach in order to prevent unnecessary delays of definitive care [1,13,30]. Haemorrhage control, which is strongly recommended within medical guidelines, was accomplished per this protocol (i.e., we did not allow further bleeding).
We recorded vital signs_{1} immediately before phase (4) of the study, which comprised restricting crystalloid fluid resuscitation. After discarding 0.2 cc of blood within the line, 0.2 cc of blood was sampled to check POCT_{1} levels (especially Hct_{1}). We determined the volume of normal saline necessary to infuse N as 0.015 × body weight (g) (cc), which corresponds to approximately 1 L for a 70 kg adult [21,30-32]. We split N into three groups and infused fluid slowly every 5 min; The first bolus was subtracted by 0.5 cc: 0.2 cc had already been replaced after sampling for POCT_{0} during the preparation phase and 0.3 cc was replaced during blood loss induction.
Five minutes after completing fluid resuscitation, we initiated component (5) of the study (i.e., study follow-up). We checked POCT_{2} levels (including Hct_{2}) along with vital signs_{2}. The rats were then euthanised
At this point, except for
Due to a calculation mistake, we withdrew 33.4% of the TBV from a rat assigned to lose 35.0% of its TBV. We analyzed this erroneous observation as though it was purposeful (i.e., we did not perform any statistical corrections and did not remove the rat from the study).
Results for body weight, V/S, and POCT were calculated as means ± standard deviations.
Linear regression analysis was performed to generate a regression equation explaining RBV in terms of
Among the nine rats that experienced haemorrhagic shock, two recovered from shock after fluid resuscitation. We performed the main analysis with seven rats showing persistent shock despite fluid resuscitation.
As a supplementary analysis, we re-conducted the analysis including all the rats regardless of persistent shock. Additionally, we performed linear regression analyses to explain RBV (%) with the following potential predictive covariates: initial and final values and interval changes for vital signs, haematocrit, and lactate.
All statistical analyses were performed using IBM SPSS statistical software, version 26 (IBM Co., Armonk, NY, USA) and MedCalc Statistical Software, version 19.2.6 (MedCalc Software Ltd., Ostend, Belgium). Statistical significance was set at a threshold of p < 0.05.
The rats suffered shock when losing ≥ 20.0% of their TBV. However, those shedding 20.0%–25.0% of their TBV recovered from shock
The rats included in the analysis weighed between 285 and 334 g and their TBV ranged from 17.87 to 20.81 cc; N spanned 4.27–5.01 cc. The mean SBP_{0}, DBP_{0}, and MAP_{0} levels were 110 ± 11, 71 ± 7, and 84 ± 8 mmHg, respectively and the mean HR_{0} was 215 ± 18 beats/min. Mean haemoglobin_{0}, haematocrit_{0}, and lactate_{0} levels were 13.2 ± 0.8 g/dl, 40.6 ± 2.5%, and 0.9 ± 0.3 mM, respectively. Changes in vital signs and POCT findings according to the study timeline are shown in Figs. 3 and 4, respectively.
Within a linear regression analysis among the rats shedding 30.0%–60.0% of their TBV, the equation to estimate RBV was updated as 0.272 N / [(Hct_{1} / Hct_{2}) – 1] + 5.64 (95% CI of
The actual RBV (%) was expressed as 5.67 / [(Hct_{1} / Hct_{2}) – 1] + 32.8% (95% CI of the slope: 3.14–8.21, p = 0.002,
As supplementary analyses, we performed the same analyses including all nine rats that initially suffered haemorrhagic shock after bleeding. RBV was estimated as 0.302 N / [(Hct_{1} / Hct_{2}) –1] + 5.72 (95% CI of the slope: 0.138–0.466, p
The results of the regression analyses examining factors associated with RBV (%) are shown in Supplementary Figs. 3–5, respectively. These figures present initial and final values and interval changes for vital signs, haematocrit, and lactate. The relevant statistics are summarised in Supplementary Table 1.
This preliminary study aimed to mathematically derive a simple equation estimating RBV (%) mathematically
To our knowledge, this is the first study to suggest an equation to estimate RBV (%) mathematically in order to promptly and correctly calculate blood loss (%) [= 100% – RBV (%)] and to update and validate this equation
We conducted a regression analysis to explain RBV as a function of N / [(Hct_{1} / Hct_{2}) – 1], generating a y-intercepts of 5.64. Modification of a prediction rule with the addition of a y-intercept is commonly implemented to fit a new target population during external validation [23,33]. The original equation to estimate RBV included
Supplementary analyses revealed that the regression equations implemented for rats suffering from persistent shock despite fluid resuscitation were superior to those implemented among all the rats regardless of persistent shock shedding (i.e., 20.0%–60.0% TBV). In estimating RBV (%), the former showed greater a
Clinicians have estimated RBV (%) or blood loss (%) using vital signs, haemoglobin/haematocrit measurements, CVP/PCWP, ultrasonography, and visual estimation. Although useful, these methods provide only rough estimations. Tachycardia and hypotension, occurring within class I, II (mild), III (moderate), and IV (severe) haemorrhagic shock, are less reliable indicators for patients receiving antihypertensive medications (especially beta or calcium channel blocking medications) and their sensitivities are unsatisfactory [11,16]. Haematocrit does not reflect acute haemorrhage adequately as the plasma volume fails to increase sufficiently for achieving an euvolemic state [36]. Neither CVP nor PCWP predicts ventricular preload (which correlates with RBV) [37]. Although ultrasonography provides some hints regarding preload with respect to the diameter and collapsibility of the inferior vena cava as well as fluid responsiveness, these indicate RBV (%) indirectly; fluid challenge is less applicable for haemorrhagic shock patients whose fluid resuscitation should be restricted [18,38]. Meanwhile, visual estimation of blood loss is inaccurate and unreliable even in the operating room [14]. Due to these limitations, researchers combined these variables to enhance diagnostic accuracy [10,12]. For example, Callcut and colleagues suggested that massive transfusion is indicated when two of following factors are present: an international normalised ratio (INR) > 1.5, SBP < 90 mmHg, haemoglobin < 11 g/dl, a base deficit of ≥ 6 mM, and fluid revealed on focused assessment with sonography for trauma (sensitivity 85%, specificity 41%) [10]. However, these rules are relatively non-specific and cannot differentiate RBV (%) quantitatively.
Some researchers previously investigated the volume of infused crystalloid fluid or serial haematocrits (the key variables of the current study) as tools for RBV (%) estimation. The response to initial fluid resuscitation is suggested to help estimate blood loss (%), with rapid, transient, and minimal/no response correspond to minimal (< 15%), moderate and ongoing (15%–40%), and severe (> 40%) loss of TBV, respectively [11]. However, this approach cannot estimate RBV (%) quantitatively in order to guide fluid/blood resuscitation delicately, as required for successful haemorrhagic shock management.
Thorson and colleagues reported that Hct_{1}–Hct_{2} > 6% reliably indicate ongoing bleeding [39]. However, only 3.9% (9/232) of their study participants suffered shock and the interval to check the serial haematocrits was 120 ± 63 min even for patients with ongoing bleeding. These rendered their results less applicable for haemorrhagic shock, which required much faster fluid resuscitation followed by a repeat haematocrit measurement; 60% of patients die within 3 h after ED presentation for haemorrhagic shock [4]. Meanwhile, the current study (that dealt with the earliest phase of haemorrhagic shock) showed some correlation between Hct_{1}–Hct_{2} and RBV (%) (Supplementary Fig. 5F, Supplementary Table 1). This association may be explained mathematically using our equation:
As mentioned above, the equation to estimate RBV (%) contains Hct_{1}–Hct_{2} as a denominator. However, considering the effect of the numerator (Hct_{2}) on the whole equation, the equation including both the numerator and denominator is more robust than Hct_{1}–Hct_{2} alone. The
By replacing N/TBV with 0.24 in rats, we simplified the equation to estimate RBV (%) from
Of course, further clinical studies are required to modify these equations, including adjustment of the slope and the addition of a y-intercept [23].
In supplementary analyses, RBV (%) was closely associated with both initial and final values of SBP, DBP, MAP, lactate, and haematocrit (
This study had several limitations. First, this study dealt with ‘non-ongoing’ haemorrhagic shock. This confines the indication of this work to patients for whom instant haemostasis is achievable (for example, patients with penetrating extremity wounds, peptic ulcers, or perioperative bleeding). For most blunt trauma, maternal haemorrhage, and ruptured aortic aneurysm cases (i.e., the other major causes of mortality due to haemorrhagic shock), instant haemostasis may be difficult to achieve, thus rendering our study results less applicable [1,3]. However, the current equations may have some value even for ongoing haemorrhagic shock patients; for example, Hct_{2} would be lower among ongoing haemorrhagic shock patients than among non-ongoing haemorrhagic shock patients (e.g., 30.0%
Considering these limitations, we believe that this preliminary concept-validation study is a starting point for further investigations. First, the equation to estimate the RBV (%) needs to be established clinically in non-ongoing, haemorrhagic shock patients and in studies with a larger sample size. Although we proposed 5.0 / [(Hct_{1} / Hct_{2}) – 1] (%) for men and 5.8 / [(Hct_{1} / Hct_{2}) – 1] (%) for women (assuming a
In summary, this concept-derivation and preliminary
Supplementary data including one text, five figures, and one table can be found with this article online at https://doi.org/10.4196/kjpp.2022.26.3.195.
kjpp-26-3-195-supple.pdfThe authors express their cordial gratitude to Prof. Sang Do Shin for his insightful mentoring in this study. We also appreciate Miss Ha Eun Lee, BS, and Ye-Hee Chon for their help in performing the experiment and drafting figures, respectively. We thank Editage.com for English language editing.
None to declare.
The authors declare no conflicts of interest.
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