Standardized blood volume changes monitored by capnodynamic hemodynamic variables: An experimental comparative study in pigs

The capnodynamic method, based on Volumetric capnography and differential Fick mathematics, assess cardiac output in mechanically ventilated subjects. Capnodynamic and established hemodynamic monitoring parameters' capability to depict alterations in blood volume were investigated in a model of standardized hemorrhage, followed by crystalloid and blood transfusion.

K E Y W O R D S blood re-transfusion, blood volume, capnodynamics, continuous hemodynamic monitoring, fluid infusion, MAP, PPV, pulse contour analyses, standardized hemorrhage, SVV

Editorial Comment
For a recently-developed and advanced cardiac output assessment method based on controlled ventilation and capnography, this study presents further validation work based in experimental alterations in blood volume in a large animal model. Associations with circulatory interventions was demonstrated for cardiac output and other central circulatory variables, for the capnography-base instrument and reference measures.

| INTRODUCTION
Perioperative fluid management for patients undergoing major surgery is common and, if not managed properly, is associated with increased postoperative morbidity and length of stay. 1,2 The primary goal of perioperative fluid treatment is to normalize or maintain patients' intravascular blood volume. 3 However, there are no means to measure blood volume during operations in a simple continuous way.
Instead, other more accessible hemodynamic variables related to intravascular volume changes are measured. The variable that is considered to best reflect blood volume is stroke volume (SV). When the blood volume decreases, the stretch of the right ventricle decreases, which according to the Frank-Starling mechanism leads to a decrease in SV, and generally also a decline in CO. A decrease in blood volume and thereby CO is usually accompanied by a decreased MAP and increased HR, explaining why these variables are used for traditional hemodynamic monitoring. 4 Medical monitoring devices shall in their technical specifications state their accuracy and precision in relation to a flawless reference method. 5 However, such an undisputed reference does not exist for continuous clinical SV measurement.
Capnodynamics for continuous non-invasive measurement of effective pulmonary blood flow (EPBF) 6,7 is a development of the differential Fick's method (CO 2 ) 8 that may be of value for hemodynamic monitoring during rapid changes in blood volume. We have in a series of pre-clinical and clinical studies demonstrated its promising performance as a future clinical tool, 6,7,[9][10][11][12] but its capability to detect intravascular volume changes has previously not been investigated.
A standardized hemorrhage will according to physiology cause a significant drop in CO, SV, and MAP accompanied by an increase in pulse pressure variability (PPV) and stroke volume variability (SVV). 13,14 A subsequent crystalloid fluid infusion should transiently reverse those primary changes and a final ensuing blood transfusion would restore all hemodynamic parameters to their baseline level.
Thus, the primary purpose with this study was to examine the capability of the capnodynamic flow variables SV EPBF and CO EPBF to distinguish different blood volume states. A secondary aim was to compare SV EPBF and CO EPBF 's performance with other common continuous hemodynamic variables.

| Animal preparations
The study was performed according to ARRIVE-guidelines at the Hedenstierna Laboratory, Uppsala University, Uppsala Sweden on two occasions in 2020. Ten domestic-bred piglets of both sexes (median weight 29.6 kg, range 27.1-31.7 kg, 6-8 weeks of age), from the same breeding colony were used. The animals were handled in accordance with the animal experimentation guidelines of the Uppsala Animal Ethics Committee and the study was approved by Uppsala Animal Ethics Committee in August 2016 (Uppsala, Sweden case number C75/16). The subjects used in the current study have previously been part of another investigation, assessing the performance of Capno-SvO 2 against CO-oximetry. 15 The pigs were anesthetized using a standardized intravenous anesthesia protocol as previously described. 10 The animals were mechanically ventilated in a volume-controlled mode (Servo-I; Maquet Critical Care AB) with tidal volume of 10 mL/kg and fraction of inspired oxygen (FIO 2 ) 0.3. Positive end-expiratory pressure (PEEP) was kept at 5 cm H 2 O after an initial 2-min period of lung expansion using PEEP 10 cm H 2 O as previously described. 16 After this lung recruitment maneuverer, an air test using FIO 2 0.21 was performed and repeated if necessary, aiming for sustained pulse oximetry saturation >97% as indicative of open lung conditions. 17 The animals were given a bolus of Ringers' acetate solution 20 mL/ kg after induction to counteract a potential volume deficit due to fasting and thereafter kept on maintenance infusion of glucose 25 mg mL À1 8 mL/kg h À1 and Ringer's acetate solution 10 mL/kg/ h. Adequate anesthetic depth and analgesic level were tested regularly during the experiment.

| Monitored hemodynamic variables
Regular physiological parameters (SpO 2 , HR, invasive MAP and CVP) were retrieved from a Philips IntelliVue MP 50 monitor (Philips Medizin-Systeme Böblingen) and were automatically transferred into a data acquisition system (Acknowledge, version 3.2.7, Bio Pac Systems). The animals were kept in a supine position throughout the study and the pressure transducers were carefully positioned on a transfusion stand at the height of the right atrium.
A 5 F PiCCO-cannula (Pulsion Medical Systems SE) intended for continuous pulse contour based cardiac output monitoring, (CO PCA ), pulse pressure variability (PPV) and stroke volume variability (SVV) was inserted in a femoral artery. The PiCCO-cannula was also used for transpulmonary thermodilution CO TPTD calibrations of the CO PCA .
The animals were given a bolus dose of intravenous heparin 5000 U (LEO Pharma) to minimize the risk of clotting due to the extensive intravascular monitoring setup.
Pulse Contour Analysis calculates CO by analyzing the systolic part of the arterial blood pressure waveform. 18 The mathematical model considers several physiologic parameters such as, aortic compliance, vascular resistance, and wave (pulse) reflection and the PiCCOsystem (Pulsion Medical Systems) used was a normal commercial device. 19

| CO EPBF
CO EPBF is derived from a set of mole balance equations of carbon dioxide across the lung over a cycle of nine breaths (the capnodynamic equation).
EELV CO2 , effective lung volume (L) containing CO 2 at the end of expiration; CO EPBF , effective pulmonary blood flow (L/min); n, current breath; n À 1, previous breath; F A CO 2 , alveolar CO 2 fraction; C v CO 2 , mixed venous CO 2 content (L gas L blood À1 ); C c CO n 2 , lung capillary CO 2 content (calculated from F A CO 2 and hemoglobin concentration); VTCO n 2 , volume (L) of CO 2 eliminated by the current, nth, breath; and Δt n , current breath cycle time (min).
For a more detailed description of the CO EPBF methodology, the reader is referred to Appendix A as well as references 7 and 10.

| Stroke volume
The stroke volume for both CO EPBF and CO PCA was calculated as CO/HR, where HR was retrieved from the Philips monitor.

| Study protocol
We designed the study protocol to mimic a common clinical situation during surgery and intensive care-moderate intravascular blood volume deficit (in this study bleeding 450 mL), treated by an initial infusion of crystalloids and subsequent blood transfusion.
Based on established physiological knowledge 13,14 and hemodynamic reasoning 20 we expected a standardized hemorrhage to cause a drop in SV, CO, and MAP, in parallel with an increase of PPV, and SVV.
A subsequent isovolumic (450 mL) crystalloid fluid infusion was anticipated to transitory increase the intravascular volume with most of the stabilizing effect of the crystalloid expected to regress after 80 min due to fluid redistribution from the intravascular space to the extracellular space. 21 The final blood transfusion was anticipated to restore the blood volume to its original level. The predicted alterations in blood volume were confirmed by determining the blood volume at each measurement point by the methodology developed by Hahn. 21,22 The blood volume for a healthy conscious piglet has been found to be 67 mL kg À1 . 23 This figure was used to determine original blood volume; thus, initial variability only depends on the pigs' different weights. Since, the exact amount of the hemorrhage, Ringeracetate infusion and blood re-transfusion is known, no important uncertainties in blood volume determination at the different measuring points exists. Hence, this method for determination of blood volume is considered valid and has previously been used in several publications. 21,22 The primary aim was to investigate the capnodynamic flow variables SV EPBF and CO EPBF capability to distinguish, and trend differences, between three different blood volume states. The secondary aim was to compare SV EPBF and CO EPBF 's performance to depict blood volume shifts against common continuous hemodynamic variables, such as SV PCA , CO PCA PPV, SVV, and MAP. Both early and late responses following the three different interventions were determined for all variables Accordingly, six measuring points from the study's three blood volume states (bleeding, fluid replacement, and blood transfusion) were investigated.
The study protocol is outlined in Figure 1.

| Baseline
A blood sample for hemoglobin (Hb), necessary for the capnodynamic calculations, was taken and analyzed by a CO-oximeter calibrated for porcine Hb (OSM3; Radiometer Medical AbS). Additional Hb-samples were then taken at each measurement point and those are shown in Figure 1 and used for the calculation of blood volume.
A CO TPTD calibration of the CO PCA system according to the manufacture's instruction followed and then baseline measurements were taken about 5 min later.

| Hemorrhage
After baseline measurements, 450 mL of blood (approximately 20% of blood volume) was drained for 5-10 min and kept in a plastic bag intended for donor blood, containing 5000 U of Heparin. All hemodynamic variables were recorded 5 and 15 min after completed hemorrhage.

| Volume replacements
Following the post-hemorrhage measurements an isovolemic bolus, 450 mL, of Ringer-acetate solution (Fresenius Kabi) was infused centrally over 5 min. New measurements were recorded 5 and 20 min following the completed Ringer-acetate infusion.

| Transfusion
Eighty minutes after completed Ringer-acetate infusion, and immediately prior to the blood transfusion, the PiCCO-system was recalibrated to ensure good performance of the pulse contour technique.
At the same point the capnodynamic method was recalibrated with a new Hb-value. The previously collected blood was thereafter retransfused (450 mL) over 5 min and final measurements were performed 5 and 20 min after the blood transfusion.

| Statistics and result presentation
Results are presented as mean and standard deviation. One-way ANOVA, repeated measurements, without assumption of sphericity and with Geisser and Greenhouse correction applied was used to identify significant changes between blood volume states. Tukey's test for multiple comparisons was used to identify significant differences between measures of each hemodynamic variable at the following six points 24 : (1a) "Hemorrhage 5 min" versus "Baseline," (1b) "Hemorrhage 15 min" versus "Baseline," (2a) "Fluid 5 min" versus "Hemorrhage 15 min," (2b) "Fluid 20 min" versus "Hemorrhage 15 min," (3a) "Blood 5 min" (5 min after completed blood transfusion) versus "Fluid 80 min" (just before blood transfusion) and (3b) "Blood 20 min" versus "Fluid 80 min." Moreover, the ANOVA parameter R 2 was calculated to quantify how large part of the total variation in the ANOVA the specific intervention represents. In this study, R 2 describes how well a hemodynamic variable detects a shift in blood volume. R 2 is calculated from sum-of-squares (SS) and is equal to partial eta squared. 25 Thus, SStreat is sum-of-squares related to treatment and where the residual sum-of-squares is denoted as SSresidual.
The mean value of the difference (with confidence interval) between two measurement points is also presented as its size is of both statistical and clinical significance.
To further assess each hemodynamic variable's ability to follow the induced intravascular volume shifts, a concordance analysis was done where each hemodynamic variable's response (PPV and SVV are negatively correlated to blood volume changes) was compared against the determined changes in blood volume. Thereby a binary situation, to concord or not concord, is created according to the change in blood volume and a concordance rate with standard deviation (SD) and Confidence interval (CI) can be calculated as previously described. 11 Finally, the correlation coefficient (Pearson) and coefficient of determination between calculated blood volume and each of the investigated hemodynamic variables were determined.  The ANOVA revealed that all investigated hemodynamic variables changed significantly during the blood volume alterations. The subsequent Tukey's test, however, showed tangible differences in the variables ability to significantly trace blood volume changes.
All results are presented in detail in Tables 1 and 2 Table 2 T A B L E 1 Early and late response for each hemodynamic variable presented as the mean difference with its 95% confidence interval and corresponding significance level after bleeding, fluid resuscitation, and blood transfusion. Note: "Hemo versus BL" describes the difference between baseline and after hemorrhage (5 and 15 min, respectively).
"Fluid versus Hemo" describes the difference between hemorrhage (hypovolemia) and after an isovolemic Ringer-acetate infusion (5 and 20 min, respectively). "Blood versus Fluid 80" depicts early (5 min) and late (20 min) response when withdrawn blood was transfused 80 min after initiation of fluid infusion. The last column presents the number of intravascular volumes shifts each hemodynamic variable was able to significantly detect and corresponding R 2 , an ANOVA-derived quality measure quantifying how large part of the variation the examined intervention was responsible for. In this study, R 2 reflects how well a hemodynamic variable detects an intravascular volume shift. Significant figures are in bold. To be noticed, the significant reductions of CO PCA at "Blood 5 and 20 versus Fluid 80" are inconsistent to the change in blood volume and are therefore underlined in the table.
shows the concordance rate for the hemodynamic variables against the calculated blood volume in a binary manner without exclusion zone, together with the correlation coefficient (r) and the coefficient of determination (r 2 ).
In summary, CO EPBF significantly identified 6 and SV EPBF 5 of the 6 blood volumes changes and tracked the different intravascular volume states with an excellent concordance, 96 and 94%, respectively.
MAP and PPV (both significantly identifying 3 out of 6 blood volume states) also performed well with a concordance of 85% and 87%, respectively. Their correlation to determined blood volume were .67 and .45, respectively. The continuous hemodynamic variables from the PiCCO-system were unable to reliably identify the changes in  blood volume. At the two measuring points after the blood re-transfusion, when blood volume was restored, CO PCA presented a significant decrease (À.42 ( p = .002) and À.34 (p = .04) L/min) in CO. CO PCA was also unable to track any of the other blood volume changes significantly and its concordance and correlation were 67% and .31, respectively. SV PCA significantly tracked 1 of 6 blood volume states.
The concordance for SV PCA was .63 and its correlation to the blood volume was .28. SVV also identified 1 of 6 blood volume states and its concordance was 76% with a correlation to blood volume of .18.

| DISCUSSION
The capnodynamic variables, CO EPBF and SV EPBF , best depicted the changes in intravascular blood volume in this experimental animal study. The conventional static hemodynamic variable MAP, and the dynamic PPV, also performed adequately but mirrored the expected physiologic pattern less consistently.
The ability of CO EPBF to adequately detect CO changes caused by alterations in intravascular volume status (preload) is in line with the results in two recently published clinical studies. 11,26 In anesthetized children CO EPBF detected the reduction in CO caused by increased PEEP ahead of, and more reliable, than non-invasive blood pressure monitoring. 11 In adults undergoing major abdominal surgery CO EPBF was observed to decrease rapidly, and in parallel with MAP, during a major surgical bleeding (>15% of the blood volume) which in contrast CO PCA , did not. 26 The inability of CO PCA to detect blood volume changes is also present in this experimental study. Since we already in our pilot animals identified performance issues for CO PCA , we decided to insert an extra trans-pulmonal thermodilution calibration point just before the transfusion of blood to ensure optimal prerequisites for the CO PCAmethod. Despite this extra calibration, CO PCA 's concordance was inferior to both MAP and PPV and was in fact not able to significantly T A B L E 2 Concordance and correlation between blood volume and the investigated hemodynamic variables. Correlation (Pearson) r = .68 r = .28 r = .78 r = .31 r = À.18 r = À.45 r = .67 Correlation, (p-value and r 2 ) p < .0001 r 2 = .47 p = .01 r 2 = .08 p < .0001 r 2 = .61 p = .007 r 2 = .10 p = .11 r 2 = .03 p < .0001 r 2 = .20 p < .0001 r 2 = .45 Note: For SV EPBF , SV PCA , CO EPBF , CO PCA and MAP concordance against calculated change in blood volume was analyzed by considering the tested variables response to calculated change in blood volume as binary, that is, to increase in response to increased blood volume and vice versa. For PPV and SVV, the calculated change in blood volume was correlated to the corresponding established response for these variables, that is, an increase in blood volume should lead to a decrease in PPV and SVV. This enables the calculation of a concordance rate and SD with subsequent 95%CI for the concordance as previously described. Values for concordance rate are: (%) (SD) and the lower boundary for the concordance's 95%CI. r 2 on the correlation line is the coefficient of determination.  Table 2.
detect any intravascular volume shift, except for a significant erroneous decline in cardiac output, 5 and 20 min after the blood retransfusion (Table 1, Figure 2B). Our healthy piglets, with normal myocardial function, had a measured SV of about 45 mL at baseline, representing a normal value for pigs of this size. 27 Moreover, the two calibrations of CO PCA against CO TPTD resulted in CO PCA becoming very similar to the CO EPBF values ( Figure 2B). A decline in SV seen for SV PCA , to a value lower than the baseline value after a blood transfusion, implicates a defect Frank-Starling mechanism which is highly unlikely in 3 months old healthy piglets.
Consequently, the indicated decrease in SV PCA and significant decrease in CO PCA after the blood transfusion is most likely incorrect, whereas the increased SV EPBF and CO EPBF with high significances, depicted the true changes in blood volume.
The poor performance of the pulse contour method in this clinically relevant situation of blood loss followed by fluid replacement SVV, based on CO PCA , had a lower concordance rate than PPV and MAP and did not provide any new reliable hemodynamic information in this study. (Table 2, Figures 3 and 4).

| Study design issues
One apparent issue with hemodynamic studies is the lack of undisputed flawless reference methods. To circumvent this problem, we decided to use the established and validated method for the determination of sequential changes in blood volume as comparator. 22

FUNDING INFORMATION
The cost for the animal lab was covered by Maquet Critical Care AB, Solna, Sweden.

DATA AVAILABILITY STATEMENT
The data that support the findings of this study are available from the corresponding author upon reasonable request. EELV CO2 Â F A CO n 2 À F A CO nÀ1 2 ¼ CO EPBF Â Δt n Â C v CO 2 À C c CO n 2 À Á À VTCO n 2 , EELV CO2 , effective lung volume (L) containing CO 2 at the end of expiration; CO EPBF , effective pulmonary blood flow (L/min); n, current breath; n À 1, previous breath; F A CO 2 , alveolar CO 2 fraction; C v CO 2 , mixed venous CO 2 content (L gas L blood À1 ); C c CO n 2 , lung capillary CO 2 content (calculated from F A CO 2 and hemoglobin concentration); VTCO n 2 , volume (L) of CO 2 eliminated by the current, nth, breath; and Δt n , current breath cycle time (min).
Briefly, the Servo-I ventilator generates short automatic expiratory pauses (4-5 s) in three out of every nine breaths resulting in small differences (0.5-1 kPa) in the alveolar concentration of CO 2 (F A CO n 2 Þ over a cycle of nine breaths. The exhaled CO 2 is measured, breath by breath, by Servo-I's mainstream infrared CO 2 sensor (Capnostat-3; Respironics), and ventilation airflow is retrieved from the regular flow sensor in the Servo-I ventilator. From each created volumetric capnogram it is possible to obtain F A CO n 2 and the actual CO 2 elimination rate (VTCO n 2 ). The mole balance equation for carbon dioxide contains three unknown variables, EELV CO2 , CO EPBF and C v CO 2 . Since each breath creates a new equation, the set of nine breaths gives us an overdetermined system of

APPENDIX B
Each subject's response to blood volume changes: