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Nephrology

Determining Lung Water Volume in Stable Hemodialysis Patients

MacRae, Jennifer M.*; Joseph, Geena; Kislukhin, Victor; Krivitski, Nikolai M.; Heidenheim, A Paul; Lindsay, Robert M.

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doi: 10.1097/01.mat.0000225269.71817.6e
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Abstract

Most hemodialysis patients are volume expanded and determining their dry weight is difficult. Any tool that might aid in this process would be welcome to the field of in-line monitoring. There is a new technique that can determine the extravascular lung water (LW) volume in a noninvasive manner in hemodialysis patients. LW reflects the water content of the interstitium. Perhaps ultimately, by targeting the ultrafiltrate to a set LW removal, we may better approximate the ideal dry weight in hemodialysis patients. However, before this technique can be applied clinically, we need to demonstrate that LW can be easily obtained in hemodialysis patients, and that it changes with ultrafiltration. Because hemodialysis patients have expanded total body and extracellular volumes, we postulate that they may also have increased LW which can be removed with ultrafiltration.

The ability to estimate LW is not new. Older studies have employed various techniques using diffusible and nondiffusible indicators like dyes, thermal dilution, radiolabeled substances, or hypertonic saline solutions.1–6 Others have measured the osmotic fluid shifts through the lung microcirculation using blood density dilution transients.7,8 Krivitski et al.9–11 developed a technique for measuring LW in a noninvasive manner using electrical impedance dilution and ultrasound velocity techniques. This technique is based on the same principle of the classic method of multiple indicators, where the diffusible indicator is water that moves across the lung capillary under the influence of the osmotic gradient. In animal studies, dilution derived LW values is in agreement with gravimetric measurements and measurements using the classic indicator dilution methods.9,11

The technique using optical density dilution and ultrasound velocity has been used in only one study to date in hemodialysis patients.12 This method was quite difficult to perform and did not translate easily to clinical use. Considering that the permeability of sodium is so much less than that of water during the passage of hypertonic saline through the lung microcirculation, the technology may be simplified to use only the ultrasound velocity dilution technique (see theory and Appendix). This noninvasive method uses 0.9% normal saline as the indicator that stays within the blood vessels (nondiffusible) and 5% hypertonic saline as the indicator that produces an osmotic gradient for water flux across the lung capillaries (the diffusible indicator). By injecting these solutions and following their transit through the cardiopulmonary circulation, the LW can be derived from the cardiac output, the amount of water transferred to blood, and the increase in blood osmolality measured at the moment of osmotic equilibrium.

The purpose of this study was to: 1) determine the feasibility of obtaining LW volume derived with blood ultrasound velocity dilution, 2) determine the LW in stable hemodialysis patients at baseline and again after ultrafiltration to their assigned goal weight, and 3) compare the changes in LW to the changes in fluid compartment shifts obtained using bioimpedance technology. A description of the principle and revised technique of LW determination using ultrasound velocity dilution is also provided.

Materials and Methods

We studied 24 chronic stable hemodialysis patients with native arteriovenous access during routine hemodialysis treatments. The subjects had all been receiving conventional 4-hour, three-times-weekly hemodialysis therapy for end-stage renal failure for at least 1 year. These patients were selected based on their known hemodynamic stability during dialysis, stable vascular access, lack of documented cardiovascular disease (congestive heart failure), and willingness to participate. All patients were over the age of 18 years and gave informed consent to participate in this institutionally approved study.

All patients were dialyzed on an Integra (Hospal, Richmond Hill, Canada) dialysis machine at blood pump speeds of 400–450 ml/min. Baseline blood pressure, heart rate, predialysis weight, and ideal body weight were recorded. Cardiac output, LW, total body water (TBW), and extracellular and intracellular fluid volumes (ECF and ICF) were measured within the first hour and last hour of the dialysis session. Cardiac output and LW were determined using ultrasound dilution technology. The LW values obtained were recorded as an absolute value and normalized (specific LW) to the patient's weight at the time of measurement (milliliters per kilogram). This was done by adjusting the predialysis weight for the amount of ultrafiltration that occurred at the time of measurement. The peripheral volumes (TBW, ECF, ICF) were measured using bioimpedance technology.

Fluid Compartment Technology

Bioimpedance was measured using the Hydra ECF/ICF Spectrum Analyzer 4 200 (Xitron Technologies, San Diego, CA) to obtain TBW, ECF, and ICF volumes. Patients' weight and height were obtained and electrodes were placed in the standard tetrapolar lead distribution to the wrist and ankle opposite to the side that contained the fistula.14 Subjects were supine with their heads elevated at 45 degrees for at least 10 minutes and the arms and legs were comfortably abducted. Bioimpedance measurements were taken within the first hour of hemodialysis and repeated after ultrafiltration during the third hour of a 4-hour dialysis session. The Bioimpedance Spectrum Analyzer measures impedance spectra using programmed frequencies ranging from 5 kHz to 1 MHz and, using the Cole-Cole mathematical model, it fits these data and calculates extracellular and intracellular resistance values.15 Volumes are then determined from these modeled resistance values using equations from the Hanai mixture theory16 and ultimately provides whole-body ECF and ICF volumes.

Lung Water Technique

Cardiac output and LW measurements were performed using the Transonic Hemodialysis Monitor, HDO1 Plus (Transonic Systems Inc, Ithaca, NY). The LW method used in this study is modified from the original optical density dilution and ultrasound velocity technique.12 The current technique only requires venous and arterial ultrasound probes and omits the need for placement of a specialized optical density probe onto the hemodialysis tubing. This new method and software allows for cardiac output, central blood volume, total peripheral resistance, LW, and osmotic pressure information to be automatically extracted from ultrasound dilution curves.

The experimental protocol involves adding an adapter, Transonic Flow-QC set (Transonic Systems) along with ultrasound probes to the venous and arterial dialysis lines in order to detect changes in the blood ultrasound velocity. Then 30 ml of normal saline (NS) prewarmed to 37°C is injected into the venous blood line over 5–7 seconds and the corresponding ultrasound dilution curve is recorded by the probe on the arterial line. After the NS arterial dilution curve is recorded and the cardiac output is calculated (described in detail elsewhere13), 20 ml prewarmed (37°C) hypertonic saline (HS) is injected into the venous line over 5–10 seconds and the subsequent arterial dilution curve is obtained. The information extracted from both dilution curves is automatically applied to equation 11 (see “Lung Water Equations”) using the transonic software version 1.03 to obtain a LW measurement. All measurements are done in duplicate at the beginning of dialysis (within 60 minutes) and during the last hour of dialysis after ultrafiltration.

Description of Lung Water Theory

The use of ultrasound dilution to determine lung water is based on the same theory as the classic indicator dilution method except that the diffusible indicator (hypertonic saline, HS) is associated with water movement caused by its osmotic gradient.

The technique involves injecting 30 ml of a nondiffusible indicator (NS) into the venous tubing of the arteriovenous access. The NS mixes with the blood and, after passing through the right heart, the lung circulation, and the left heart, it enters the arterial tubing of the arteriovenous access where the arterial flow dilution probe records a transient decrease (Figure 1) in the ultrasound velocity because NS has ultrasound velocity (1533 m/s) less then blood (1560–1585 m/s). The velocity of sound through the blood decreases with NS injection. Because NS is a nondiffusible indicator, it is assumed to pass through the lung without any flux of sodium or water. While blood ultrasound velocity is recorded (Y scale, m/s in Figure 1), in the following equations a coefficient K0.9 is used to establish the relationship between the recorded changes of ultrasound velocity and the concentration of the isotonic saline in blood: (ml, NS) / (ml, blood).

Figure 1.
Figure 1.:
The Effect of 30 ml Normal Saline (NS) Injection on Blood Ultrasound Velocity in the Venous Line (upper trace) and the Arterial Line (lower trace). The value S is used to determine the cardiac output. The area Sc0.9 is required to determine the calibration coefficients, K0.9. This coefficient establishes relationship between the recorded changes of ultrasound velocity (Y scale, m/sec) and the concentration of indicator saline in blood: (ml, NS)/(ml, blood).

The dilution curve is different for HS, the diffusible indicator (Figure 2). The ultrasound velocities of blood and HS are very similar, and thus the sound velocity of blood mixture does not change much after the injection of HS (see Figure 2, the upper curve for the venous sensor). If HS passed through the lung as a nondiffusible indicator (which we know it is not), then the dilution curve would look like one of the theoretical curves line in Figure 3 depending on the hemoglobin concentration in the blood.

Figure 2.
Figure 2.:
The Effect of 20 ml Hypertonic Saline (HS) Injection on the Blood Ultrasound Velocity in the Venous Line (upper trace) and the Arterial Line (lower trace). The bottom curve shows that HS injection produces a biphasic effect on the blood ultrasound velocity. The initial decrease in blood ultrasound velocity is due to the flux of water from the lung capillary produced by the osmotic gradient of the HS. As the bolus passes through the lung capillary the osmotic gradient then reverses and causes water to flux into the lung. The amount of water flux from lung to blood is an indirect measure of the extravascular lung water content. The area Sc5 is required in order to determine the calibration coefficients, K5. Velocity (m/s) is on the y axis and time (seconds) on the x axis.
Figure 3.
Figure 3.:
Theoretical Curve of Hypertonic Saline as a Non-diffusible Indicator. If hypertonic saline, HS passed through the lung as a non-diffusible indicator then depending on the concentration of proteins in the blood the dilution curve would look like the solid (if HS has higher ultrasound velocity than blood producing an increase in sound velocity) or dashed if HS has lower ultrasound velocity than blood producing a decrease in sound velocity. The difference between the theoretical dilution curve (if HS was a non-diffusible indicator, dashed curve) and the actual dilution curve (thin line) dS(tp) is solely due to the flux of water. dS(tp) is the area calculated until the point of crossing, tp.

After the HS mixture passes the lungs, it generates a flux of water from the lung tissue into the blood, because of the difference in osmotic pressure between the HS and the lung tissue. The osmotic pressure in the lung tissue increases until it equals the osmotic pressure of blood. As the bolus then passes through the capillary bed, the osmotic pressure of the blood drops, the direction of the osmotic pressure gradient reverses, and water begins to return to tissue. The change in osmotic pressure gradient produces the biphasic aspect of the dilution curve (Figure 2). The amount of time that the lung tissue is actually exposed to the hypertonic saline at first pass is relatively short, about 10–20 seconds (Figure 2). During a single pass through the lung capillaries, the capillary wall is impermeable to NaCl19 and the flux of sodium can be ignored in the determination of lung water.

Lung Water Equations

The LW calculation compares the time lag between the dilution curves of the NS and HS.17,18 The lung water can be determined from the osmolarity of the lung tissue, P and N, the quantity of osmotically active particles within lung tissue20:

Initially the osmolarity of the lung tissue is equal to the osmolarity of the blood, Pb. Assuming that the quantity of osmotically active particles within the lung water does not change during the pass of the hypertonic saline the following formula applies:

Equation 2 can be rewritten as the equation for LW:

Thus, if osmotic pressure varies, we can obtain LW from the relation of induced changes of LW, dV(t), to the changes in the lung tissue osmolarity, dP(t). Because P(t) = p + dP(t), to get LW, we need only the amount of water withdrawn from lung at time t, dV(t), and the increase of osmotic pressure within the LW at the same time, dP(t).

Determining dV(tp)

If HS were a nondiffusible indicator, then the HS dilution curve would either approximate the dotted line, if the ultrasound velocity of blood is higher, or the solid line, if the ultrasound velocity of blood is lower (Figure 3). Nevertheless, the difference between the real hypertonic dilution curve and this theoretical dilution curve is solely due to flux of water.

Point tp is the cross point of two curves: the real curve of the hypertonic indicator and the hypothetical curve of the hypertonic indicator if no water was exchanged. Up until tp the net direction of flux is from tissue to blood; after tp water begins to return to lung tissue, and at point tp there is no flux of water. It is assumed that the flux of water into the blood until time tp occurs because the “average” osmotic pressure in blood within lung microcirculation is higher than “average” osmotic pressure within lung tissue. After tp the gradient reverses, and at tp P(lung) = P(blood). The area between the HS dilution curve and the theoretical dilution curve in Figure 3, dS(tp), is generated by the flux of water due to the osmotic gradient. The transfer of the recorded area dS(tp) into actual milliliters of water can be performed by using the classic indicator dilution equation for CO where generated flux of water dV(tp) considered as an indicator:

Where CO and dS(tp) are known and kH2O is the calibration coefficient for water. kH2O establishes the relationship between actually recorded changes of ultrasound velocity (Y scale, m/s in Figure 3), and the concentration of indicator (ml of water)/(ml of blood) and may be calculated from the calibration coefficients for NS and HS (Appendix). The equation for dV(tp) is simply a modification of Equation 4:

The point tp, in Figure 3, is a convenient point not only for the calculation of the amount of withdrawn water from lung but also for the estimation of the osmolarity increase, dP(tp) within the lung tissue at time tp.

Estimation of Osmolarity Increase within Lung Tissue, dP(tp)

The assumption that the osmotic pressure within the lung, P(lung), is the average lung tissue osmotic pressure provides the opportunity to measure P(tp) and dP(tp). We assume that when a hypertonic solution is mixed with blood, the resultant osmolarity is derived from the following equation:

A major problem in directly applying Equation 6 to the mixture of blood and the hypertonic solution arises from the variability of the amount injected over time (time of injection is usually about 3-4 seconds). To circumvent this problem, the equation for the amount of injected volume from time t to t + dt can be determined (Equation 7). Figure 4 shows the distribution curve for the injection of the 30 ml NS. Because HS passes the lung microcirculation without any flux of water in the vicinity of point tp, we can therefore use the dilution curve from Figure 4 to calculate the volume of the hypertonic solution passing around point tp. However, because 20 ml HS is injected instead of 30 ml, then this distribution curve must be reduced by two thirds. Equation 7 is as follows, where S(t, dt) is area under the distribution curve within time interval (t, t + dt), and ST is the area under curve within time interval T, h is the height of the curve at time t, and Vinj is the volume injected (Figure 4).

Figure 4.
Figure 4.:
Distribution Curve for Volume of Normal Saline Injected. From the distribution of injected volume we can determine the fraction of injected volume that passes from time t to t + dt., S(t, dt) = h * dt

In Equation 7, h and ST are taken from dilution curve of normal saline, and in equations below, they are denoted as h0.9and S0.9. Again, at the point tp there is no flux of water, and the osmotic pressures of the blood and the lung tissues are equal. Because there is no water flux at point tp, we can estimate the osmolarity of blood at time tp from Equation 6:

Substituting the expression for V(tp,dt) from Equation 7 into the above Equation 8 leads to the following equation for P(tp,dt):

Because Equation 9 does not depend on dt it can be omitted, leaving us with the equation for dP(tp):

We now have all the parameters for the LW calculation: p(tp), dv(tp), and dP(tp).

Statistical Analysis

Descriptive data are presented as mean and standard deviation, median (range), or percentages as appropriate. Student's t test for paired data was used where applicable using SPSS version 12.0 (SPSS Industry, Chicago, IL). Statistical significance was defined as p < 0.05. Associations between variables were assessed by Pearson's correlations and considered significant at p < 0.05.

Results

We obtained LW and hemodynamic measurements in 24 chronic stable hemodialysis patients. The average age of the patients was 64.3 ± 13.9 years; 62.5% were male, and the prevalence of diabetes was 42%. All patients had native arteriovenous fistula most of which were located in the lower arm (18), with very few in the upper arm (6).

The infusion of 5% HS increased the blood osmolarity by 24.4 ± 5.7 mOsm/l which resulted in 18.4 ± 4.4 ml water flux from the lung into the blood vessels. This amount of water flux did not significantly change with ultrafiltration (18.5 ± 4.8 ml). The cardiac output and LW measurements appeared to be reproducible with a mean difference within the cardiac output and LW replicates of 9.4 ± 8.2% and 11.8 ± 8.9% respectively.

During these dialysis sessions there was a mean net fluid removal of 1.88 ± 0.96 l, which produced significant hemodynamic changes in the dialysis patients (Table 1). Ultrafiltration produced a significant drop in the cardiac output and CBV compartment. Despite a significant increase in the total systemic resistance, there was a trend to a decrease in the mean arterial pressure.

Table 1
Table 1:
Hemodynamic Effects of Ultrafiltration

Table 2 shows the effect of ultrafiltration on the distribution of body fluid as well as the effect on the lung water changes. Ultrafiltration produces a significant drop in the TBW, the majority of which is associated with a significant decrease in the ECF volume. The decrease in ICF volume did not reach statistical significance (p = 0.084). At the onset of dialysis the LW and specific LW volumes were 298.8 ± 90.2 ml and 3.67 ± 1.47 ml/kg respectively. Ultrafiltration significantly decreased the LW to 250.8 ± 55.8 ml or 3.12 ± 0.96 ml/kg, p < 0.05. The patients had expanded ECF volumes at baseline with an ECF: ICF ratio of 1.00 ± 0.07 as compared with the expected ECF:ICF ratio of 0.50. This ratio significantly decreased with ultrafiltration but still remained elevated at 0.96 ± 0.58, p < 0.05.

Table 2
Table 2:
Fluid Compartment and Lung Water Changes due to Ultrafiltration

There was no correlation between the changes in LW and TBW (r2 = 0.0083), ECF (r2 = 0.004), ICF (r2 = 0.0014), or ECF: ICF (r2 = 0.0679) that occur with ultrafiltration (graphs not shown). Similarly, no relationship was found when using the specific LW values (data not shown). As can be seen from Figure 5, there is a slight relationship between the decrease in LW volume and the amount of ultrafiltrate removed (r2 = 0.22, p < 0.05). There also is a trend to a correlation between the change in the CBV and the change in the LW (r2 = 0.26, p > 0.05). When the CBV is normalized to the body weight at the time of the measurement (specific CBV, ml/kg), the relationship between the change in specific CBV and the change in LW becomes significant (r2 = 0.21, p < 0.05) (Figure 6).

Figure 5.
Figure 5.:
Relationship between the Change in Lung water, delta LW (dL W) and Ultrafiltration. There is a slight relationship between the decrease in LW volume and the amount of ultrafiltrate removed (r2 = 0.22, p < 0.05).
Figure 6.
Figure 6.:
Scatter Plot of the Change in Specific Central Blood Volume (dCBVi) (ml/kg) and the Change in Lung Water. There is a weak but significant relationship between the change in the central blood volume index and the change in the lung water volume (R2 = 0.21, P < 0.05).

Discussion

Measuring LW volume using ultrasound dilution technique appears to be feasible, reliable, and easy to perform in hemodialysis patients. This technology is noninvasive and does not require any specialized equipment other than ultrasound flow probes which, now that access flow monitoring is the standard of care, should be available in most hemodialysis units. This is the first study to perform LW measurements in hemodialysis patients using only ultrasound flow probes and, furthermore, it is the first study to examine the reproducibility of this technique as well. We found that the difference between replicates for cardiac output and LW is within physiologic variation (9.4 ± 8.2% and 11.8 ± 8.9% respectively). To date, the only other study in hemodialysis patients (Garland et al.12) used an older more complex method requiring both optical density and ultrasound flow probes. Although Garland et al. did not have the opportunity to perform reproducibility data for LW measurements, our LW results are consistent with this previous study. We found that chronic stable hemodialysis patients have specific LW values of 3.12 ± 0.96 ml/kg similar to the specific LW of 3.02 ± 1.04 ml/kg obtained by Garland and colleagues. As one would expect, when hemodialysis patients are at their most volume expanded state they have specific LW values (3.67 ± 1.47 ml/kg) that are higher than what is reported in the normal population (approximately 2 ml/kg). These values, however, appear to be much lower than the 4–5 ml/kg reported by classic multiple indicator dilution studies in patients with overt congestive heart failure (CHF).2 This finding is not surprising considering that we selected patients who did not have a history of CHF and who thus have LW values that are much lower than those found in CHF patients.

We also demonstrated that ultrafiltration can significantly reduce the specific lung water (3.67 ml/kg vs 3.12 ml/kg, p < 0.05); however, this decrease in LW was only slightly correlated to the volume of ultrafiltrate. One possibility for the lack of a strong correlation is that the ultrafiltrate volume is not a surrogate for euvolemia, and perhaps with more aggressive ultrafiltrate removal a stronger correlation may have been found. Another explanation may be that in patients with elevated pulmonary capillary wedge pressures, the difference between the osmotic pressure gradient and the hydrostatic pressure gradient may be lessened, and thus the degree of LW will be underrepresented. When we looked at the change in CBV normalized to body weight (specific CBV), we found a positive relationship with the change in the LW that occurred with ultrafiltration (p < 0.05). This suggests that perhaps those patients with more LW have higher blood volume in their central veins and perhaps higher central venous pressures.

We have shown that hemodialysis patients are volume overloaded at the onset of the dialysis session with elevated ECF volumes and ECF:ICF volume ratios. Despite the expanded ECF volumes, we did not show a correlation between the decrease in ECF and the decrease in LW that occurs with ultrafiltration. However, this is not altogether surprising given that the bioimpedance method of determining ECF changes is probably insensitive to small changes in the thorax region. Bioimpedance studies have shown that most of the changes in the ECF compartments occur in the extremities (legs).21 Thus, perhaps the small changes in the lung may not be reflected by the changes in the ECF. In fact, whole-body bioimpedance analysis is fairly insensitive to changes in the fluid content of the abdomen of peritoneal dialysis patients22 and, therefore, is likely to be fairly insensitive to volume changes in the thorax.

There are several limitations to this study. The first is that we did not compare our results directly with the “gold standard,” the multiple indicator dilution method. However, our results for specific LW are consistent with other human and animal studies using either the ultrasound or various other indicator dilution techniques. Another limitation of this study is that we did not obtain echocardiographic evidence to document the absence of cardiac disease. The patients selected for the study did not have a known history of cardiovascular disease, however, given the prevalence of cardiac disease in the hemodialysis population, it is quite likely that some of our patients had occult left ventricular dysfunction. Furthermore, we did not examine the variability of our technique in between hemodialysis sessions in this study; however, this is currently underway.

The injection of a hypertonic solution is known to dehydrate red cells and decreases their ability to deform; subsequently, they pass through the lung microcirculation more slowly. This phenomenon (the retention of red cells within the microcirculation after exposure to HS) leads to an overestimation of the water drawn from the lung tissue and subsequently overestimates the LW. However, data from earlier papers23 suggest that the contribution from the retention of red cells is modest and probably results in an overestimation of LW by approximately 5–10%.

Some of the assumptions with respect to the theory of the LW technique may also be considered as limitations. The first assumption is that there is no sodium flux across the lung capillary membrane as the HS bolus passes through the lung capillary. The relative impermeability of the lung capillary to sodium has been shown in an older study,19 and indeed the sodium flux is very small when one considers that the permeability to water is 10 times higher. The ultrasound probes are more sensitive to the change in water than to the sodium flux. Furthermore, the previous hemodialysis study using both ultrasound and optical probes demonstrated that the sodium flux is extremely small and thus could be ignored.12 This would not be true, however, when there is a significant degree of lung injury leading to increased lung capillary permeability,11 as may be found in patients with severe valvular heart disease or a large pulmonary shunt.

The second assumption is that the hydrostatic pressure gradients are negligible compared with the osmotic gradient generated by the HS, which may not be true in the case of elevated pulmonary pressures from chronic lung disease or severe cardiac disease.

The final assumption is that the osmolarity in the blood at the equilibrium time point corresponds to the average osmolarity of all the lung tissue. This is actually only true for the perfused areas of the lung; thus the LW values represent the water content from the perfused or functional areas of the lung. If in fact there were regional osmotic pressure differences, then the peaks of the osmotic pressures would arrive at different times and affect the accuracy of the LW calculation. Generally, this would only become problematic for the patients who have a large defect in their lung that causes a shunt.

In conclusion, regardless of the study limitations, we demonstrate that it is feasible and relatively easy to obtain the LW volume in a noninvasive manner in stable hemodialysis patients. Furthermore, these LW values are consistent with expectations and have been shown to decrease with ultrafiltration. The relationship between ultrafiltration and LW will be explored in more detail in both stable and CHF hemodialysis patients in future studies in order to ascertain the role of LW monitoring in hemodialysis patients.

Appendix

Determining the Calibration Coefficients

To determine the amount of water withdrawn from the lung, dV(t), at time t, the calibration constants for the normal and hypertonic saline dilution curves must be determined (K0.9 and K5, respectively). This calibration procedure utilizes the definition of dilution curves for flow measurement in hemodialysis blood line Qb:

Where Vinj is the volume of injected indicator (NS or HS); S is the area under dilution curve from NS or HS, K is a coefficient that establishes relationship between actually recorded changes of ultrasound velocity (Y scale, m/s in Figures 1–3), and concentration of indicator (ml of NS)/(ml of blood) or (ml of HS)/(ml of blood) needed for Equation A1.

The calibration coefficients K0.9 and K5 are determined from the changes in the density of the blood in the venous line as the substances are injected (see upper curves in Figures 1 and 2). The S0.9 and S5 are the areas under the dilution curves for the NS and HS solutions, respectively. The equations for K0.9 and K5 by analogy with Equation 4, where Qb, the flow through the venous line, is substituted for CO:

Equation 3A (see Equation 4) is produced base on assumption of linearity of ultrasound velocity of water versus isotonic saline and 5% saline versus saline concentration.

As mentioned above, if a hypertonic solution passes through the lung as a nondiffusible indicator, its dilution curve would be similar to the lines drawn on Figure 3. The exact expression for the hypertonic dilution curve if it was a nondiffusible indicator would be:

Where x(t) is the dilution curve from injection of the NS and V5 and V5 are the volume of HS and NS injected.

Glossary of Terms: CO, cardiac output (l/min); CI, cardiac index (l/min/body surface area); TPR, total peripheral resistance (mm Hg/[l/min]); CBV, central blood volume (l); CBVi, specific central blood volume, (CBV/body weight, l/kg); LW, lung water (l); ECF, extracellular fluid volume (l); ICF, intracellular fluid volume (l); TBW, total body water (l); P, osmolarity of lung tissue (mOsm/l); Pb, osmolarity of blood (mOsm/l); P5, osmolarity of hypertonic saline (HS) injected (mOsm/l); PH, osmolarity of a solution with concentration of HS (mOsm/l); dPt, change in lung tissue osmolarity (mOsm/l) at time t; Pmix, osmolarity of blood due to mixing of blood with HS (mOsm/l); N, number of osmotically active particles in the lung tissue (mOsm); Vinj, volume injected (ml); VH, volume (ml) of solution (with a given concentration of HS) injected; V5, volume of HS injected (ml); V0.9, volume of normal saline (NS) injected (ml); dVt, change in lung water (ml; amount of lung water withdrawn) at time t; Units of area under ultrasound velocity changes (dilution curve; m/s × s = m); dS(tp), area between the HS dilution curve and the theoretical HS dilution curve if it was a nondiffusible indicator (Figure 3; m); S0.9, area under the NS dilution curve (m); S5, area under the HS dilution curve (m); ST, area under curve within the time interval T (m); S(t, dt), area under the dilution curve within time interval (t, t + dt) (Figure 4; m); dS(tp), area between real HS dilution curve and the theoretical HS curve (if it acted as normal saline) until point of crossing, tp (Figure 3; m); P(tp, dt), osmolarity of blood at point of cross, tp (Figure 3; mOsm/l); dP(tp), increase osmolarity of blood above initial level at time tp (mOsm/l); P(tp), P(tp, dt) (Equation 9; mOsm/l); dV(tp), amount of water withdrawn from lung to time tp (ml); V(tp, dt), amount of injected volume passed lung during t and t + dt time interval (Figure 4; ml); h, height of ultrasound velocity changes for normal saline (Figure 4; m/s); h0.9, height of NS dilution curve (m/s); h5, height of HS dilution curve (m/s); kH20, calibration coefficient for water (m/min); K 0.9, calibration coefficient of NS (m/min); K5, calibration coefficient of HS (m/min); kH, calibration coefficient for solution with HS concentration (m/min).

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