Alterations in total body sodium (TBSodium) that covered the range from moderate deficit to large surplus were induced by 10 experimental protocols in 66 dogs to study whether large amounts of Na+ are stored in an osmotically inactive form during Na+ retention. Changes in TBSodium, total body potassium (TBPotassium), and total body water (TBWater) were determined by 4-day balance studies. A rather close correlation was found between individual changes in TBSodium and those in TBWater (r2 = 0.83). Changes in TBSodium were often accompanied by changes in TBPotassium. Taking changes of both TBSodium and TBPotassium into account, the correlation with TBWater changes became very close (r2 = 0.93). The sum of changes in TBSodium and TBPotassium was accompanied by osmotically adequate TBWater changes, and plasma osmolality remained unchanged. Calculations reveal that even moderate TBSodium changes often included substantial Na+/K+ exchanges between extracellular and cellular space. The results support the theory that osmocontrol effectively adjusts TBWater to the body's present content of the major cations, Na+ and K+, and do not support the notion that, during Na+ retention, large portions of Na+ are stored in an osmotically inactive form. Furthermore, the finding that TBSodium changes are often accompanied by TBPotassium changes and also include Na+/K+ redistributions between fluid compartments suggests that cells may serve as readily available Na+ store. This Na+ storage, however, is osmotically active, since osmotical equilibration is achieved by opposite redistribution of K+.
- water-electrolyte balance
- total body sodium
- total body potassium
it is widely accepted that the osmolality of body fluids is controlled within tight boundaries, as mechanisms of osmocontrol ensure that alterations in osmolality are effectively adjusted by the excretion or intake of water. Thus the organism maintains its content of isotonic fluid, that is, of total body water (TBWater), by maintaining its content of osmolytes, in particular, total body sodium (TBSodium) and total body potassium (TBPotassium). According to this prevailing theory, osmocontrol adjusts TBWater to the body's present content of the major cations, Na+ and K+.
The debate has attracted increasing attention since the publication of a series of papers by Titze et al. (41–43), in which a new concept of Na+ homeostasis was put forward. From a balance study in humans performed by Heer et al. (16) and their own studies in rats the authors (41–43) concluded that, during Na+ retention, large portions of Na+ are usually stored in an osmotically inactive form. This notion questions the prevailing theory and was already noticed as an imminent change of paradigm (18, 23).
To examine the relationship between changes in TBSodium and those in TBWater, we performed balance studies of four days duration in dogs. In a first set of experimental protocols, we studied the effects of changes in Na+ intake, in analogy to Heer's and Titze's studies (16, 41–43). However, because the effects of changes in Na+ intake on TBSodium are usually very small in normal dogs and rats (17, 36, 41), other experimental approaches are necessary to induce more pronounced changes in TBSodium. We wanted to study alterations in TBSodium that cover the whole range from moderate deficit (about −10%) to large surplus [about +50%; TBSodium without bone Na+ is about 34 mmol/kg body mass (26)]. To this end, we performed another set of experimental protocols, and, in addition, we reanalyzed and included results of specific protocols from previously published studies (10, 35, 37, 38). As we had observed in previous studies (28, 35) that TBSodium changes are often accompanied by changes in TBPotassium, we routinely determined K+ balances.
MATERIALS AND METHODS
A total of 81 chronically instrumented female Beagles, about 2 years of age, and weighing 12–16 kg, were studied by standardized methods described in detail in previous papers (10, 24, 29, 30, 34, 36, 37). On completion of the experiments, implants were removed and the dogs were given to suitable private individuals. The studies were approved by the Berlin Government according to the German Animal Protection Law.
The dogs were equipped with a urinary bladder catheter, an inflatable aortic cuff above the renal arteries (used for servocontrolled reduction of renal perfusion pressure in specific protocols), one femoral vein catheter (used for infusions) and two femoral artery catheters. The left femoral artery catheter was advanced into the abdominal aorta well above the renal arteries (used for plasma sampling), the tip of the right catheter was placed directly below the renal arteries (used to obtain the pressure signal for servocontrol of renal perfusion pressure). The lines were exteriorized in the nape region. The dogs were allowed at least 3 weeks for recovery. Catheter-related infections were prevented with a catheter-restricted antibiotic-lock technique (24). Daily assessments of general status, and daily measurements of body temperature, weight, and erythrocyte sedimentation rate ensured that only healthy dogs were studied.
The dogs were housed individually in large kennels (9 m2) in a sound protected, air-conditioned animal room. For reasons of social well-being, dogs in adjacent kennels accompanied the dog under investigation. During the 4-day balance study, the chronic lines of the accustomed dog were connected to a swivel system that allows free movement within the kennel (10, 30). From the swivel, the lines were led to the adjoining laboratory. All actions necessary to run the experiment (except feeding) were performed from the laboratory without drawing the attention of the dogs in the animal room.
Beginning 5 days before the experiment, food intake was controlled with regard to amount [per kg body mass (bm)], composition (including the whole intake of Na+, K+, and water), feeding time (0830–0900), and completeness of intake as detailed by Seeliger et al. (37). In all experiments, K+ intake was 3.5 mmol per kg bm per day, and water intake was 100 ml per kg bm per day. Na+ intake varied with protocols (see Protocols), it was either 0.5 mmol per kg bm per day (low sodium intake, LSI), or 5.5 mmol per kg bm per day (high sodium intake, HSI).
Urine was continuously collected throughout the 4 study days by means of a computerized collection system (30). Urine volume was measured gravimetrically. Blood samples were taken at the end of day 4 as described in detail by Reinhardt et al. (29). The blood withdrawn was always replaced by an equal amount of stored blood collected from the respective dog about 2 wk before the experiments. Concentrations of Na+ and K+ in urine and plasma ([Na+]pl, [K+]pl) were determined by flame photometry, plasma osmolality ([Osmol]pl) by freezing point depression.
Dogs were randomly assigned to protocols. Two control protocols without interventions served to obtain reference data for balance calculation and plasma parameters: protocol CoLSI in dogs on LSI (n = 7 dogs) and protocol CoHSI in dogs on HSI (n = 8).
In two protocols, the effects of steplike changes in Na+ intake were studied. For protocol LtoHSI, dogs were on LSI during the first 2 study days, on day 3, Na+ intake was switched to HSI, which was also fed on day 4 (n = 8), and for protocol HtoLSI, Na+ intake was switched in the opposite direction, from HSI on the first 2 study days to LSI on days 3 and 4 (n = 7).
In five protocols, different degrees of surplus in TBSodium (+TBS) were induced, using endogenous stimulation of the renin-angiotensin-aldosterone system via servocontrolled 20% reduction in renal perfusion pressure (rRPP, for details, see Refs. 29 and 34) in combination with different Na+ intake or low-dose infusion of aldosterone (Aldocorten, Ciba, 10 pg·min−1·kg−1) and ANG II (Hypertensin, Ciba, 4 ng·min−1·kg−1). The protocols are named according to the average change in TBSodium achieved over the 4 days (mean value in mmol Na+/kg bm, at the end of day 4). For protocol +1.3TBS, rRPP was applied in dogs on LSI (n = 6); for protocol +2.6TBS, rRPP was applied in dogs during a switch decrease in Na+ intake, as in protocol HtoLSI (n = 7); for protocol +3.9TBS, rRPP was applied in dogs on HSI (n = 7) (37); for protocol +8.8TBS, rRPP + aldosterone was applied in dogs on HSI (n = 7) (35); for protocol +13.1TBS, rRPP+aldosterone+angiotensin was applied in dogs on HSI (n = 6) (35).
In two protocols, different degrees of deficit in TBSodium (-TBS) were induced. For protocol −0.9TBS, continuous ACE-inhibition (ACE-I: Captopril, Bristol-Myers Squibb, New York, NY; 3.5 μg·min−1·kg−1) was used to block endogenous renin-angiotensin-aldosterone system stimulation by rRPP in dogs on HSI (n = 5), as described by (10). For protocol −3.4TBS, TBSodium was reduced by peritoneal dialysis in the morning of the first study day in dogs on LSI (n = 6), according to a previously described method (36). By peritoneal dialysis, TBSodium was reduced by exactly 3.50 mmol Na+ per kg bm, whereas TBWater and TBPotassium were not changed by the procedure itself. After completion of the dialysis (around 11:00 AM on the first study day), however, all three variables were free to change according to endogenous control processes and, on days 2–4, the effects of ACE-I.
Finally, in protocol ±TBS, a large surplus of TBSodium was induced by rRPP+aldosterone+angiotensin in dogs on HSI on day 1, at the end of which, rRPP and the hormone infusions were stopped to study whether normal TBSodium is regained within the remaining 3 days (n = 7) (38).
Balance Calculations and Statistics
Cumulative balances were used to determine the changes in TBSodium, TBPotassium, and TBWater. Because of the 5 prestudy days on the respective Na+, K+, and water intake, dogs are in balance at the beginning of the 4-day study period. Dogs in the control protocols (CoHSI, CoLSI) remain in balance; thus the data from their 4-day study provide the reference for balance calculation in the other protocols. The amounts of extrarenal Na+, K+, and water loss are known to depend on Na+ intake. Therefore, the extrarenal losses assessed by protocol CoHSI provided the reference for dogs on HSI, those assessed by protocol CoLSI provided the reference for dogs on LSI. Extrarenal loss is calculated by the difference between 24-h intake and 24-h urinary excretion in the control protocols. As room temperature and moisture were kept constant, and the dogs' body temperature and physical activity did not change, extrarenal losses in the other protocols are assumed to equal those observed in the respective control protocol. Therefore, individual 24-h balances for dogs studied in the other protocols were calculated as differences between the excretion in the respective control protocol and the individual dog's excretion on the respective day. All fluid administered via arterial and venous lines was accounted for in balances. The individual dog's cumulative balance was calculated by summing up the 24-h balance values over the 4 consecutive study days.
Daily measurements of the dogs' body mass were done to ensure that, even in protocols with massive changes in TBWater (e.g., surplus in protocol +13.1TBS, deficit in protocol −3.4TBS), the accuracy of water balance data was not compromised, as would be the case, if such changes in TBWater would alter the amount of extrarenal water loss, especially, evaporative loss with breathing (the major portion of extrarenal water loss in dogs). Throughout the protocols, water balance data completely corresponded with body mass data.
Statistics were calculated using Number Cruncher Statistical Software (Hintze, Kaysville, UT). Differences between the control protocol, CoHSI or CoLSI, and the protocols with the respective Na+ intake were assessed by unpaired t-test with Bonferoni's multiple comparison adjustment (P < 0.05/m, where m is the number of comparisons made). Data are presented as means ± SE.
To determine whether changes in TBSodium are accompanied by osmotically adequate changes in TBWater, a correlation analysis (Fig. 1A) was done from data of all dogs (except control protocols). The data were best fitted to a simple linear regression. This overall analysis reveals a relatively close correlation between individual changes of TBSodium and those of TBWater: the coefficient of determination r2 indicates that 83% of TBWater changes are attributable to changes of TBSodium. However, scanning individual data, we found deviations accumulated in dogs studied in four protocols, namely in protocols +1.3TBS, +8.8TBS, −0.9TBS, and −3.4TBS. Accordingly, the coefficient of determination was 91%, when the data of these protocols were not included.
Comparison between Fig. 1A and 1B reveals that the correlation of all dogs' data becomes markedly closer, when changes of both TBSodium and TBPotassium are taken into account. Changes in TBPotassium were observed in the majority of protocols. In three protocols, including +1.3TBS and −3.4TBS, significant amounts of K+ were retained; in four protocols, including +8.8TBS and −0.9TBS, significant amounts of K+ were lost. Collectively, 93% of TBWater changes are attributable to simultaneous changes in both TBSodium and TBPotassium. Thus the sum of changes in TBSodium and TBPotassium was accompanied by osmotically adequate TBWater changes, as also revealed by the numerical values of the regression equation (Fig. 1B, inset; for 15 mmol of cations, the computed value is 109 ml of water). In accordance, no significant correlation is found between [Osmol]pl and the sum of changes in TBSodium and TBPotassium (Fig. 1C), and in none of the protocols did [Osmol]pl change significantly (Table 2). Furthermore, in the collective correlation analysis between individual changes in TBSodium+TBPotassium and those in TBWater (Fig. 1B), the absolute term (the intercept) of the regression equation took on a slightly positive value (not significantly different from zero); if a considerable portion of these cations had been regularly stored in an osmotically inactive form, the intercept would have taken on a negative value.
Descriptive statistics (means ± SE) for the protocols are given in Fig. 2 and Tables 1 and 2. Please note that, in the following, all data concerning volumes and amounts are given per 1 kg of body mass. Step changes in Na+ intake (protocols LtoHSI and HtoLSI) did not leave sustained changes in TBSodium or TBWater after two days; however, a significant K+ retention was observed in the HtoLSI protocol (Table 1).
In protocol +1.3TBS, Na+ and water were retained. As shown by Fig. 2A, however, the amount of retained Na+ (ΔTBSodium) is far too small compared with the retained fluid volume (ΔTBWater) to give an isotonic fluid. As ΔTBWater represents a volume (the retained one), and ΔTBSodium represents an amount of Na+, a virtual Na+ concentration of the retained fluid can be calculated: [Na+]retained fluid = ΔTBSodium/ΔTBWater = 1.33 mmol Na+/19.3 ml H2O = 69 mmol/l. This is only half normal [Na+]extracell. Adding the same concentration of anions for electro-neutrality, the osmotic concentration of the retained fluid would be about 50% of isotonic fluid (∼300 mosmol/kgH2O; isotonicity represented by dotted lines in Fig. 2). Thus, judging from Na+ and water retention only, about half of the retained water appears to be osmotically free. However, dogs retained K+ alongside Na+. Taking the retained amounts of both cations into account (ΔTBSodium+ΔTBPotassium), isotonicity is almost exactly achieved (see Fig. 2A). Calculated [K+]retained fluid = ΔTBPotassium/ΔTBWater = 65 mmol/l is 16-fold higher than normal [K+]extracell. Addition of this fluid with low [Na+] and very high [K+] to normal extracellular fluid is expected to decrease [Na+]extracell and to dramatically increase [K+]extracell. However, neither [Na+]pl nor [K+]pl changed significantly (Table 2). The most probable explanation for this finding is an almost quantitative exchange of Na+ and K+ between extracellular and cellular space, as revealed by calculations (see Appendix); about 1.16 mmol of K+ left the extracellular space, entering the cells, whereas about 1.27 mmol of Na+, coming from cellular fluid, entered the extracellular space.
In protocol +8.8TBS, the amount of retained Na+ is far too large compared with the retained fluid volume to give an isotonic fluid (Fig. 2B). Calculated [Na+]retained fluid = ΔTBSodium/ΔTBWater = 227 mmol/l is equal to about 150% of normal [Na+]extracell. Thus a large portion of retained Na+ (the ΔTBSodium portion above the line of isotonicity in Fig. 2B) appears to be osmotically inactive. However, dogs lost large amounts of K+. Taking both cations into account, the retained amount of Na+ and the lost amount of K+ (ΔTBSodium+ΔTBPotassium), isotonicity is almost exactly achieved (Fig. 2B). In accordance, [Osmol]pl remained unchanged (Table 2). [K+]pl decreased dramatically (Table 2). Most intriguingly, however, the lost amount of K+ (3.39 mmol) is more than fourfold larger than the amount of K+ that is contained in the whole extracellular space (ECK+ = 0.8 mmol, assuming that normal [K+]extracell is 4 mmol/l and normal extracellular fluid volume (ECFV) is 20% of body mass, that is, ECFV = 0.200 l). Thus, even if all extracellular K+ had been lost (resulting in [K+]extracell of 0 mmol/l), the major portion of the lost K+ must have come from a source other than extracellular space, most probably, from inside the cells. Calculations revealed that an almost quantitative exchange of Na+ and K+ must also have occurred in this protocol, this time, however, in the opposite direction: about 2.32 mmol of K+ left the cells, while about 2.55 mmol of Na+ entered the cells (see Appendix).
In protocol −3.4TBS, the lost amount of Na+ is too large compared with the lost fluid volume to give isotonic fluid (Fig. 2C). Calculated [Na+]lost fluid = ΔTBSodium/ΔTBWater = 203 mmol/l is equal to about 140% of normal [Na+]extracell, but [Na+]pl did not decrease significantly (Table 2). Because of K+ retention, however, isotonicity is almost exactly achieved (Fig. 2C). K+ retention led to a marked increase in [K+]pl. However, the extent of [K+]pl elevation should have been much larger, if all changes were limited to the extracellular space. Again, the cellular space appears to be involved. The same applies for protocol −0.9TBS (see Fig. 2D), in which the deficit in TBSodium was accompanied by loss of K+ (see Appendix for both protocols).
In protocols +2.6TBS and +3.9TBS, moderate amounts of Na+ and water were retained, while changes in TBPotassium did not reach statistical significance (Table 1). In protocol +13.1TBS, the largest amounts of Na+ and water were retained, and a significant amount of K+ was lost. In protocol ±TBS, normal TBSodium was restored, yet small deficits in TBPotassium and TBWater were observed.
The present results corroborate the prevailing theory that osmocontrol effectively adjusts TBWater to the body's present content of the major cations, Na+ and K+. Alterations in TBSodium that cover the range from moderate deficit to large surplus were induced by various methods, yet the sum of simultaneous changes in TBSodium and TBPotassium was accompanied by osmotically adequate changes in TBWater. This result does not support the notion that, during Na+ retention, large portions of Na+ (up to 75%) are usually stored in an osmotically inactive form (41–43).
It has long been known that Na+ retention is often accompanied by K+ loss, and, vice versa, Na+ loss with K+ retention. This was observed with changes in Na+ intake (1, 9, 19, 27, 32) and with TBSodium changes induced by a variety of interventions (3, 20, 28, 31, 37). Accordingly, opposite changes in TBSodium and TBPotassium occurred in several of the present protocols. However, parallel changes in TBSodium and TBPotassium were also observed. In one protocol both Na+ and K+ were retained, and in another, both Na+ and K+ were lost.
Furthermore, changes in TBSodium apparently often include redistribution of substantial amounts of Na+ and K+ between extracellular and cellular space, as indicated by the calculations from results of four protocols, two that showed an increase in TBSodium and two that showed a decrease in TBSodium. In each case, the calculation revealed that an (almost) quantitative, osmotically neutral Na+/K+ exchange between the fluid compartments must have occurred. Because this redistribution was observed even with moderate TBSodium changes and occurred rather rapidly and because Na+ moved into cells in two protocols, and out of cells in two others, we conclude that cells may serve as a readily available Na+ store. This Na+ storage would be osmotically active, as osmotical equilibration is achieved by opposite changes in cellular K+ content.
It is generally known that primary changes in TBPotassium almost regularly include compartmental redistribution of K+ (7, 22); even the transient TBPotassium increase resulting from a K+-rich meal is accompanied by rapid cellular K+ uptake. Several early reports also support the concept that changes in TBSodium often include Na+/K+ exchange between cells and extracellular space; however, this concept, published decades ago, appears largely forgotten. In 1968, Reinhardt and coworkers (3) found that large amounts of cellular Na+ had been exchanged against extracellular K+ in a protocol comparable to our −3.4TBS protocol. Laragh (21) observed a similar Na+/K+ exchange in hyponatremic patients following K+ administration. In their seminal 1952 study on “mineralocorticoid escape,” Relman and Schwartz (31) noted a Na+/K+ redistribution in the opposite direction. Several authors reported that, during administration of “K+-wasting” diuretics, extracellular Na+ enters cells in an osmotically neutral exchange for cellular K+, that is, water does not follow Na+, which substantially contributes to the associated hyponatremia (4–6, 14).
A considerable amount of Na+ resides in the bones. A small portion of bone Na+ belongs to the fluid phase that is in equilibrium with extracellular fluid, (i.e., this Na+ is osmotically active), whereas the major portion belongs to the crystal phase (i.e., this Na+ is osmotically inactive) (Refs. 11 and 15). We cannot exclude the possibility that the latter portion contributed to the Na+/K+ exchanges observed. Under physiological conditions, the rate of exchange of crystal phase Na+, as estimated from whole body isotope measurements, is low [<1% of exchangeable TBSodium per day (12)]. Under conditions of prolonged severe hyponatremia and acidosis crystal phase Na+ is lost, whereas short-term hyponatremia reduces fluid phase Na+ only (15). Considering the time frame of our experiments in conjunction with the finding that plasma Na+ concentration was largely unaltered, it thus appears not likely that crystal phase Na+ accounted for a significant portion of Na+/K+ exchanges. On the other hand, we cannot rule out from the present results that crystal phase bone and other osmotically inactive or neutral storage [e.g., cartilage glycosaminoglycans (13)] may play a role in long-term homeostasis.
Furthermore, our calculations of transmembranal Na+/K+ exchange allow global, but not tissue-specific conclusions. It is conceivable that this exchange does not occur (to the same extent) on all cells, but (preferentially) on cells of specific tissues, since intracellular Na+ and K+ concentrations differ considerably among tissues (26), and compartmental redistributions of K+ during primary TBPotassium changes occur preferentially in skeletal muscles (7, 22). Clearly, studies that include electrolyte measurements in various cells are needed to test this notion.
Titze's notion of osmotically inactive Na+ storage originated from a balance study in humans by Heer et al. (16) and own studies in rats (41–43). Heer et al. observed that an abrupt increase in Na+ intake immediately resulted in positive 24-h Na+ balances for a couple of days; this Na+ retention was not accompanied by osmotically adequate water retention. Titze et al. (41–43) compared groups of rats that had been offered food of different Na+ content for several weeks and reported that differences in TBSodium were not accompanied by adequate differences in TBWater, as assessed by postmortem drying and ashing procedures. Unfortunately, TBPotassium or its changes were not assessed in these past studies (16, 41–43). In a very recent study in rats, however, Titze et al. (40) assessed TBPotassium in addition to TBSodium and TBWater, by drying and ashing. In one protocol of this new study, they administered DOCA and drinking fluid of 1% NaCl concentration for 5 wk to induce a marked rise in TBSodium. This protocol has certain experimental conditions in common with our present protocol +8.8TBS: elevated mineralocorticoid levels and high Na+ intake. In the DOCA+NaCl rats, Titze et al. (40) found body weight (wet and dry wt) reduced, TBWater/wet wt ratio increased, TBSodium increased, and TBPotassium decreased. Quantitative estimations indicated that one portion of the retained Na+ was osmotically active (accompanied by water), and another portion was osmotically balanced by K+ loss. This is in line with our protocol +8.8TBS (see Fig. 2B). In contrast to our results, however, Titze's estimations indicated that a third portion of the retained Na+ in the DOCA+NaCl rats was osmotically inactive (neither accompanied by water, nor exchanged for K+). Possible reasons for this discrepancy include, but are not limited to, study duration (4 days vs. 5 wk) and species difference. It is possible that osmotically inactive Na+ storage does not occur within 4 days even during massive Na+ accumulation (as in protocol +8.8TBS) but may require weeks of TBSodium surplus to be induced. The data of Heer's study in humans (16) that hitherto appeared to demonstrate that osmotically inactive Na+ storage is a rapid process, can no longer be regarded as positive proof for this storage, because K+ balances were not assessed. Furthermore, kinetics of Na+ homeostasis and the response to changes in Na+ intake vary considerably among species (8, 16, 17, 25, 33, 41). Thus it is also conceivable that osmotically inactive Na+ storage during Na+ retention takes place in rats but not in dogs. In conclusion, further studies are needed that address the time course of TBSodium changes, involve different species, and must include measurements of TBPotassium or its changes.
Pathways for transmembranal movements of Na+ and K+ are well known. The mechanism(s) that connect external Na+ balance with transmembranal Na+/K+ exchange, however, are largely unknown, as was also noted for K+ redistribution during primary TBPotassium changes (22). Are small changes in Na+ concentration the trigger for this exchange? Is it controlled by hormones? Considering the known effects of aldosterone and ANG II on transmembranal cation traffic in various nonrenal cells, it is also conceivable that Na+/K+ redistributions may rely on nonrenal effects of these hormones. However, comparing protocols with Na+/K+ redistributions, we found no clear-cut relationship between hormonal changes and the direction of Na+/K+ redistributions. For instance, aldosterone plasma concentrations are markedly elevated both in protocol +8.8TBS (35) and protocol +1.3TBS (E. Seeliger and H. W. Reinhardt, unpublished observation); however, Na+ ions were shifted from extracellular space into cells in protocol +8.8TBS but redistributed in the opposite direction in protocol +1.3TBS. Considering that even moderate TBSodium changes were accompanied by substantial transmembranal Na+/K+ exchange, which must have changed intracellular Na+ and K+ concentrations markedly, thereby possibly altering membrane potentials of a variety of cells, these questions certainly warrant further investigations.
APPENDIX: Example Calculations of Compartmental Na+/K+ Redistributions
For calculation, the mean values obtained at the end of day 4 in protocol +1.3TBS are used with the index “4”, and those of the control protocol (CoLSI) with the index “Co”. For simplicity, plasma concentrations of Na+ and K+ are equated to extracellular concentrations (ignoring Gibbs-Donnan distribution). All data concerning volumes and amounts are given per 1 kg bm. Because normal ECFV is ∼20% of body mass in dogs (27, 39), ECFVCo is assumed to be 0.200 l/kg bm. Thus control extracellular amount of Na+ (ECNa+Co) = ECFVCo·[Na+]plCo = 0.200 l·143.6 mmol/l = 28.7 mmol, and the control extracellular amount of K+ is
ECK+Co = ECFVCo·[K+]plCo = 0.200 l·4.12 mmol/l = 0.82 mmol.
If we assume that all changes in the +1.3TBS protocol occur within and are limited to extracellular space, then, after 4 study days, ECFV4 = ECFVCo + ΔTBWater = 0.200 liter + 0.0193 liter = 0.2193 liter, ECNa+4 = ECNa+Co + ΔTBSodium = 28.7 mmol + 1.33 mmol = 30.0 mmol, and ECK+4 = ECK+Co + ΔTBPotassium = 0.82 mmol + 1.25 mmol = 2.07 mmol.
Extracellular = plasma [Na+] and [K+] after 4 study days are calculated: calculated [Na+]pl4 = ECNa+4 / ECFV4 = 30.0 mmol/0.2193 liter = 137.1 mmol/liter. Thus, compared with control, [Na+]pl should have decreased by Δ[Na+]pl = −6.5 mmol/l.
Calculated [K+]pl4 = ECK+4 / ECFV4 = 2.07 mmol/0.2193 l = 9.46 mmol/l.
Thus, compared with control, [K+]pl should have dramatically increased by Δ[K+]pl = 5.34 mmol/l.
However, the measurements in the dogs of protocol +1.3TBS reveal that neither [Na+]pl nor [K+]pl was significantly changed; there were only small numerical deviations in the mean values from those of CoLSI (see Table 2): measured Δ[Na+]pl = −0.7 mmol/l; measured Δ[K+]pl = 0.05 mmol/l. Taking these small changes into account, there remain large differences between the calculated and the measured concentration changes. Compared with calculation, actual [Na+]pl had seemingly increased by 5.8 mmol/l, whereas actual [K+]pl had seemingly decreased by 5.29 mmol/l.
The assumption, that all changes were limited to the extracellular space, is obviously invalid, as the most probable explanations rely on the involvement of the intracellular space.
Normal [K+]extracell could have been maintained either by net K+ flux from extracellular space into cells, or by expansion of ECFV (net water flux from cells). The extracellular K+ efflux necessary to maintain [K+]extracell is calculated by Necessary ΔECK+ = ECFV4·seeming decrease in [K+]pl = −1.16 mmol. The extracellular water influx necessary to maintain [K+]extracell is calculated by Necessary change in the amount of extracellular water (ΔECH2O) = −1·ECFV4·seeming decrease in [K+]pl/[K+]pl4 = 0.2870 liters.
Likewise, normal [Na+]extracell could have been maintained either by net Na+ flux from cells into extracellular space: Necessary ΔECNa+ = ECFV4·seeming increase in [Na+]pl = 1.27 mmol, or by a small contraction of ECFV (net water flux into cells): Necessary ΔECH2O = −1·ECFV4·seeming increase in [Na+]pl/[Na+]pl4 = −0.0089 liters. As the extent of ECFV expansion (+140%) that would be necessary to maintain [K+]extracell is not plausible and, moreover, is contrary to the small ECFV contraction (−5%) necessary to maintain [Na+]extracell, there remains only one explanation: an (almost) quantitative exchange of Na+ and K+ took place. About 1.16 mmol of K+ left the extracellular space, entering the cells, while about 1.27 mmol of Na+, coming from cellular fluid, entered the extracellular space.
For protocol +8.8TBS, the calculation leads to similar conclusions. Here, normal [Na+]extracell could have been maintained by expansion of ECFV (ΔECH2O = 0.017 liter), or by Na+ flux into cells (ΔECNa+ = −2.55 mmol); normal [K+]extracell by ECFV contraction (ΔECH2O = −0.794 liter), or by K+ flux into extracellular space (ΔECK+ = 2.32 mmol). The extent of ECFV contraction necessary to maintain [K+]extracell exceeds the sum of cellular and extracellular water (∼0.600 liter; Ref. 2), and the amount of K+ lost exceeds ECK+ fourfold. As explanation remains an (almost) quantitative exchange of Na+ and K+, this time, however, in the opposite direction. About 2.32 mmol of K+ left the cells, while about 2.55 mmol of Na+ entered the cells.
In protocol −3.4TBS, the changes in ECFV necessary to simultaneously maintain both [Na+] and [K+] contradict each other. Thus, ∼0.63 mmol of K+ must have entered the cells, whereas about 0.89 mmol of Na+ left the cells. In protocol −0.9TBS, the exchange went in the opposite direction: about 0.62 mmol of K+ must have left the cells, while about 0.76 mmol of Na+ entered the cells.
This work was supported by the Deutsche Forschungsgemeinschaft.
We thank K. Dannenberg, S. Molling, D. Bayerl, T. Rebeschke, A. Bierwagen, and H. Kändler for expert technical assistance.
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked “advertisement” in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
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