ku...patient age sex bodywt. transudate diagnosis k kidneydisease no. yrs. 17 47 28 58 33 58 62 36...

INTERRELATIONS BETWEENSERUMSODIUMCONCENTRA-TION, SERUMOSMOLARITYANDTOTAL EXCHANGEABLE

SODIUM, TOTAL EXCHANGEABLEPOTASSIUMANDTOTAL BODYWATER1

BY I. S. EDELMAN,2 J. LEIBMAN,8 M. P. O'MEARA,4 AND L. W. BIRKENFELD5

(From the Department of Medicine, University of California School of Medicine, and the SanFrancisco Hospital, San Francisco, Calif.)

(Submitted for publication March 4, 1958; accepted May 2, 1958)

Although much is known about the effects ofchanges in electrolyte and water balance on se-rum sodium concentration, the quantitative rela-tionships between body composition and the con-centration of sodium in serum have not been es-tablished. Also, no definitive study has been madeof the correspondence between serum sodium con-centration and total serum osmolarity. It is neces-sary that these relationships be defined to permitclassification and interpretation of abnormalitiesof serum sodium concentration in clinical states, aswell as to extend present understanding of the ef-fects of electrolyte equilibria and acid-base disturb-ances on serum sodium concentration.

It has been definitively demonstrated that nooverall correlation exists between body sodiumcontent, or external balance of sodium, and serumsodium concentration (1-4). Serum sodium con-centration, of course, is not independent of loss orgain of body sodium. Excessive loss of sodiumleads to a fall in serum concentration; administra-tion of hypertonic saline elevates serum levels(5-8). Retention of water in excess of sodiumhas been shown to occur, and accounts, at least inpart, for the hyponatremia seen after major sur-gery and in patients with coexistent edema and hy-ponatremia (3, 4, 9). This phenomenon hasbeen demonstrated experimentally by administra-tion of vasopressin to patients with congestive

1 This work was supported by grants-in-aid from theAmerican Heart Association, the United States PublicHealth Service (Grant No. . H-1441), the MontereyCounty Heart Association and the San Francisco HeartAssociation.

2During tenure as an Established Investigator of theAmerican Heart Association.

3 Research Fellow of the San Francisco Heart Associ-ation.

4 5 Research Fellows of the National Heart Institute ofthe United States Public Health Service.

heart failure (10). An integrated account of con-comitant alterations in serum sodium concentra-tion and body composition was first achieved byDeming and Gerbode (11), who observed thatchanges in serum sodium concentration parallelednet changes of sodium and potassium balance inrelation to water balance in patients undergoingmitral valvulotomy. The influence of potassiumbalance on serum sodium concentration was con-firmed by correlative studies in postoperative hy-ponatremia and by demonstration that administra-tion of potassium can raise the serum sodium con-centration in hyponatremic patients (4, 7, 12).

The dependence of serum sodium concentrationon body sodium, potassium and water content hasseveral important implications. The magnitudeand character of this dependence will modify orextend current concepts of ionic redistributionsbetween body fluids, of osmotic gradients acrosscell membranes, and of the participation of hy-drogen ion in the regulation of serum sodiumconcentration (13-17).

Simultaneous measurements of total exchange-able sodium (Nae), total exchangeable potassium(Ke), total body water (T.B.W.), and serum elec-trolyte concentrations, pH and osmolarity weremade in a heterogeneous group of chronically illpatients. Statistical analyses were made of thecorrelations of serum sodium concentration (Na8)with serum osmolarity (7r.), Na8/body weight,Ke/body weight, T.B.W./body weight, Nae/T.B.W., Ke/T.B.W. and (Nae + K8)/T.B.W.These data reveal striking correlations betweenNa8, 7rs and (Nae + Ke)/T.B.W.

METHODS

Ninety-eight patients were studied. The age, sex,state of hydration of these subjects and the clinical diag-noses are listed in Table I. Maximum heterogeneity in

1236

SERUMSODIUM CONCENTRATIONAND BODY COMPOSITION

TABLE I

Summary of clinical data

Patient Age Sex Body wt. Transudate Diagnosis

Kg.M 64.1M 53.9F 85.0M 119.5M 80.0M 59.8M 41.8M 59.8F 55.2M 47.7M 75.8M 60.9F 38.6M 62.3M 44.8M 48.6F 51.8M 56.4M 49.8M 58.0M 53.6M 71.4F 63.6M 86.4F 103.9M 53.2M 65.9M 55.7F 70.0M 86.6F 56.1F 60.9F 55.0

50 M

47 M

51 M

51 M

66 M

74 M

28 F45 M

37 F59 M

66 F51 M

43 F67 M

56 M

43 F67 M

39 F27 F48 M

85 M

50 F48 F64 M

64 M

39 M

51 M

46 M

50 M

59 M

42 M

45 M

67.380.041.837.788.4

101.339.650.939.867.082.578.851.879.3

112.556.8

65.755.755.5

57.778.281.484.666.476.860.067.764.060.0

Heart disease

+2 Hypertensive and arteriosclerotic cardiovascular disease+2 Hypertensive and arteriosclerotic cardiovascular disease+3 Arteriosclerotic heart disease+4 Arteriosclerotic heart disease+2 Hypertensive and arteriosclerotic heart disease+1 Arteriosclerotic heart disease; bronchiectasis+ 1 Cor pulmonale; chronic pulmonary disease

0 Cor pulmonale; chronic bronchitis; pneumonia+2 Cor pulmonale; chronic pulmonary disease+1 Cor pulmonale; chronic empyema; auricular fibrillation+4 Hypertensive heart disease+2 Arteriosclerotic heart disease; chronic pyelonephritis

0 Arteriosclerotic heart disease; cerebrovascular disease+1 Hypertensive heart disease

0 Cor pulmonale; asthma; bronchopneumonia+3 Arteriosclerotic heart disease; duodenal ulcer+1 Arteriosclerotic heart disease+2 Arteriosclerotic heart disease+2 Arteriosclerotic heart disease+2 Arteriosclerotic heart disease+2 Arteriosclerotic heart disease+2 Malignant hypertension+1 Arteriosclerotic heart disease+4 Arteriosclerotic heart disease+ 1 Arteriosclerotic heart disease+4 Hypertensive heart disease+4 Arteriosclerotic heart disease+3 Rheumatic heart disease

o Essential hypertensiono Essential hypertension0 Essential hypertension0 Essential hypertension0 Essential hypertension

Liver disease+4 Cirrhosis+2 Cirrhosis+3 Cirrhosis+2 Cirrhosis

0 Cirrhosis+4 Cirrhosis+ 1 Cirrhosis+2 Cirrhosis+ 1 Cirrhosis+3 Cirrhosis

0 Cirrhosis+3 Cirrhosis

. +3 Cirrhosis+4 Cirrhosis

0 Cirrhosis+3 Cirrhosis+4 Cirrhosis+3 Cirrhosis+1 Cirrhosis+2 Cirrhosis

0 Cirrhosis+3 Cirrhosis+4 Cirrhosis+4 Cirrhosis+4 Cirrhosis+4 Cirrhosis+3 Cirrhosis+2 Cirrhosis+3 Cirrhosis+4 Cirrhosis+2 Cirrhosis+4 Cirrhosis

no. yrs.

1 645 647 67

10 6611 7612 6818 5521 6023 5125 6726 5827 8936 7237 7942 7147 5449b 8651 8453 5461 7175 6678 4080 8280a 7582 5390 6093 7494 7756 5457 4658 4067a 2794a 33

2368

131619202224293035384344b48a506066677173798184868788899192

1237

I. S. EDELMAN, J. LEIBMAN, M. P. 0 MEARA, AND L. W. BIRKENFELD

TABLE I-Continued

Patient Age Sex Body wt. Transudate DiagnosisKKidney disease

no. yrs.

17 4728 5833 5862 3674 40

Kg.M 70.7M 47.7M 51.1M 69.8F 40.0

69 M 48.048 M 52.329 F 51.362 M 52.164 M 60.2

4 68 M 86.99 45 M 69.2

44a 60 M 39.846 78 M 44.9

40 78 F41 73 M

.65 45 M

68 70 M

72 77 F77 55 F83 72 F34 90 M

41.460.5

43.239.138.643.6

14 67 F 59.515 72 M 59.332 39 M 168.239 28 F 36.445 74 M 57.052 70 M 50.955 41 M 53.670 62 M 61.876 62 M 62.554 49 M 63.969 61 F 47.7

+3 Nephrotic syndrome0 Chronic glomerulonephritis; gastric ulcer

+3 Chronic glomerulonephritis+4 Diabetic glomerulosclerosis+2 Chronic pyelonephritis

Lung disease0 Pulmonary emphysema0 Pulmonary tuberculosis; cirrhosis of liver

+1 Pulmonary tuberculosis+3 Pulmonary tuberculosis; cirrhosis of liver; diabetes+3 Carcinoma of lung, postoperative

Gastrointestinal disease0 Gastric ulcer0 Duodenal ulcer

+2 Rectal carcinoma, postoperative+1 Duodenal ulcer; chronic pyelonephritis

Neurological disease0 Cerebrovascular disease0 Cerebrovascular disease

+2 Transection of spinal cord0 Subdural hematoma0 Subdural hematoma, postoperative0 Cerebrovascular disease0 Cerebrovascular disease0 Cerebral arteriosclerosis

Miscellaneous0 Multiple abscesses0 Cellulitis

+2 Obesity0 Adrenal insufficiency0 Senility; anemia0 Chronic bromide intoxication0 Primary aldosteronism0 Panhypopituitarism0 Panhypopituitarism

+4 Carcinomatosis, primary unknown+4 Carcinoma of cervix with peritoneal metastases

clinical and metabolic status was sought to assure that ceived more than 360 microcuries of Ku and 150 micro-any correlations between body composition and serum curies of Nan. The periods of isotope equilibration were

electrolyte concentrations would have general validity. 40 hours for K", 24 hours for Na' and 6 hours for DO.The group consisted of 33 patients with a variety of These periods were previously shown to be adequate forheart diseases, 32 patients with cirrhosis of the liver, 5 isotope equilibration, even in very edematous subjectspatients with renal disease, 5 patients with pulmonary (19). Blood was drawn from the femoral artery justdisease, 4 patients with gastrointestinal disease, 8 pa- before injection of Na". Glycolysis in these samplestients with neurological disease and 11 patients with other was inhibited either by the addition of 0.5 ml. of satu-illnesses, including panhypopituitarism, adrenal insuffi- rated NaF or by icing.ciency and primary aldosteronism. Sixty-six of these The analytical methods for isotope assay have beenpatients had one to four plus edema by clinical criteria. described in earlier papers (18, 19). Serum osmolarity

All subjects were given an analyzed diet which con- (Tr) was estimated by freezing point depression with a

tained 10 mEq. of sodium and 28 mEq. of potassium each thermistor probe, using NaCl standards (20).ff Sodiumday for one or two days prior to and for the three daysof study. Food and fluid were withheld for the six hour 6 Freezing point depression actually is a measure ofperiod of DOequilibration. osmolality. Since osmolality is virtually equivalent to

The sequence and technique of isotope administration osmolarity at constant temperature, however, the latterand collection of urine and blood for isotope assay have term has been used in this communication to providebeen described previously (18, 19). No subject re- units comparable with the electrolyte concentration data.

3148b636459

1238

- SERUMSODIUM CONCENTRATIONAND BODY COMPOSITION 13

TABLE II

Summary of laboratory data: Serum values

ArterillPatient Na'. K'. Cis (HCOO) pH NPN* Glucose we vS,

no. mEq./L. of mEq./L. ofserum water serum water

1. 155.6. 4.585- 142.7 4.647 153.1 4.03

10 149.0' 4.7711 147.7 4.1912 130.1 4.9118 147.9 4.7221' 136.9 4.8923 137.3 5.4425 144.5 4.1926 137.9; 6.4927- 120.6 5.1736 145.5 2.5237 146.1 4.6842 132.7 4.3847 138.5 4.5549b. 141.6 2.8551' 120.3 4.77"53 117.6 4.3961 123.4 4.9975 126.1 5.9278 140.8 3.3680. 123.0 4.9180a 142.3 4.3582 159.0 4.0690 139.4 4.2893 145.0 3.3994 148.7 5.1656 150.8 4.6057 148.0 4.9758 143.2 3.9767a 152.6 4.5894a 150.4 3.88

2 146.0 3.093 145.7 3.946 128.5 5.218 143.5

13 150.0 4.7516 140.8 3.2119- 139.5 3.7020 127.9 4.9022 141.3 4.0524 133.9 3.9129 141.8 3.1130 147.2 3.5835 139.1 4.4438 138.1 3.9743 141.2 4.0344b 131.6 3.9348a 108.9 2.5450 139.6 3.2660 156.4 6.4966 151.2 4.3667 170.671 112.0 4.8273 130.7 3.7279 124.0 3.5681 144.4 3.9684 144.4 4.1386 144.6 6.1587 126.5 3.5488 141.2 3.8089 136.4 3.9691 144.3 4.3092 135.7 4.41

* Nonprotein nitrogen.

mHeart disea

iEq./L. mEq./L.

104.6 27.5 796.3. 31.4 7

103.2' 32.4 799.3 23.9 7

104.0 25.2 786.2 27.8 798.7 30.9 784.9 404 785.2 35.7. 794.7 36.4 7

102.9 19.0 786.8 12.2 793.1 34.0 7

109.7 21,8 795.8 25.9 7

12.8 725.3 7

72.6 21.5 772.6 26.8 777.2 29.2 788.5 22.8 2

25.9 783.5 22.4 7

28.0 727.5 728.4 7

108.2106.584.498.195.3

101.895.094.1

100.898.6

101.1108.3105.6101.7

94.3

125.6104.0

76.685.6

Liver disea17.1 ;21.7 7285 723.9 728.2 722.7 726.3 719.1 723.9 721.5 725.9 724.9 718.8 722.7 7

26.5 7

23.0 78.1 7

23.5 7

20.732.9

21.124.725.6

mg. %

7.47. 247.40 297.41 177.47 177.46 247.51 18

.35 177.34 217.2S 43F.34 127.37 72.r.19 1267.45 167#49 ; 457.34 29A.48 142'.54 21

7.58 1I7.49 987.48 10'.52 22'.39 767.49 23

3213

7.45 48.44 36

r.27 834927201515

*se,7.48 347.52 177.38 177.46 227'38 95'.45 447.39 117.39 317.40 137.45 457.40 197.47 197.48 307.47 16

237.49 12

587.54 237.35 1457.47 14

1027.28 727.44 32

191922

1037.36 1737.54 207.54 19

1816

mg. % MOsM.i/. mOsm./L.

8993

1181129197

10186

10087

116149114100111

127198

8095

100144

8312076

11614297

11210098

108108

89

12110111785

148118

661168375

11286

104109112

7080

100317

86164160502127

9012295

1501251209294

289.2274.6287.2276.9285.2245.3280.9271.1274.0275.728&.6273;4272.4292.2264.7311.0272.0232.0.24810228.0254.5290A.243A4281,0298,0..289,0-283k3060283.8.286.1277.0283.0275.0

280.0275.0245.8276.1303.6280.3262.3258,4269.2265.0274.5'279.8274.0267.4277.1252.1227.6257.0360.0285.0356.0243.0285.0240.5280.0276.5304.0295.0268.5262.0271.0266.0

275.7259.0274.$'264.6271;5233.5269.2,258.8253.1266A6256.5-214.6260.4270.6248.1256.4253;S224.0208.0218.8238.5258.2228.5265.0287.0264.0264.7270.2260.7271.1263.9271.6265.0

261.2263.3233.?263.5;261.5;258.0254.7240.9260.0244.7261.5268.2257.5255.6262.7243.9202.5243.2290.6275.0310.0208.4245.7226.6268.0261.8262.0225.0254.5248.5259.5255.1

1239-

77

777


TABLE II-Continued

ArteralPatient Na'. K'. Cla (HCOs)p pH NPN* Glucose a. a'.

vv.I 1.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

So. mEq./L. ofserum water

17 146.428 144.033 111.262 134.374 137.3

mEq./L. ofserum water

7.003.904.765.134.54

mEq./L.

103.6103.3

76.3

Kidney diseasemEC.IL.

15.319.322.428.117.7

7.287.317.407.497.30

.31*48b636459

146.3134.6145.7125.5134.1

4 147.39 148.7

44a 116.246 155.0

40 143.941 133.165 131.368 192.572 135.877 158.183 161.534 144.5

5.253.674.373.805.55

4.443.976.324.69

3.654.484.78

4.092.283.974.40

90.6

96.576.686.1

100.7106.2

89.7

113.7116.8

80.0

92.0103.8

101.5

Lung disease31.5 7.4127.1 7.5226.4 7.4532.0 7.5428.6 7.59

Gastrointestinal disease29.0 7.4624.0 7.4611.5 7.3115.7

Neurological disease25.9 7.4423.4 7.4224.5 7.55

30.434.1

26.8

7.507.47

7.39

37 10913 1009 121

16 29542 137

23 10333 14939 150

128 127

301330

23815343436

91127139367

95100102136

280.3241.0266.0250.0268.0

277.6282.8239.0320.0

278.0256.7254.0450.0258.0301.7317.0286.5

Miscellaneous14 147.315 146.132 148.339 138.545 129.552 142.355 154.670 119.776 135.054 132.369 123.3

Mean 140.1Range 108.9-

192.5

4.354.624.024.135.143.803.504.484.655.636.87

4.402.28-7.00

103.7106.1

97.1111.4

94.9

98.987.6

87.3

96.472.6-

125.6

28.125.834.322.822.433.231.717.5

18.722.0

7.417.417.357.447.437.557.457.58

7.437.52

25.0 7.448.1- 7.19-

40.4 7.59

16 83 278.727 100 280.9

283.720 95 262.024 98 252.925 105 263.030 90 292.0

9 78 224.023 83 262.061 103 273.014 97 236.0

45.39-

238

120 276.666- 224.0-

502 450.0

and potassium were measured in dilutions of urine andserum with a lithium internal-standard flame photometer.Serum water was determined gravimetrically by drying1 ml. aliquots, delivered from calibrated pipettes, at 1040C. for 72 hours. Serum chloride (Cl.) was estimated byelectrometric titration (21), plasma glucose by color-imetry (22) and plasma nonprotein nitrogen (NPN) bya modification of the Folin-Wu method (23). TotalCO2 content of arterial plasma was determined by themanometric method of Van Slyke (24). Arterial bloodpH was measured at 370 C. with a Beckman model GpH meter, calibrated with buffer standards preparedfrom high purity salts provided by the National Bureau

of Standards. All chemical determinations were done induplicate or triplicate.

Calculations, statistics, and analytical error. Standardformulas were used in calculating specific activities, Na.,K. and T.B.W., including the appropriate corrections forisotope excretion in the urine (25-27). The measuredNa, was back corrected to the time of determinations ofK. and T.B.W. by metabolic balance for sodium duringthe period of Na' equilibration. This correction was

applied to provide simultaneous estimates of Nae, K. andT.B.W. since Na, was measured 24 hours after measure-

ment of K. and T.B.W.The osmotic contributions of glucose and NPN were

1240

mg. %

100139127165212

mg. %

87109136157139

mOsm./L.

304.8317.3260.0309.0310.0

mOsm./L.

264.3261.6207.0241.4226.6

261.0230.8256.0228.0245.0

263.7262.7216.8267.2

262.2245.0235.0345.0247.3284.0304.2266.0

268.4265.7

249.6238.9248.0276.0216.5249.2245.0225.6

254.5202.5-345.0

I SERUMSODIUM CONCENTRATIONAND BODY COMPOSITION

TABLE III

Summary of laboratory data: Body composition

Na. + K.Patient Nae Na./Body wt. K. Ks/Body wt. T.B.W. T.B.W./Body wt. T.B.W.

Heart diseaseno. mEq. mEq./Kg. mEq. mEq./Kg. L. % mEq./L.

1 3,122 48.7 2,454 38.3 34.1 53.1 163.85 3,189 59.2 1,963 36.5 33.8 62.7 152.57 4,876 57.4 1,936 22.8 44.8 52.7 152.2

10 6,983 58.4 3,293 27.6 69.6 58.3 147.611 3,812 47.7 2,681 33.5 39.9 50.3 162.912 2,359 39.5 2,599 43.5 35.0 58.5 141.718 1,953 46.7 1,862 44.5 24.9 59.5 153.321 3,149 52.7 2,168 36.3 33.5 56.1 158.523 3,486 63.2 1,704 30.9 36.3 65.7 143.125 3,051 64.2 1,665 34.9 30.9 64.8 154.626 5,116 67.5 2,772 36.6 49.5 65.9 159.327 2,880 47.3 1,639 26.936 2,230 57.8 1,279 33.1 23.6 61.2 148.537 2,971 47.7 1,986 31.9 32.4 52.0 150.642 2,495 55.7 1,650 36.9 29.8 66.5 139.347 3,046 62.7 1,750 36.0 31.6 65.0 151.949b 3,176 61.3 1,245 24.0 30.3 58.4 146.151 3,385 60.0 1,424 25.2 36.8 65.2 130.853 3,734 75.0 1,211 24.3 37.6 75.4 131.661 3,451 59.5 2,048 35.3 40.0 68.9 137.575 3,659 68.2 1,699 31.7 38.9 72.5 137.878 3,702 51.9 3,723 52.1 50.4 70.5 147.580 1,957 30.8 1,164 18.3 24.0 37.7 130.180a 6,400 74.1 2,213 25.6 60.6 70.1 142.382 3,105 29.9 3,021 29.0 39.2 37.7 156.590 3,733 70.2 1,571 29.5 36.3 68.3 146.093 4,770 72.4 1,937 29.3 47.2 71.6 142.194 1,804 32.4 39.2 70.456 2,227 31.8 2,227 31.8 28.5 40.8 156.157 3,447 39.8 4,222 48.9 45.6 52.7 168.158 2,180 38.7 2,063 36.8 27.9 49.7 152.067a 2,363 38.8 2,281 37.5 29.2 48.0 158.294a 2,276 41.4 1,882 34.2 27.9 50.8 148.8

Liver disease2 4,152 61.7 1,785 26.5 39.3 58.3 151.23 3,541 45.1 3,205 40.1 44.5 55.6 151.76 2,417 57.9 1,438 34.4 26.9 64.3 143.58 2,906 77.1 1,044 27.7

13 3,327 37.6 2,889 32.716 5,153 50.9 2,350 23.2 50.1 49.5 149.619 2,228 56.3 1,203 30.4 22.7 57.4 151.220 2,359 46.3 1,665 32.7 27.7 54.2 145.522 1,995 50.2 1,266 31.8 22.0 55.3 148.224 3,511 52.4 2,140 31.9 37.4 55.4 151.029 2,716 32.9 2,265 27.5 32.5 39.4 153.230 5,386 68.4 2,819 35.8 52.3 66.3 156.935 3,772 72.8 1,525 29.4 35.5 68.6 149.138 4,236 79.3 2,624 33.1 45.0 56.8 152.343 3,337 29.7 3,637 32.3 45.4 40.4 153.644b 2,941 51.8 1,683 29.6 32.6 57.3 142.148a50 3,376 51.4 2,133 32.5 36.0 54.8 153.060 1,665 29.9 23.7 42.666 3,085 55.6 1,816 32.7 32.6 58.7 150.56771 1,504 38.173 1,802 31.2 32.7 56.779 4,300 55.0 1,680 21.5 43.5 55.7 137.381 5,510 67.7 2,308 28.4 52.1 64.0 150.184 5,470 64.7 2,775 32.8 55.6 65.7 148.486 2,943 44.4 2,487 37.587 2,852 37.1 2,521 32.8 40.0 52.1 134.388 3,284 54.7 2,197 36.6 37.9 63.2 144.589 3,116 46.0 1,762 26.0 35.6 52.6 137.291 3,308 51.7 2,415 37.7 38.3 59.9 149.392 3,103 51.7 2,349 39.2 38.0 63.4 143.4

1241

I. S. EDELMAN, J. LEIBMAN, M. P. O'MEARA, AND L. W. BIRKENFELD

TABLE III-Continued

Nae + K.Patient Na. Na./Body wt. K. Ks/Body wt. T.B.W. T.B.W./Body wt. T.B.W.

Kidney diseasemEq. mBq./Kg.2,510 35.52,017 42.31,671 32.72,884 41.31,595 39.9

Lung disease2,105 43.91,771 33.92,035 39.71,569 30.12,196 36.5

Gastrointestinal disease3,4273,1261,3131,608

39.445.233.035.8

Neurological disease1,218 29.51,805 29.92,404

1,6671,0971,2911,491

38.628.133.334.2

Miscellaneous2,0402,1125,4441,3581,9962,1802,5042,0392,1803,0061,611

2,0991,044-5,444

34.335.632.437.435.042.846.733.034.947.033.7

33.918.3-52.1

evaluated by measuring the freezing point depression ofstandard solutions of glucose and urea. The observeddepression of freezing point was directly proportional tothe molar concentrations up to 500 mg. per 100 ml. ofglucose and 300 mg. per 100 ml. of urea. The "corrected"serum osmolarity (ir'.) in mOsm. per liter was thereforecalculated as:

71 Gp NPNp't8 = '8- 18 2.8 1)

where 7r. is the measured serum osmolarity, Gp is theplasma glucose concentration in mg. per 100 ml. and NPNpis the plasma NPNconcentration in mg. per 100 ml. Thefactor 1/2.8 is derived from the mean nitrogen content of

NPN (28) and is based on the assumptions that, like urea.the other components of NPNhave an activity coefficientof 1.0 at physiological concentrations and that the relativeamounts of each constituent of NPNare constant, regard-less of absolute values. The "corrected" serum sodiumconcentration (Na'.), expressed as mEq. per liter of serum

water, is calculated from the measured serum sodium con-centration and serum water content, since spuriously lowserum sodium concentrations may be recorded when thelipid or lipoprotein content of serum is large (29).

Conventional statistical equations were used to calcu.late standard deviation (r), correlation coefficient (r) andsample standard deviation from regression (Sy.1) (30).The regression equations were obtained by the method of

no.

1728336274

mEq.4,8992,8742,8395,0622,247

mEq./Kg.70.860.255.572.656.2

47.146.148.369.2

40.643.9

76.8

51.940.5

48.873.380.352.5

3148b636459

49

44a46

4041656872778334

2,2572,4112,4793,602

3,5113,040

3,451

2,1462,4462,752

2,1102,8673 1032,287

L.47.6

'31.536.056.425.4

27.829.329.837.038.7

43.837.825.231.3

22.229.934.8

26.025.525.125.2

67.365.970.480.863.5

58.056.058.071.264.6

50.454.663.269.6

53.749.4

60.165.265.057.8

mEq.1L.155.7155.4125.3140.8151.2

156.7142.7151.6139.8

158.4163.1

160.8

151.5142.4148.3

145.6155.4175.1149.9

1415323945525570765469

MeanRange

2,6242,6465,2471,2282,7073,2942,7102,4792,6453,7822,037

3,2631,228-6,983

44.144.631.233.847.564.750.640.142.359.243.4

53.229.7-80.3

30.232.369.818.032.135.233.835.634.446.127.0

36.118.0-69.8

50.755.141.549.456.469.163.057.655.072.156.6

58.937.7-80.8

154.7147.1153.3143.9146.4155.6154.4126.9140.3147.4135.2

148.6125.3-175.1

1242


VS 8 2.63 MRS-6S.4$Y.J, v oZ4

0

A00

a

a

A

/A

a 0

a a

A A,

S * 0

±

/ 0

00~~~~

00~~~~0

0

o *@00 00

000a

* NO EDEMA0 EDEMAA NO EDEMA, EXPIRED WITHN 2 WEEKSOc STUDY,a EDEMA, EXPIRED WITHIN 2 WEEKS OF STUDY

100 105 110 115 120 125 130 135 140 145 150 155 160 165 170 175 180 185

SERUM SODIUM CONCENTRATION (mEq./L)

FIG. 1. THE RELATION BETWEENSERUMOSMOLARITY AND SERUM SODIUM CONCENTRATIONThe statistical data were calculated as described in the text. The regression is assumed to

be linear.

least squares, and the probability (p) of a correlationcoefficient being obtained by chance was evaluated by thet test (30). Some of the correlations encountered were

very high. The possibility was therefore considered thatthese very high correlations might represent perfect rela-tionships masked only by errors of measurement. Thispossibility was explored in the highly significant regressionrelations by correcting the correlation coefficients for atten-uation (31). The correlation coefficient corrected forattenuation is an estimate of the correlation between twovariables free of errors of measurement. The formula forthis correction is:

r

r Y., = I 2)

where r'y.1 is the amended correlation coefficient, r is thecorrelation coefficient computed from the data and:

ry y = 1 --2y 3)O2y

r.z = 4m)dfr2

y.VM is the standard deviation of reproducibility of meas-

urement of the y parameter and x.m is the standard devia-tion of reproducibility of measurement of the x parameter.y and = are the standard deviations of the observed values.To compute x.m for the parameter of the form (a + b)/c,the following formula was used:

O~2x~ [ra>2.m + T2b.m + R2 O2c.m]X.wm -= L 2 f 5)

where x = (a + b)/c. This formula assumes that theerrors of determination in a, b, and c are unrelated to one

another, which is a reasonable assumption.Errors of measurement were evaluated from n number

of observations on pooled specimens or by serial estima-tions in given subjects. The standard deviations of repro-

ducibility were as follows: aN.,.. = 1.05 mEq. per liter(n = 21); OTI.m = 1.44 mOsm. per liter (n = 16); oNw*.m- 65 mEq. (n = 20); oKe.m = 57 mEq. (n = 23); OT.B.W.m= 0.71 liter (n = 28). ONb.m, 0x.m and qT.B.w.m were

calculated from previously established values using the

standard formula Mm= (19). These estimates are

slightly lower than previously published values (32, 33).

450y

360

3501-

340F

F

FI_

Z 330

a 320

t 310It

N "300a

*0 290

l 280

Ii o

,FLI

2601

250

2401

230

1243

_

z , r

I. S. EDELMAN, J. LEIBMAN, M. P. 0'MEARA, AND L. W. BIRKENFELD

7): / 75 ( ND.) * /. /sy.x 5.6

:0.97

*

o / A

* NOSEMWAo EDEMA* NO EDEMA,EXIARED WITH/N 2 WEEKSOP STUDY

EDEMA, EXPIRED WIrHIN 2 WEEKSO STMDY.a

I , 7 , I

101 106 111 116 121 126 131 136 141"CORRECTED" SERUMSODIUM

I I

146 15 156 161 166 171 176 181 166 191 196CONCENTRATION(mEq/L SERUMWATER)

(Na' )

FIG. 2. THE RELATION BETWEEN"CORRECTED" SERUMOSMOLARITYAND THE "CORRECTED" SERUMSODIUMCONCENTRATION

The regression is assumed to be linear. See text for calculations of "corrected" serum osmolarity and "corrected"serum sodium concentration.

RESULTS

The data obtained in this study are listed inTables II and III. The heterogeneity of the sub-jects is indicated by the wide range of values: Na'8varied from 108.9 to 192.5 mEq. per liter of serum

water, K'8 from 2.28 to 7.00 mEq. per liter of se-

rum water, Cl8 from 72.6 to 125.6 mEq. per liter,(HCO3)p from 8.1 to 40.4 mEq. per liter, arterialblood pH from 7.19 to 7.59 units, NPNfrom 9 to238 mg. per 100 ml. of plasma, and glucose from66 to 502 mg. per 100 ml. of plasma.

Serum osmolarity and serum sodium concentration

The total osmotic pressure of any fluid is thesum of the partial pressures of solute and may be

expressed as equivalent osmotic concentrations or

milliosmols. Sodium, the principal extracellularcation, must influence serum osmolarity consider-ably. Its quantitative contribution is depicted inFigure 1. While the correlation coefficient of theregression of total serum osmolarity with respectto serum sodium is highly significant (r = 0.81,p < 0.001), the large sample standard deviationfrom regression (Sy.. = 17.4 mOsm. per liter)indicates that other substances probably contributesignificantly to Tr. The value of the amended cor-

relation coefficient r' (0.82) indicates that errors

of measurement contributed little to the observedscatter. These data corroborate the findings re-

ported by Talso, Spafford, Ferenzi and Jacksonin patients with congestive heart failure and cir-

1244

350-

340 -

330-

320-

t 310

t 300

)S..,' 290

x _ 280

270

t 260

Q 250

i 240

:0 t%T0

0 0o


rhosis of the liver (34). The estimated contribu-tions of plasma NPNand plasma glucose to se-rum osmotic activity were subtracted to evaluatethe separate relationship of Na'8 to ir'8; this isdemonstrated in Figure 2. The correlation coeffi-cient of this relationship, r = 0.97 (see Table IVand Figure 2), shows the primary dependence ofIr'8 on Na'8, as has long been assumed (35). Thedata in patients who died within two weeks ofstudy did not differ from those in the remainingpatients. This is in contrast to the findings ofRubin, Braveman, Dexter, Vanamee and Roberts(36), who noted hyperosmolarity of plasma incritically ill patients in excess of measured soluteconcentration. The data in Figure 2 indicate alinear dependence of serum osmolarity on the con-centration of sodium in serum water when cor-

170

1 160

| 155

150

145

rections are made for the osmotic contributions of*NPNand glucose. Total serum osmolarity (7ra),therefore, is given by:

Tro = 1.75 Na'8 + 0.0556 Gp+ 0.357 NPNp+ 10.1 6)

with an amended correlation coefficient, r' = 0.98,and a sample standard deviation from regression,Sy.. = 5.6 mOsm. per liter. The values of theintercept of 10.1 mOsm.per liter and of S... of 5.6mOsm. per liter can be attributed to the osmoticcontributions and variations in concentrations ofthe salts of K+ (,- 7.0 mOsm. per liter), Ca++(,- 1.5 mOsm. per liter), Mg++ (,-- 0.5 mOsm.per liter) and of trace substances (,- 1.0 to 3.0mOsm. per liter) (37).

r 0.20

0

0

0 0

0

0

00 0*0.0 0 o

0° 0o °*

0

000

0

lk(b 0

0

0 0

0

0o0

d000 00 0

0 0

0 @0 0.0~~~

00 0

0 0

0 0

0

0

0

0

* NOEDEMA0 EDEMA

0

15 20 25 30 35 40Kg/BODY WEIGHT (mEq./KG)

Il145 50 55

FIG. 3. THE RELATION BETWEENTHE "CoRREcTED" SERUMSODIUM CONCENTRATIONAND TOTAL EXCHANGEABLEPOTASSIUM

The correlation is equally minor for both edematous and nonedematous subjects and does not justify calculation of a

regression equation.

14000

0

90.

0o00

0

0

0

135

130

125

120

1 15

110

0

I)

*4 4.4

0

I -

I

L

1245

I

-

.ah

-

-

-

-

-

-

I I I I


0

00

I 00* 0so0 @ 0

0 *31 *

0 @

0. 0 0 0Oo

* 00 0

0.00

0000

0

00

* NO EDEMA0 EDEMA

0

* 0

000

o @0

%0 800

0

40 45 50 S5 60 65 70T.B.W. / BODY WEIGHT(%)

FIG. 4. THE RELATION BETWEEN"CORRECTED" SERUMSODIUM CONCENTRA-TION AND TOTAL BODYWATER

Neither the. edematous nor the nonedematous patients shows a correlationgreat enough for calculation of a regression equation.

Serum sodium concentration and body composition

Variations in serum sodium concentration oftenparallel variations in sodium balance, but we foundno correlation between Na'8 and Nae/body weight(r = 0.003). This confirms many similar stud-ies in the past (1-4, 6). The negative result,however, does not explain the known effects ofalterations in sodium balance on Na8.

Potassium balance modifies the level of Na8,but as shown in Figure 3 the correlation betweenNa'8 and Ke/body weight (r = 0.20) is minor.Therefore, differences in body potassium alonewould not account appreciably for the variationsin Na8 in this group of subjects.

Figure 4 is a scattergraph of Na'8 as a functionof total body water expressed as per cent of bodyweight. The coefficient, r =-0.25, indicates a

minor negative correlation. Variations in body fatin these subjects may account in part for the poor

correlation with either Ke or T.B.W. Further

analysis of these relationships requires measure-

ment of body fat.The concept of "dilution hyponatremia" suggests

that retention of water in excess of sodium mayaccount for the poor correlation of Na'8 with either

Na. alone or T.B.W. alone. The relationship be-

tween Na'8 and the ratio Nae/T.B.W. is shown in

Figure 5. The coefficient, r = 0.27, indicates onlyminimal correlation of Na'. with the ratio of bodysodium to body water.

Since an inverse relation between retention of

water and serum sodium concentration has been

noted during periods of negative potassium bal-ance, Na'8 may be related to the ratio of Ke to

T.B.W. Figure 6 is a plot of Na'8 and the ratioKe/T.B.W., which shows a modest correlation(r = 0.40). The choice of coordinates probablydoes not conceal any closer correlations since log-

1246

165 F

0160F

ISSik150 -

145 F

140F

135 F

130

125 _

I'd

I0

'II

0

%0

"I

I.3,

14%

'hi

0

0

120 -

I I 5 _

0 o

0

0 0

0

0

110

00

30 35 75 80 85

0o


log plots of Na'9 to Nae/T.B.W. and to KE/T.B.W.are equally disappointing.

The partial correlation of Na'8 with Nae/T.B.W.and with Ke/T.B.W., as well as the evidence thatbody sodium, body potassium and body water af-fect Na8, suggests that osmotic adjustments be-tween body fluids may determine the relationshipof Na8 to body composition (7, 11, 38-41). Theprecise correlation between Na'8 and 7''8 may beparalleled by a similar correlation between intra-cellular osmolarity and intracellular K+ concentra-tion. The ratio (Nae + Ke)/T.B.W., therefore,may be a primary determinant of Na'8, providedthat water is passively distributed across cell mem-branes. This hypothesis is tested in Figure 7.The high degree of correlation between Na'8 and(Nae + Ke)/T.B.W. is obvious and in strikingcontrast to the lesser correlation of Na'8 to theseparate elements in this ratio. The coefficient

r = 0.83 is especially impressive since there mustbe a propagation of methodological errors in cal-culating this ratio. Figure 8 demonstrates thesame high degree of correlation between zr'8 and(Nae + Ke)/T.B.W., and Table IV lists the sta-tistical data describing these relations. The likeli-hood that these findings are chance phenomena isextremely small. Indeed, the correlation coeffi-cents [r = 0.83 and r' = 0.92 for Na'8 versus(Nae + Ke)/T.B.W., and r = 0.82 and r' = 0.91for 7r', versus (Nae + Ke)/T.B.W.] suggest thatNae, Ke and T.B.W. are the primary determinantsof Na'8. The standard deviations from regressionfor the parameters Na'8, (Nae + Ke)/T.B.W. andlres, (Nae + Ke)/T.B.W. were 5.6 mEq. per literand 10.2 mOsm. per liter, respectively (see TableIV). These variations from regression are partly,if not wholly, a reflection of methodological errorssince the standard deviation of reproducibility of

r: 0.270

0

0

00

0 0.

0 0 0

a * 0 0

0 0

0

0

0

00

0 00 0

0 o 80 0.0 0

0000 0 0 00 0 0.0

0 0

0

0

0 0

0 0 0

0

0

* NOEDEMAo EDEMA

65 70 75 80 85 90 95 100 105 110 115 120 125Nag /T.B&W. (mEq/L)

FIG. 5. THE RELATION BETWEEN"CORRECTED" SERUMSODIUM CONCENTRATIONAND

THE RATIO OF TOTAL EXCHANGEABLESODIUMTO TOTAL BODYWATERThe correlation is quite limited for both edematous and nonedematous patients and

a regression equation is not justified.

1247

165 r-

160F

155k

150 -

145 I

140

I'

'1I)

'44

%

'4

0

0

0

135 I

130 h

125 -

120 F

115s

110

60


00

0

00

00 0

00 000 0 0 0

0 (a9 0 0

00 00 0 0000 (b *

* * 000

0

00 0

0

0

00

0

0

0

* 0

00

00

00

.

.

0

0

* NO EAEMA0 EDEMA

30 35 40 45 50 SS 60 65 70 75 80K.S/T.B.W (mEq./L)

FIG. 6. THE RELATION BETWEEN"CORRECTED" SERUMSODIUM CONCENTRATIONANDTHE RATIO OF TOTAL EXCHANGEABLEPOTASSIUM TO TOTAL BODY WATER

Although there is a modest correlation, neither the edematous nor the nonedematouspatients fall into a precise relation.

TABLE IV

Summary of statistical relationships between serum sodium concentration, serum osmolarity and body composition

Standarddeviation

from Correlationregression

Parameters Regression equation SY.X r t p r'

Serum osmolaritySerum sodium 1r8 = 2.63 Na, - 65.4 17.4 0.81 23.1 <0.001 0.82

concentration

"Corrected" serumosmolarity sr' = 1.75 Na', + 10.1 5.6 0.97 121 <0.001 0.98

"Corrected" serumsodium concentration

"Corrected" serum Nsodium concentration Na' = 1.1 (Nae+I) - 25.6 5.6 0.83 24.4 <0.001 0.92

(Nae + Ke)/T.B.W. T.B.W.

"Corrected" serum Nosmolarity 7', - 2.09 ( + e) - 56.7 10.2 0.82 19.8 <0.001 0.91

(Nae + Ke)/T.B.W. T.B.W.

1248

r'O.400

165 r

160F

1551-

150 F

145 F 0

0 0

1%

g.k

'I

0

140 F

135 h

130 -

12SF120F

0 0

0 0

0

0

115 -

110-0 0

8s 90 9s


It

it

%.e

A!

4.p

165r-

160

155p

150k

145

140k

135

130

125

1201-

Na' DI q)/Z&W -2S.6

s~~~~~~~~~~~~~~~~s

Sy.x z S.6

r °0O.83

0

0

0

000 0 0°° odv

00 8o

o 0

00

%00 0

00 0

0~~~~~~

0~~~~~*~~~~ 0

0

0

* 0

0

0

0 0

0

0

* NOEDEMAEDEMA11 [-

110

110 115 120 125 130 135 140 145 150 155 160 165 170 175 180(Nac*K)/T.B.W. (mEq./L)

FIG. 7. THE RELATION BETWEENSERUMSODIUM CONCENTRATIONAND THE RATIO OF

(NA. + K.)/TOTAL BODYWATER

The statistical data were calculated as described in the text. The regression is assumedto be linear. The presence or absence of edema does not appear to affect the regressionrelation.

the ratio (Nae + K43)/T.B.W. estimated from in-dividual reproducibility of each component is 3.8mEq. per liter.

The regression relation between Na', and (Nae+ Ke)/T.B.W. and between 7rT and (Nae + Ke)/T.B.W., despite the high correlations, may includetwo or more populations. At least two sets of cir-cumstances may alter the quantitative dependenceof Na', or 7r'. on (Nae + Ke)/T.B.W.: a) acid-base disturbances and b) osmotic inequalities be-tween cells and extracellular fluid (ECF). Bonesodium consists of exchangeable and nonexchange-able fractions, and most of the exchangeable bonesodium is osmotically inactive (15). Since aci-dosis will considerably reduce bone sodium con-

tent (17, 42), acid-base disturbances may shiftthe relationship between Na', and body composi-tion. Figure 9 depicts the distribution of Na',versus (Nae + Ke)/T.B.W. in subjects with ar-

terial pH < 7.36 and in a second group with ar-

terial pH > 7.48. Although the observations are

too few to allow definite conclusions, there is no

apparent deviation or variation from the generalregression equation, and most of the data fallwithin + 1 S.,. The quantitative relation be-tween Na', and (Nae + Ke)/T.B.W., therefore,appears to be independent of arterial pH. Os-motic inequalities among body fluids may influ-ence this relation. Hyperglycemia particularly,and to a lesser extent azotemia, may be associatedwith transient or possibly even sustained osmoticdifferences across cell membranes (38, 41). Ac-cordingly, Figure 10 shows the relation of Na'8 to(Nae +Ke)/T.B.W. in patients with NPN> 50mg. per 100 ml. of plasma or with glucose > 130mg. per 100 ml. of plasma. There is no apparentdeviation from the general regression equation,and no separation into different populations.

1249


:S 2.09 (N# *)/Wa.W -56.Sy.x r 10.2, : 0.62

0

0

0 0

Qo0 0

0 g /

0

'- 0000

0 .

00

00

0

0

* NOEDEMAo EDEMA

0

I I

17S 180120 125 130 135 140 145 150 155 160 165 170(NaD.+Ke)/T.B.W (mEq/L)

FIG. 8. THE RELATION BETWEENTHE "CORRECTED" SERUMOSMOLARITYAND THE

RATIO OF (NA.+ K.)/TOTiL BODY. WATERThe statistical data were calculated as described in the text. The presence or

absence of edema does not appear to affect the regression relation.

ASSUMED:(FRO/ FG. N.; :/4// (Ab. *Ke)l/r8W -25.6s Y.

a 5.6Igo

10% I

1SO

-% 140

U 130

l 120a-

% 110

; 100

AR74

_-

_

/s

/ / /

/9 /0

100.1////

100 110 120 130

ARTERIAL pH >7%48 /4v /

* / .////

/O

/O~~~

//

140 150 160 100 110 120 130 140 150 160(Na6+ KS)/T.W. (mEqA)

FIG. 9. THE RELATION OF NA'. AND (NA. + K.)/TOTAL BODY WATERIN PATIENTS WITH

ACmosis (PH < 7.36) OR ALKALosIs (pH > 7.48)The regression line is taken from the relation depicted in Figure 8. Each broken line is one

standard deviation from regression.

1250

SOOI

1-

F

290

280

't 270I

4 2608040

250

:S1240

| 230

lk 220.8

210

F-

F

F

H

310 r

/

I


TABLE V

Serial studies of serum sodium concentration, serum osmolarity and body composition

1st study 2nd study A 1st study 2nd study A 1st study 2nd study

Patient, no. 28 33 70 76 47a 53Diagnosis chronic glomerulonephritis panhypopituitarism hypertension and congestive

heart failureClinical status no edema 2 + edema no edema no edema 2 + edema 2 + edemaDate 3/21/56 4/26/56 1/8/57 2/19/57 8/30/56 10/19/56Body weight, Kg. 47.6 51.1 +3.5 61.8 62.5 +0.7 48.6 49.8 +1.2r',, mOsm./L. of

serum water 261.6 207.0 -54.6 216.5 249.2 +32.7 256.4 208.0 - 48.4Na'., mEq./L. of

serum water 144.0 111.2 -32.8 119.7 135.0 +15.3 138.5 117.6 -20.9Na., mE*. 2,874 2,839 -35 2,497 2,645 +166 3,046 3,734 +688K., mE*. 2,017 1,671 -346 2,039 2,180 +141 1,750 1,211 -539T.B.W., L. 31.5 36.0 +4.5 35.6 34.4 -1.2 31.6 37.6 +6.0

T.RB. E /L- 155.4 125.3 -30.1 126.9 140.3 +13.4 151.9 131.6 -20.3

The data summarized above indicate that Na'8predominantly reflects the ratio of (Na, + Ke)/T.B.W. and that this correlation is independentof differences in the pH of extracellular fluid or inglucose or NPN concentrations. The regressionequation of this relation has a slope of 1.11 (seeTable IV) and implies almost a 1: 1 correspond-ence between changes in (Nae + Ke)/T.B.W. andchanges in Na'b. The equation relating serial dif-ferences in Na'. and (Na. + Ke)/T.B.W. is:

Na..1 - Na,.2 = 1.11 [(Na. + Ke)/T.B.W.]i- 1.11 [(Nae + K.)/T.B.W.12

or,ANa'. = 1.11A[(Nae + Ke)/T.B.W.]. 7)

In three instances serial observations were made.The results, summarized in Table V, confirm theprediction of proportional changes between Na'8and (Nae + Ke)/T.B.W. independent of the pres-ence or absence of edema. The proportionality tochanges in I'l is also obvious. These data con-firm the report of Deming and Gerbode (11) onthe synchronous changes in Na8 and sodium, po-tassium and water balance in patients after mitralvalvulotomy and of Wynn (39) in similar stud-ies. Wilson, Edelman, Brooks, Myrden, Harkenand Moore (4) made serial observations of Na8,Nae, Ke and T.B.W. in patients before and aftermitral valve surgery. When analyzed in terms ofserial differences between successive observations,their data, combined with the values from Table V,demonstrate the same close correlation betweenANa, and A(Na. + K.)/T.B.W. (see Figure 11).

The slope, 0.83, and the intercept, 0.1, are in ex-cellent agreement with the derived prediction(Equation 7), considering that in the earlier study(4) Na5 is expressed per liter of serum and thatK. was determined at 24 hours and T.B.W. at 3hours. There is little doubt, therefore, that bothamong individuals and in any one individual, Na'.is strongly dependent on (Nae + Ke)/T.B.W.

170

' 160

4150

X 140

I%130

pi120

) 110

E 100'IIZs

I-

F-

I-

I-

* APNI >50 MG/IOOMZ. PLASAMAX GOLOSE>/30 M6/100 MLPLASMAASSUMED:(FROMt FI6. d)

NtI. I/ (NatGtf KI/ -25.6W2 /Sy.x g S.6

//

,5(/ /

//-

/ /A/110 120 130 140 150 160 170

(Nan,+ Ka)/T. S.W.(mnEqL).FIG. 10. THE RELATION OF NA'. TO (NA. + K.)/

TOTAL BODY WATERIN PATIENTS WITH AZOTEMIA ORHYPERGLYCEMIA

The regression line is taken from the relation de-picted in Figure 8. Each broken line is one standarddeviation from regression.

1251


+ 30

%s1 +20

!+102%I._ 0O

q,- tO

q - 20a

t -30

'O -40

x,x xx

xy

xx x /x

/ x

/ ~ ~~~~~*HIraS71sz MBLAE VJ* X WILSONV Fr AZ frAJ?,f r))

r: 0.89

a Iva ' 0.83 A(NA 'I-eJ/Z&W o.

Sy.,, 5.5 mE9./L.

40 30 20 10 0 10 20 30& (NnCs Ke)/T.8.W. (mEg/L)

FIG. 11. SERIAL DIFFERENCES IN SERUM SODIUMCONCENTRATION AND THE RATIO (NA. + K.)/ToTALBODYWATER

The data from Wilson and co-workers (4) are suc-

cessive observations where the change in Na. exceeded3 mEq. per liter. The regression equation was calculatedon the assumption of a linear relationship.

DISCUSSION

Figure 2 shows a linear regression of 7T. on

Na'. over a concentration range of Na'. from108.9 to 192.5 mEq. per liter of serum water. Theslope, X = 1.75, indicates that there is little or no

binding of sodium in serum. Multivalent anions,such as phosphates, sulfates, organic anions andserum proteins, provide some electrochemical butlesser osmotic equivalence for sodium in serum, so

that probably little or no difference exists betweenthe activity and concentration of sodium salts inserum when referred to aqueous NaCl standards.Glucose and NPN contribute to total serum os-

molarity in proportion to their concentrations.These observations confirm the findings of Leaf,Chatillon, Wrong and Tuttle (38), and accountfor the apparent discrepancies between 7r. and Na3reported by Talso and associates (34) and byRubin and associates (36). The general equationrelating 7r,, Na3, glucose and NPNappears to holdfor the full range of clinical variations and withoutregard to the seriousness of illness (see under Re-sults). The residual osmotic activity (i- 10mOsm. per liter), which is given by the zero in-tercept of Equation 6, furthermore, can be reason-

ably assigned to the known amounts of other saltsand trace substances in serum (37).

The data demonstrate poor correlations betweenNa'. and Nae, K8, T.B.W., Nae/T.B.W. and K8/T.B.W. (see under Results and Figures 3 through6). The linear correlation between Na'8 and(Nae + Ke)/T.B.W. (r = 0.83, r' = 0.92) ac-counts for the reported effects of each of thesecomponents of body composition on Na8 (1-12,14, 34, 38, 39). That Na'3 is a reflection of theratio of the sum of exchangeable monovalent cat-ion (Nae + K8) to T.B.W. is confirmed by theapproximately 1: 1 correlation between sequentialchanges in Na'8 and (Nae + Ke)/T.B.W. in thesame individual (see Table V and Figure 11).

In 1944, Elkinton, Winkler and Danowski (43),using Na8 as the primary index of ECFosmolarity,tested the hypothesis of body fluid iso-osmolarityby comparing the sum of sodium balance (b.Na)and potassium balance (b.K) with the change intotal osmotically active base. The expression theyderived relating total base balance to changes inNa8 and in T.B.W. is:

(b.Na + b.K) = T.B.W.1 (0.95 Na..1 + 10)-T.B.W.2 (0.95 Na..2 + 10). 8)

Despite very good correlations between observedand predicted base balances, the authors concludedthat a significant and variable fraction of cell baseis osmotically inactive. Deming and Gerbode ( 11 )showed that the change in serum sodium concen-tration correlated closely with net change in so-dium and potassium balance per unit change inbody water. Recently, Wynn (39) compared theobserved and predicted changes in serum cationconcentration and found that the formulation ofElkinton and associates (43) predicts such changeswithin the limits of experimental error. Thesefindings agree with ours since, assuming that so-dium and potassium balance are equal to ANaeand AKe, Equation 8 is equivalent to Equation 7except for minor details.

Variations in extracellular pH, glucose or NPNconcentrations appear to have no influence on thecharacter of the correlation between Na. and Na.,K8 and T.B.W. (see Figures 9 and 10). Thesedata do not exclude the possibility that factorsother than Nae, K8 and T.B.W. alter Na8. Todemonstrate the existence of such factors, how-ever, it would be necessary to show changes in

1252


Na'8 independent of changes in the ratio (Nae +KE,)/T.B.W. The concept of internal redistribu-tion or "shifts" in electrolytes, so often invoked toexplain changes in Na9 in disease states, needs tobe re-examined since no evidence for the existenceof such shifts without simultaneous changes in theamounts of sodium, potassium or water in the bodyis apparent in our data or in those referred to above(11, 39).

The relationships between 7T', Na'5 and (Nae +Ke)/T.B.W. are compatible with the concept of apassive distribution of water across cell membranesin proportion to solute activity. The possibility ofparallel changes in intracellular and extracellularosmolarity with either a constant ratio or a con-stant difference between phases is not definitivelyexcluded, but seems unlikely. Current evidenceindicates that there are no sustained osmotic gra-dients across cell membranes, although transientgradients occur almost continuously as a result ofcellular metabolic activity and absorption of in-gested solute and water (8, 38, 39, 40, 4 447).The influence of potassium on Na, is presumablya reflection of its contribution to intracellular os-molarity. The zero intercept of the regressionequation for Na'5 versus (Na, + KIC) /T.B.W. isa negative constant (- 25.6 mEq. per liter), whichprobably is a measure of the quantity of osmoticallyinactive exchangeable sodium and potassium perunit of body water. Since body water in thisgroup of subjects averaged 36.1 liters (see TableIII), the estimated osmotically inactive Na + Kis approximately 920 mEq. Osmotically inactiveexchangeable bone sodium, which is about 750mEq., probably accounts for almost all of thisquantity (15). The calculated ratio of osmoticallyinactive to total exchangeable potassium, there-fore, is less than 10 per cent (i.e., - 170/2099),which suggests that there is little or no discrep-ancy between exchangeable and osmotically activepotassium. However, this calculation is validonly if Na, and (Nae + Ke)/T.B.W. are linearlyrelated over the entire range of their possiblevalues.

Figures 7, 9 and 10 indicate that Na'8 reflectsthe proportion of (Nae + Ke) to T.B.W. Thisobservation provides a rational basis for the classi-fication of hyponatremic and hypernatremic states.Hyponatremia may reflect either a) primary so-

dium deficit, b) primary potassium deficit, c)primary water excess or d) combinations of these.Conversely, hypernatremia may reflect either a)primary sodium excess, b) primary potassium ex-cess, c) primary water deficit or d) combinationsof these. Hyponatremia in patients with gastro-intestinal fluid loss probably results from loss ofsodium and potassium (16, 48, 49). Hypona-tremia in edematous subjects, on the other hand,appears to be a consequence of the loss of potas-sium and gain of water, as exemplified by Patients28 and 47a in Table V. This pattern is also promi-nent in postoperative hyponatremia; in all but 2of the 11 patients studied by Wilson and associ-ates, (4) the postoperative fall in Na, was associ-ated with a rise in Na, a fall in Ke, and a rise inT.B.W. Hypernatremia has not yet been studiedin terms of these components of body composition,but relative or absolute body water depletion isprobably its most frequent cause. Diabetes in-sipidus and water deprivation are two classicalexamples of this state. Primary excess of potas-sium is probably not involved in the pathogenesisof hypernatremia, inasmuch as no instance of anabnormally high body potassium content as a con-sequence of disease has been reported (1, 18).However, reversal of hyponatremia by potassium-loading in patients who presumably were potas-sium-depleted has been observed (12), and thisstrategem promises to be valuable in the treatmentof this disturbance in edematous subjects (7).

The correction of the hyponatremia presumedto result from sodium depletion is usually basedon the formula:

Na deficit = (140 - Na.)T.B.W. 9)

This equation, which is supported by clinical ex-perience, is based on the assumption that isotonicconditions prevail throughout body water (7).Wolf and McDowell (40) emphasized that thisformula assumes that T.B.W. is unchanged bytherapy and revised Equation 9 to include theeffect of changes in T.B.W.

Na deficit = (140 - Na5) T.B.W.1+ (AH20) 140, 10)

where T.B.W.2 - T.B.W.1 = AH20. By sub-stituting and rearranging terms their equation may

1253

I. S. EDELMAN, J. LEIBMAN, M. P. 0PMEARA, AND L. W. BIRKENFELD

be expressed:

Na deficit = 140T.B.W.2 - NasT.B.W.1. 11)

Both Equations 9 and 10 are special cases ofthe general regression equation derived in Fig-ure 8. There are, in-fact, three equations whichmay be derived from the general relation betweenNa. and body composition (see Equation 7).This equation can be simplified if it is assumedthat either a) T.B.W. is unchanged by therapy(T.B.W.C) or b) Ke is unchanged by therapy(Ke.c), or c) both T.B.W. and K. remain con-stant. These three assumptions each lead to sepa-rate modifications of Equation 7. The generalrelation expressed in Equation 7 may be written:

Na..2- Na.., = 1.11

r Na..2+ Ke.2 Nae. + Ke.]X T.B.W-2 T.B.W.

a) For the special case where T.B.W. is con-stant and both Na. and Ke change as a result oftherapy, the equation becomes:

Na..2- Na..l = [140 - Na..1T.B.W./1.11- [Ke.2- Ke,.1]. 12)

b) For the special case where K. is constantbut Na. and T.B.W. are altered by therapy:

Na,.2- Nae.. = [140 T.B.W.2- Na,.. T.B.W.1 + AH20*25.6] 1/11. 13)

c) Finally, for the special case where onlyNa. is variable but K,.2 = Ke.1 and T.B.W.2 =T.B.W.j:

Nae.2- Na..1 - (140 - Nav.e) T.B.W.,/1.1l. 14)

Equations 14 and 9 are identical, except for thefactor 1/1.11, if the sodium deficit is equated withANae. The Wolf-McDowell formulation, Equa-tion 11, is similar to Equation 13, except for theterm AH20 25.6, which appears as a consequenceof the difference between total exchangeable cat-ion and total osmotically active cation. A similarset of equations may also be derived from Equation8. Our data, therefore, provide an experimentalbasis for the formulas used in clinical manipula-tions and demonstrate the coordinated influence ofthe three major components of body compositionon serum sodium concentration.

SUMMARY

The relationships between serum sodium con-centration (Na.), serum osmolarity (Xr.), totalexchangeable sodium (Na,), total exchangeablepotassium (K.) and total body water (T.B.W.)were explored by simultaneous measurements ina heterogeneous group of chronically ill patients.

Serum osmolarity correlates closely with serumsodium concentration expressed as mEq. per literof serum water (Na'.) when appropriate correc-tions are made for the osmotic contributions ofglucose and nonprotein nitrogen (NPN). Serumsodium concentration is only partially or poorlycorrelated with total exchangeable sodium/bodyweight, total exchangeable potassium/body weight,total body water/body weight, total exchangeablesodium/total body water and total exchangeablepotassium/total body water. A high degree ofcorrelation, however, exists between serum so-dium concentration (Na',) or "corrected" serumosmolarity (7r'.) and the ratio (Nae + Ke)/T.B.W. This relation is confirmed by the highcorrelation between the simultaneous serial differ-ences in Na'. and (Nae + Ke)/T.B.W. The re-gression of Na'. on this ratio appears to be inde-pendent of arterial pH, plasma glucose or plasmaNPNconcentrations.

The implications of these data with respect toosmotic gradients in various components of bodywater and to evaluation of osmotic activity ofbody potassium are explored. Body water ap-pears to be passively distributed in proportion toosmotic activity, and all or almost all of bodypotassium is osmotically active.

A classification scheme for hyponatremia andhypernatremia is presented, and equations for esti-mating sodium deficits are derived.

ACKNOWLEDGMENT

The technical assistance of Mary Rose MacKerrowand Mary Frances Anderson is appreciated. The ad-vice and guidance of Lincoln E. Moses and Calvin Zippinwere most helpful in our statistical formulations.

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ku...patient age sex bodywt. transudate diagnosis k kidneydisease no. yrs. 17 47 28 58 33 58 62 36...

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