Physiology · Unit 1: The internal environment and its control

Body Water and Its Compartments

Where is the water in an adult body, how do you measure a compartment you cannot reach, and why does a retained litre of water swell your cells while a litre of isotonic saline does not? This lesson gives the reference volumes and their limits, measures them by indicator dilution, counts particles as osmolality and tonicity, and uses conservation of effective osmoles to predict how cells and extracellular fluid change after infusions, losses and water retention.

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Here is a puzzle. In the textbook model of an adult man, retain one litre of pure water, with no solute in it. About two thirds of that litre ends up inside cells. Now retain one litre of isotonic saline instead. Once it has spread, none of it ends up inside cells. Same body, same volume. Why does the water go to different places? First, the tanks. Physiology texts use a 70 kilogram reference man, whose body is 60 % water. That is a convention for arithmetic, not a measurement of anyone. Total body water is about 42 litres. About two thirds of it, 28 litres, is intracellular fluid, the water inside cells. About one third, 14 litres, is extracellular fluid, the water outside them.

Water crosses most cell membranes quickly. So picture two rooms joined by a door that only water can pass. The guests stuck in each room decide how much water it holds. Inside cells, the stuck guests are anions that cannot leave, and the potassium that balances their charge. Outside, they are sodium, with chloride and bicarbonate. Sodium leaks into cells, but the sodium-potassium pump moves it back out. So sodium salts are the effective solute of the extracellular fluid. Now count the guests. In the model, both rooms sit at 300 milliosmoles per kilogram. These numbers are made up, and rounded. Measured adult values run a little lower. 28 litres of cells hold 8,400 milliosmoles.

14 litres of extracellular fluid hold 4,200 mOsm. The model is a closed body, with no urine, sweat or breath losses, and added sodium chloride stays outside cells. Retain 1 litre of isotonic saline. Its particles stay outside, so the concentration does not change. Cells stay at 28 litres. Extracellular fluid grows to 15. Now retain 1 litre of solute-free water. In the model, it first sits outside cells, so extracellular fluid also reads 15. Then water crosses until both rooms match. They end at about 293 milliosmoles per kilogram. Cells gain two thirds of a litre. Extracellular fluid gains one third. The rule to keep: water follows effective solute.

Each compartment holds water in proportion to its effective osmoles. In the model, retained saline stays in the extracellular fluid, because its sodium stays outside. Retained pure water is shared, two thirds to cells. This is equilibrium arithmetic. It predicts where a retained load goes, not how long it stays.

In the textbook model of an adult man, retain one litre of solute-free water and about two-thirds of it ends up inside cells. Retain one litre of isotonic saline and, once it has spread, none of it does.

Water crosses cell membranes freely and settles wherever the solute that cannot cross is. Claude Bernard’s internal environment (tissues and homeostasis) is, in the reference man, about 14 litres. This lesson measures the compartments, counts their particles, and predicts how they change.

Sixty percent is a convention, not a constant

Physiology texts use a 70-kg reference man whose body is 60 percent water: total body water (TBW) of about 42 L, a convention for arithmetic, not a measurement of anyone. It divides like this:

  • Intracellular fluid (ICF), the water inside cells: about two-thirds of TBW, 28 L.
  • Extracellular fluid (ECF), all the water outside cells: about one-third of TBW, 14 L. About three-quarters of it is interstitial fluid (ISF), the fluid that bathes cells (10.5 L), and one-quarter is plasma, the fluid part of blood (3.5 L).

These are fractions of water, not of body mass: two-thirds of 70 kg would be 47 L, more than all the body’s water. Transcellular fluid (cerebrospinal, synovial and pleural fluid) is usually counted with the ECF. The 3.5 L of plasma is a convention; many measured adult plasma volumes are lower, so do not derive a blood volume from it (blood cells and hemostasis).

People differ, mostly because of fat: lean tissue is roughly 73 percent water, adipose tissue little. The water fraction is about 75 percent of body mass in infants by one textbook estimate and can fall to about 45 percent in old age. The Institute of Medicine’s 2005 water report, citing earlier measurements, gives young-adult averages of about 59 percent for men and 50 percent for women, who carry more fat on average, with wide individual ranges. Treat 60 percent as the middle of a range.

A volume is a dose divided by a concentration

To size a tank you cannot see into, add a known amount of dye, let it mix and measure its concentration. Indicator dilution does this in a person:

V = (amount given - amount lost) / (equilibrated concentration - baseline concentration)

This assumes the marker mixes evenly through its space and no further, is not metabolized, and its urinary loss is measured. Each marker reports the space bounded by barriers it cannot cross. Heavy water (deuterium oxide) crosses capillary walls and cell membranes: TBW. Inulin or bromide crosses capillary walls but mostly not cell membranes: ECF. Evans blue, a dye that binds albumin, or labelled albumin stays mostly in the vessels: plasma. ICF and ISF have no marker of their own: ICF = TBW - ECF and ISF = ECF - plasma, and each subtraction inherits both errors.

These spaces are operational, not anatomical. Deuterium exchanges with hydrogen on proteins and other non-water molecules, so raw heavy-water space overestimates TBW, by about 4 percent in the usual correction. Albumin markers leak slowly out of plasma, so samples taken after mixing are extrapolated back to the time of injection.

A worked example, with invented numbers. An adult man receives 1.50 g of inulin; 0.10 g is in his urine by the time of sampling, and equilibrated plasma inulin is 0.100 g per L (baseline zero). ECF = (1.50 - 0.10) / 0.100 = 14.0 L. He receives 14 mg of Evans blue, and plasma concentration extrapolated back to injection time is 4.0 mg per L: plasma = 14 / 4.0 = 3.5 L. His raw heavy-water space is 43.7 L; dividing by an exchange factor of 1.04 gives TBW = 42.0 L. So ICF = 42.0 - 14.0 = 28.0 L and ISF = 14.0 - 3.5 = 10.5 L. Forget the inulin in urine and ECF comes out 15.0 L.

Osmolality counts particles; tonicity counts the ones that stay on one side

Osmoregulation defined osmolality: osmoles of dissolved particles per kilogram of water. Osmolarity is osmoles per litre of solution; plasma is about 93 percent water, so the two differ slightly. Laboratories measure osmolality by freezing-point depression. Each osmole per kilogram lowers the freezing point about 1.86 degrees C, so plasma at 290 mOsm per kg freezes near -0.54 degrees C. Adult plasma osmolality is typically about 275 to 295 mOsm per kg.

A common estimate is

Estimated osmolality (mOsm per kg) = 2 x [Na+] + glucose / 18 + BUN / 2.8

with sodium in mmol per L and glucose and blood urea nitrogen (BUN) in mg/dL. Doubling sodium counts its accompanying anions. Glucose / 18 converts mg/dL to mmol per L (molar mass 180). BUN counts only urea’s nitrogen, 28 g per mol, hence 2.8; for whole urea in mg/dL divide by 6. In mmol per L the estimate is 2[Na+] + glucose + urea. For sodium 140 mmol per L, glucose 90 mg/dL and BUN 14 mg/dL: 280 + 5 + 5 = 290 mOsm per kg.

Tonicity, or effective osmolality, counts only solutes that cannot cross the membrane in question over the time considered, because only those hold water on one side. Urea crosses most cell membranes and equilibrates, so it raises osmolality without moving water out of cells. Estimated tonicity is 2[Na+] + glucose / 18, here 285 mOsm per kg. Glucose is counted because, when insulin action is low, it enters cells such as muscle slowly.

The osmolal gap is measured osmolality minus estimated osmolality; a wide gap points to an unmeasured solute, such as an alcohol (not the anion gap of acid-base balance).

Water follows effective solute: what holds fluid in each compartment

Water crosses most cell membranes quickly (membrane transport), so at steady state ICF and ECF share one osmolality and each holds water in proportion to its effective osmoles. Picture two rooms joined by a door only water can pass: the guests stuck in each room decide how much water it holds.

Inside cells, the stuck guests are anions that cannot leave (proteins, nucleotides, organic phosphates) and the potassium that balances their charge. Outside, they are sodium with chloride and bicarbonate. Sodium leaks in, but the sodium-potassium pump moves it back out, so it behaves as if it could not enter: sodium salts are the ECF’s effective solute.

Across most capillaries outside the brain, small solutes cross freely and do not divide plasma from ISF; the blood-brain barrier is an exception. Plasma proteins, mainly albumin, cross slowly and exert a colloid osmotic (oncotic) pressure that holds fluid in the vessels against capillary blood pressure. Starling’s 1896 balance of these forces is in blood and vessels; the revised view, with the glycocalyx and slight net filtration in most tissues, is in capillary exchange and lymph.

If water follows effective solute, plasma sodium should report solute per water, not the body’s sodium stock. Isidore Edelman and colleagues tested this in San Francisco (1958) in 98 chronically ill adults chosen for variety (heart, liver, kidney, lung, gut, neurological and endocrine disease; 66 had edema), on an analyzed low-sodium diet. In most they measured exchangeable sodium (sodium-24 dilution), exchangeable potassium (potassium-42), TBW (heavy water, six-hour equilibration) and sodium per litre of serum water.

Earlier studies, including Moore’s, had found that body sodium did not predict serum sodium. Here too, serum sodium correlated poorly with exchangeable sodium, potassium or water per kilogram, or with sodium/water or potassium/water alone, and closely with the sum:

Serum-water [Na+] (mEq per L) = 1.11 x (Na_e + K_e) / TBW - 25.6, with r = 0.83

That fit passive water distribution in proportion to osmotically active solute, with cell potassium counting about as much as extracellular sodium. It confirmed that serum sodium is not a measure of body sodium: edematous patients with excess body sodium could be hyponatremic. Limits: it is a correlation in sick patients, not an intervention; exchangeable cation is not total cation (much bone sodium does not exchange); and the line is for serum-water sodium.

Predicting the shifts: infusions, losses and hyponatremia

Worked problem: where does the litre go?

These numbers are made up. A 70-kg reference man has ICF 28 L and ECF 14 L, both at an effective osmolality of 300 mOsm per kg (rounded; measured adult values are about 275 to 295). Assume a closed system (no urine, sweat or breath losses), free water movement across cell membranes, no solute gain or loss by cells, added sodium chloride staying outside cells, ideal behaviour, and 1 kg of water = 1 L. In separate trials he retains 1 L of (A) isotonic saline, 300 mOsm; (B) solute-free water, the model for 5% dextrose after its glucose is metabolized; or (C) sodium chloride at 900 mOsm per L (a model value).

  1. Count osmoles. ICF = 28 x 300 = 8,400 mOsm; ECF = 14 x 300 = 4,200 mOsm. Total water after each trial is 43 L.
  2. Final osmolality. C = (12,600 + added osmoles) / 43; then ICF = 8,400 / C and ECF = 43 - ICF.
  3. Trial A. C = 12,900 / 43 = 300 mOsm per kg. ICF stays 28.0 L; ECF becomes 15.0 L. With a 3:1 ISF-to-plasma split, plasma gains 0.25 L and ISF 0.75 L.
  4. Trial B. C = 12,600 / 43 = 293.0 mOsm per kg. ICF = 28.67 L (+0.67 L, two-thirds of the litre); ECF = 14.33 L (+0.33 L, of which plasma gains only about 0.08 L). Plasma sodium falls about in proportion: 140 x 42/43 = 136.7 mmol per L.
  5. Trial C. C = 13,500 / 43 = 313.95 mOsm per kg. ICF = 8,400 / 313.95 = 26.76 L (-1.24 L); ECF = 5,100 / 313.95 = 16.24 L (+2.24 L, more than the litre given). Plasma sodium follows sodium balance, (140 x 14 + 450 added) / 16.24, to about 148.4 mmol per L; scaling by osmolality would give 146.5, but the added salt raises sodium’s share of the particles. Splitting this gain between plasma and ISF needs an added assumption.
  6. Check. ICF + ECF = 43.00 L each time, and volume x C returns the osmoles (26.756 x 313.95 = 8,400).
Where does the litre go? Compartments after a retained load⚙ original · interactive
Marks:
Body water (a 70-kg body)
Where the solute goes, in this sketch
ECF (ISF + plasma), before → after
Final osmolality, all solutes (mOsm per kg)
Tonicity, effective osmolality (mOsm per kg)
Plasma sodium estimate (mmol per L)

In this sketch (all of this is made up for the sketch unless the lesson gives it): start at 300 mOsm per kg, the lesson’s rounded value (measured adult values are about 275 to 295), with plasma sodium 140 mmol per L; a 70-kg body, so total body water is the water fraction × 70 kg (60 percent gives the textbook 42 L; the 0.45 and 0.75 figures are the lesson’s textbook estimates for old age and infants); cells hold about two-thirds of body water; the ECF is about three-quarters ISF and one-quarter plasma (3:1), an added assumption that is also used to split any ECF gain; urea is treated as equilibrating across all water (the lesson works no urea load); 900 mOsm per L is a model value; ideal behaviour, 1 kg of water = 1 L; plasma sodium after a sodium chloride load is found by sodium balance, (140 × ECF before + sodium added) / ECF after, with sodium added = osmoles added / 2 (sodium chloride gives two osmoles per mole), and with urea it is a sketch estimate, 140 × effective osmolality / 300.

Closed model at equilibrium: no excretion, and cells gain or lose no solute (no cell solute adaptation).

Rule to keep: water crosses cell membranes freely, so each compartment ends up holding water in proportion to its effective osmoles. Only a solute that stays outside cells changes how a load divides between cells and ECF.

Equilibrium arithmetic predicts where a retained load goes, not how long it stays. Dileep Lobo and colleagues in Nottingham (2001) gave ten healthy men 2 L of 0.9% saline or 2 L of 5% dextrose over one hour on separate occasions, in a double-blind randomized crossover. The static model expects dextrose water to spread mostly into cells and saline to stay outside them. The kidneys added a time course: all the dextrose water had been excreted by two hours after the infusion ended, but only about one-third of the saline’s sodium and water by six hours. Serum albumin fell by about 20 percent after saline and 16 percent after dextrose, in both cases more than dilution alone explained, and bioimpedance seemed to track the infusate’s electrolyte content more than its volume. The study did not measure compartment volumes with dilution markers, and ten healthy men say little about women, older adults or illness.

In hypotonic hyponatremia from water retention (water, sodium and potassium covers the causes), let the reference man retain 3 L of solute-free water. C = 12,600 / 45 = 280 mOsm per kg; ICF = 8,400 / 280 = 30.0 L (+2.0 L, cells swell about 7 percent); ECF = 4,200 / 280 = 15.0 L (+1.0 L); plasma sodium falls to about 140 x 42/45 = 130.7 mmol per L. Body sodium did not fall; the ratio of cation to water did, the relation Edelman’s data describe. (His fitted line is for serum-water sodium and gives a somewhat different number from simple dilution.) Brain cells swell inside a rigid skull, so acute severe hyponatremia can cause dangerous cerebral edema. Over hours to days they lose potassium and chloride, then organic osmolytes more slowly, which limits swelling; that is why a fast rise in plasma sodium can then shrink the adapted cells.

Low sodium does not always mean swollen cells. With sodium 130 mmol per L, glucose 630 mg/dL and BUN 14 mg/dL, osmolality is 260 + 35 + 5 = 300 and tonicity 295 mOsm per kg: glucose has drawn water out of cells. Establish tonicity first.

Acute hemorrhage removes isotonic whole blood, so plasma sodium does not change at first and there is no net water shift across cell membranes. Over hours, as capillary pressure falls, ISF moves into plasma, so hematocrit falls later. Pure water loss shrinks both compartments, about two-thirds of the deficit coming from cells.

Design problem

You want to test, in healthy adult volunteers, whether 1 L of isotonic saline infused over 30 minutes ends up one-quarter in plasma and three-quarters in ISF, as a simple model that divides ECF by its reference volumes predicts, and how fast the kidney removes it. Design the measurements and say what each possible result would mean.

One way to do it

Use a crossover: each volunteer has an infusion session and a control session (no infusion or a tiny volume) in random order. Measure plasma volume with a plasma marker, such as labelled albumin or indocyanine green, before and at several times after the infusion, and ECF with bromide. Hemoglobin dilution also works if red-cell mass is assumed constant. Collect all urine for volume and sodium, so that retained = infused - excreted.

Predict first. At equilibrium with no excretion, plasma rises by about 0.25 L, from 3.5 to 3.75 L (a 7 percent albumin dilution if albumin stays in plasma), and ISF by about 0.75 L. A plasma gain near one-quarter of the retained volume supports the model; a larger gain may mean distribution is still under way or that vessels and tissues are not filling in proportion to their volumes, which the time course and the bromide space help separate.

Do not rely on albumin alone. For Lobo’s 2 L, with nothing excreted, the model predicts a 12.5 percent fall (3.5/4.0); he saw about 20 percent, which could mean the load had not yet left the plasma or that albumin itself left.

Limits: marker spaces are operational, markers leak, excretion overlaps distribution, and young healthy adults are not patients.

How we measure it

Indicator dilution

Give a known amount of a marker, let it mix, and measure its concentration in plasma. The amount retained divided by the concentration gives the volume of the space the marker reaches: heavy water for total body water, inulin or bromide for extracellular fluid, Evans blue or labelled albumin for plasma.

Radioisotope dilution of exchangeable cations

Inject sodium-24 or potassium-42, wait for it to exchange with the body's pool, and divide the retained dose by the plasma specific activity. The result is exchangeable sodium or potassium, the part of the body's store that mixes with the tracer in that time, which leaves out much of the sodium in bone.

Freezing-point osmometry

Measure how far below 0 degrees C a sample freezes. Each osmole per kilogram of water lowers the freezing point by about 1.86 degrees C, so the reading measures osmolality directly instead of estimating it from three analytes.

Bioelectrical impedance

Pass a small alternating current through the body and measure its resistance and reactance, from which fluid volumes are estimated. Because the reading depends on electrolyte content as well as volume, it can mislead after infusions of different fluids.

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Isidore S. Edelman

Isidore S. Edelman

With Leibman, O'Meara and Birkenfeld, measured exchangeable sodium, exchangeable potassium and total body water in a group of 98 patients and found that serum-water sodium tracked (exchangeable sodium + exchangeable potassium) / total body water, not body sodium alone.

By the 1950s, studies including Moore's had shown that serum sodium did not track body sodium, but what it did track was not established. Isidore Edelman, at the University of California School of Medicine and the San Francisco Hospital, asked what serum sodium does track, with J. Leibman, M. P. O'Meara and L. W. Birkenfeld. They studied 98 chronically ill adults chosen to differ as much as possible: heart disease, cirrhosis, kidney, lung, gut and neurological disease, and a few endocrine disorders, and 66 of them had edema. In most patients they measured exchangeable sodium with sodium-24, exchangeable potassium with potassium-42 and total body water with deuterium oxide, along with serum sodium per litre of serum water and serum osmotic concentration by freezing point. Serum sodium followed none of the single stores closely. It followed the sum of exchangeable sodium and potassium divided by body water, with a correlation coefficient of 0.83. The 1958 paper gave a quantitative reason to read plasma sodium as a ratio of cation to water, with cell potassium counting alongside extracellular sodium. Edelman's laboratory later studied how aldosterone acts on sodium transport.

✓ verbatim Edelman, Leibman, O'Meara and Birkenfeld, Interrelations between serum sodium concentration, serum osmolarity and total exchangeable sodium, total exchangeable potassium and total body water, Journal of Clinical Investigation 37:1236-1256 (1958).
Francis D. Moore

Francis D. Moore

A surgeon whose group, with Edelman among the co-authors, built isotope dilution methods for measuring total body water and exchangeable sodium and potassium in patients, and found that body stores of these ions did not correlate with their plasma concentrations.

Francis Moore was a surgeon, and surgical patients change their body composition quickly: they lose blood and gut fluid, stop eating and receive infusions. Around 1950 his group turned isotope dilution into a way of measuring the body's stores in living people. One 1950 paper, by Schloerb, Friis-Hansen, Edelman, Solomon and Moore, measured total body water in human subjects by deuterium oxide dilution and examined how the deuterium distributed. Another, by Corsa and colleagues with Moore, measured exchangeable potassium in people by isotope dilution. A 1954 series titled Body sodium and potassium, by Moore, Edelman and co-workers, reported in its third paper that in alimentary, renal and cardiovascular disease the body stores of these ions did not correlate with their plasma concentrations. Edelman's 1958 study, which cites that paper first, set out to find what plasma sodium does track. A 1963 monograph by Moore and colleagues, The Body Cell Mass and Its Supporting Environment, took up body composition in health and disease. Deuterium dilution remains a reference method for total body water.

✓ verbatim Schloerb, Friis-Hansen, Edelman, Solomon and Moore, The measurement of total body water in the human subject by deuterium oxide dilution, Journal of Clinical Investigation 29:1296 (1950); Moore, Edelman and colleagues, Body sodium and potassium III, Metabolism 3:334 (1954).
Daniel C. Darrow and Herman Yannet

Daniel C. Darrow and Herman Yannet

Changed the amount of extracellular electrolyte in dogs, rabbits and monkeys with little change in total body water, and concluded from blood changes that water moved into cells when extracellular salt fell and out of cells when it rose.

Darrow and Yannet, in the Department of Pediatrics at Yale University Medical School, set out to change the salt outside cells while leaving total body water nearly the same, and then see where the water went. They used the peritoneal cavity as an exchanger. A 5 percent glucose solution placed there gained sodium, chloride and bicarbonate from the blood while its glucose was absorbed; after four to six hours the fluid in the cavity was about the volume injected but resembled a fluid in equilibrium with plasma. The animal had temporarily lost extracellular electrolyte into the cavity fluid, and little water. To add salt they injected 1.8 percent sodium chloride instead. The animals were healthy dogs, rabbits and rhesus monkeys. After salt removal, serum sodium and chloride fell, serum protein and the proportion of red cells rose, and protein concentration inside red cells fell, as if water had left the extracellular fluid and entered cells. Adding salt did the reverse and produced few signs except thirst. The 1935 paper gave animal evidence, inferred from blood measurements, that extracellular electrolyte sets how water divides between cells and the fluid around them.

✓ verbatim Darrow and Yannet, The changes in the distribution of body water accompanying increase and decrease in extracellular electrolyte, Journal of Clinical Investigation 14:266-275 (1935).
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In the 70-kg reference man, how is intracellular fluid usually described?
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Simulations

  • Where does the litre go? · Original interactive — Biochemistrypedia (Deppmann Lab).

Scientist profiles & quotes

  • Isidore S. Edelman — Edelman, Leibman, O'Meara and Birkenfeld, Interrelations between serum sodium concentration, serum osmolarity and total exchangeable sodium, total exchangeable potassium and total body water, Journal of Clinical Investigation 37:1236-1256 (1958).
  • Francis D. Moore — Schloerb, Friis-Hansen, Edelman, Solomon and Moore, The measurement of total body water in the human subject by deuterium oxide dilution, Journal of Clinical Investigation 29:1296 (1950); Moore, Edelman and colleagues, Body sodium and potassium III, Metabolism 3:334 (1954).
  • Daniel C. Darrow and Herman Yannet — Darrow and Yannet, The changes in the distribution of body water accompanying increase and decrease in extracellular electrolyte, Journal of Clinical Investigation 14:266-275 (1935).

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Animated explainer

Water Goes Where the Solute Stays · narration: an AI narrator voice (ElevenLabs, Sarah) reading narration written from this lesson's text · animation: AI-generated in code (Manim) by Claude, a schematic with no drawn molecular structures, plots computed from their equations · captions from the narration script.

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Like I'm five

Most of your body is water. Most of that water is inside your cells, and the rest is outside them, partly in your blood. Water moves toward the side with more salt and sugar that cannot cross. Drink a lot of plain water and your cells puff up a little; eat a lot of salt and water moves out of your cells to the salty side.
High school

In a textbook adult man, about 60 percent of body mass is water, about 42 litres. Two-thirds is inside cells and one-third outside; of the outside part, about a quarter is blood plasma and the rest bathes the cells. Babies have a higher water fraction, and people with more fat a lower one. Scientists measure some spaces by adding a known amount of a tracer that reaches only that space and seeing how diluted it gets, and find the others by subtraction. Water crosses cell membranes freely, so it ends up wherever the dissolved particles that cannot cross are: sodium salts outside cells, potassium salts and proteins inside.
College

Reference values for a 70-kg man are TBW 42 L, ICF 28 L, ECF 14 L (ISF 10.5 L, plasma 3.5 L), a convention that varies with age, sex and adiposity. Compartments are measured by indicator dilution, V = (dose - loss) / (equilibrated concentration - baseline): deuterium oxide for TBW (corrected for about 4 percent nonaqueous exchange), inulin or bromide for ECF, Evans blue or labelled albumin for plasma, with ICF and ISF by subtraction. Osmolality is osmoles per kg water, estimated as 2[Na+] + glucose/18 + BUN/2.8 (sodium in mmol/L, glucose and BUN in mg/dL); tonicity leaves out urea. Because water equilibrates across cell membranes and the Na+/K+-ATPase makes sodium effectively impermeant, conservation of effective osmoles predicts the shifts: isotonic saline expands only ECF, solute-free water distributes two-thirds into cells, and hypertonic saline expands ECF by more than its volume at the expense of ICF.
Graduate

For a closed system with fixed intracellular osmoles, the final common osmolality after a load is C = (Osm_total + Osm_added) / (TBW + V), and ICF_final = Osm_ICF / C. Edelman and colleagues (1958) showed in 98 chronically ill patients that serum-water sodium = 1.11 x (Nae + Ke) / TBW - 25.6 (r = 0.83), consistent with passive water distribution in proportion to osmotically active solute and with nearly all exchangeable potassium being osmotically active; they read the intercept as osmotically inactive exchangeable cation, largely bone sodium. This is a correlation across patients, measured as exchangeable rather than total cation. Equilibrium arithmetic says where a retained load goes, not how long it is retained. In ten healthy men, Lobo and colleagues (2001) found the water from 2 L of 5% dextrose excreted within two hours of the infusion's end, but only about a third of 2 L of saline excreted by six hours. The open question is how well a two- or three-compartment model describes people in whom the parameters change: exchangeable cation that is not osmotically active, such as bone sodium, a glycocalyx-limited capillary barrier, and brain cells that shed osmolytes during sustained hyponatremia.
Osmolarity, measured as osmolality

Edelman's group estimated serum osmotic concentration by freezing-point depression with a thermistor probe, calibrated with sodium chloride standards. A footnote concedes that freezing-point depression actually measures osmolality, particles per kilogram of water. The authors used the word osmolarity anyway, explaining that the two are virtually equivalent at constant temperature and that osmolarity gave units comparable with their electrolyte data, which were per litre of serum water. The distinction still matters in the clinical laboratory: the osmometer reports per kilogram of water, and the estimating equation uses concentrations per litre.

— Edelman, Leibman, O'Meara and Birkenfeld, Journal of Clinical Investigation 37:1236-1256 (1958), methods section and footnote.
Sodium that does not count

Edelman's regression line did not pass through zero: its intercept was -25.6 mEq per L. The authors read this as exchangeable sodium and potassium that is not osmotically active. Body water in their patients averaged 36.1 L, so the inactive cation came to about 920 mEq, and they estimated that exchangeable bone sodium, about 750 mEq, probably accounts for almost all of it. That left less than 10 percent of exchangeable potassium unaccounted for, which they took to mean that almost all body potassium is osmotically active. It is an interpretation of an intercept, not a direct measurement.

— Edelman, Leibman, O'Meara and Birkenfeld, Journal of Clinical Investigation 37:1236-1256 (1958), discussion.
The simplest formula held up

Many equations estimate plasma osmolality from laboratory values. Worthley and colleagues measured osmolality in three groups of 100 people, normal subjects, general hospital patients and intensive care patients, and compared the measurements with five published equations. The simplest, 2[Na] + glucose + urea with all values in mmol per L, gave the smallest difference between calculated and measured values in these groups. That is a result for these populations and these assays, not a proof that the simple equation is always best.

— Worthley, Guerin and Pain, Anaesthesia and Intensive Care 15:199 (1987).

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