How To Calculate Plasma Osmolarity

Plasma osmolarity, or more often in clinical reporting its close counterpart plasma osmolality, is a measure of the tendency of the blood plasma to attract water as a result of certain components floating it its substance to act as osmoles, a concept you'll be "sucked into" in a moment.

You probably think of blood primarily as a transport fluid, bringing needed fuels, gases, hormones and sometimes drugs to their target locations and cells in the body. Blood is also collecting waste products from those same places to be exhaled as gas molecules by the lungs or excreted in urine. But blood itself, in particular the watery fluid component called plasma, is sensitive in its own right to chemical changes, in particular osmolarity.

• Osmolarity is millimoles of solute per liter of solvent (mmol/L); osmolality is moles of solute per kilogram of solvent (mmol/kg). Since 1 L H₂O is very close to 1 kg, with the relationship varying almost imperceptibly with temperature, the terms are for all practical purposes equivalent.

When a substance enters plasma, it increases the concentration of matter in that plasma. As a result, the plasma "seeks" to return the value of osmolarity to its equilibrium value, which is in the range of 275 to 295 mmol/L in humans.

It can do this either by increasing the amount of water in plasma or by excreting the molecules and matter contributing to the increased concentration of solutes in plasma; more on these processes shortly.

The main contributors to serum osmolality are sodium ions (Na⁺), blood glucose (C₆H₁₂O₆) and blood urea nitrogen (abbreviated BUN). As you will see from the formula for plasma osmolality, sodium levels are the overwhelming determinant of the value of osmolality, and very low sodium levels, or hyponatremia, can be fatal if not corrected in a timely manner.

There are a number of formulas in circulation for calculating plasma osmolality, but the most common is probably the Dorwart and Chalmers formula:

• Serum osmolality = 1.86(Na⁺) + (glu)/18 + (BUN)/2.8 

Input values are in milligrams per deciliter (mg/dL), and the formula converts the output to mmol/L. The coefficient before the sodium level accounts for the fact that Na+ ions are accompanied by chloride and bicarbonate anions (not included separately in the formula) that are needed to maintain a neutral electrochemical environment.

The denominators in the glucose and BUN terms adjust for the molar masses (mg, g, kg, etc. per mole) of the relevant substances.

Example: A patient is admitted with a sodium level of 140 mmol/dL, a glucose level of 360 mg/dL and a BUN of 5.6. What is the patient's serum osmolality?

Serum osmolality = 1.86(140) + (360)/18 + (5.6)/2.8 = 260.4 + 20 + 2 = 282.4 mmol/L

This level is in the normal range in spite of a very high glucose value (normally about 70 to100 mg/dL).

Clearly, if you drink more water than leaves your body in the form of urine, sweat and other losses, your plasma osmolality should drop because your blood will become more dilute. But what triggers this to occur?

Usually, the pituitary gland in the base of the brain releases a hormone called vasopressin or antidiuretic hormone (ADH) in response to high plasma osmolality, triggering thirst and fluid retention by the kidneys; low osmolality leads to low ADH, lower levels of thirst and high urine output (diuresis).

Other hormones exert their functions elsewhere, including, most vitally, at the kidneys, the paired abdominal organs that filter the body's blood supply.

The renin-angiotensin-aldosterone (RAS) "cascade" of hormones can greatly influence how much water and what amount of each electrolyte (e.g., sodium, potassium) should be spared excretion. This allows the body to compensate for disruptions to the osmotic internal equilibrium very quickly.

See the Resources for a fun tool that allows you to experiment with the factors that influence serum osmolality and how a medical professional might proceed in a given situation faced with a set of abnormal lab results.