Calculations

These formulas are vital for assessing fluid and electrolyte balance, as well as identifying underlying metabolic disturbances

Osmolality

Definition: A measure of the concentration of solute particles in a solution. It reflects the number of dissolved particles per kilogram of solvent (water)
Units: milliosmoles per kilogram (mOsm/kg) or millimoles per kilogram (mmol/kg)
Measured Osmolality: Determined using an osmometer, which measures colligative properties of the solution (e.g., freezing point depression or vapor pressure depression)
Calculated Osmolality: Estimated from the concentrations of major solutes in the plasma
Osmolal Gap: The difference between measured osmolality and calculated osmolality. An elevated osmolal gap suggests the presence of unmeasured osmotically active substances in the plasma

Calculation of Osmolality

Formula
- \(Osmolality (mOsm/kg) = 2[Na^+] + \left( \frac {[Glucose (mg/dL)]} {18} \right) + \left( \frac {[BUN (mg/dL)]} {2.8} \right)\)
- Where:
  - [\(Na^+\)] = Sodium concentration in mmol/L
  - [\(Glucose\)] = Glucose concentration in mg/dL
  - [\(BUN\)] = Blood urea nitrogen concentration in mg/dL
  - 18 = Conversion factor for glucose (mg/dL to mmol/L)
  - 2.8 = Conversion factor for BUN (mg/dL to mmol/L)
SI Units
- \(Osmolality (mmol/kg) = 2[Na^+] + [Glucose] + [Urea]\)
- Where:
  - [\(Na^+\)] = Sodium concentration in mmol/L
  - [\(Glucose\)] = Glucose concentration in mmol/L
  - [\(Urea\)] = Urea concentration in mmol/L
Normal Range
- 275-295 mOsm/kg
- Most contributions to the measured serum osmolality comes from sodium, chloride, potassium, urea, and glucose

Clinical Significance of Osmolality

Assessment of Hydration Status: Osmolality reflects the balance between water and solutes in the blood
Evaluation of Kidney Function: Osmolality can be used to assess the kidney’s ability to concentrate or dilute urine
Diagnosis of Electrolyte Imbalances: Changes in osmolality can indicate electrolyte disorders
Detection of Toxic Substances: An elevated osmolal gap can suggest the presence of unmeasured osmotically active substances (e.g., ethanol, methanol, ethylene glycol)

Increased Osmolality

Causes
- Dehydration: Water deficit leads to increased solute concentration
- Hypernatremia: Elevated sodium levels
- Hyperglycemia: Elevated glucose levels (e.g., in diabetes)
- Uremia: Elevated BUN levels (e.g., in kidney failure)
- Toxic Ingestions: Presence of unmeasured osmotically active substances (e.g., ethanol, methanol, ethylene glycol)
Symptoms
- Thirst, confusion, lethargy, seizures, coma

Decreased Osmolality

Causes
- Overhydration: Water excess leads to decreased solute concentration
- Hyponatremia: Low sodium levels
- SIADH (Syndrome of Inappropriate Antidiuretic Hormone Secretion): Excessive ADH leads to water retention
- Adrenal Insufficiency: Impaired cortisol production affects water and electrolyte balance
Symptoms
- Nausea, headache, confusion, muscle cramps, seizures, coma

Increased Osmolal Gap

Causes
- Presence of unmeasured osmotically active substances:
  - Ethanol
  - Methanol
  - Ethylene Glycol
  - Isopropanol
  - Propylene Glycol
  - Acetone
- Less Common Causes:
  - Mannitol
  - Glycerol
  - Severe Hyperlipidemia or Hyperproteinemia
  - Lactic Acidosis

Anion Gap

Definition: The difference between measured cations (positively charged ions) and anions (negatively charged ions) in serum or plasma. It is used to assess acid-base balance, particularly in cases of metabolic acidosis
Purpose: The anion gap helps identify the cause of metabolic acidosis by distinguishing between conditions that increase unmeasured anions and those that result in a loss of bicarbonate
Measured Ions
- Cations: Sodium (\(Na^+\)) and Potassium (\(K^+\))
- Anions: Chloride (\(Cl^-\)) and Bicarbonate (\(HCO_3^-\))

Calculation of Anion Gap

Formula
- Anion Gap = (\(Na^+\) + \(K^+\)) - (\(Cl^-\) + \(HCO_3^-\))
- Anion Gap = \(Na^+\) - (\(Cl^-\) + \(HCO_3^-\)) (when potassium is not measured)
Normal Range
- With Potassium: 8-16 mEq/L or mmol/L
- Without Potassium: 10-20 mEq/L or mmol/L

Clinical Significance of Anion Gap

Normal Anion Gap Metabolic Acidosis (NAGMA)
- Also known as hyperchloremic metabolic acidosis
- The decrease in bicarbonate is compensated by an increase in chloride, maintaining a normal anion gap
- Causes:
  - Gastrointestinal Bicarbonate Loss: Diarrhea, ileostomy
  - Renal Tubular Acidosis (RTA): Impaired reabsorption of bicarbonate or impaired excretion of acid by the kidneys
  - Administration of Chloride-Containing Solutions: Saline infusion
  - Certain Medications: Acetazolamide, cholestyramine
Elevated Anion Gap Metabolic Acidosis (HAGMA)
- The decrease in bicarbonate is accompanied by an increase in unmeasured anions, resulting in an elevated anion gap
- Causes:
  - Ketoacidosis: Diabetic ketoacidosis (DKA), alcoholic ketoacidosis, starvation ketoacidosis
  - Lactic Acidosis: Anaerobic metabolism due to shock, sepsis, or severe exercise
  - Renal Failure: Accumulation of sulfates, phosphates, and other organic acids
  - Toxic Ingestions:
    - Methanol: Metabolized to formic acid
    - Ethylene Glycol: Metabolized to glycolic acid and oxalic acid
    - Salicylates: Disrupts cellular metabolism
- Mnemonic for High Anion Gap Acidosis: “MUDPILES”
  - M: Methanol
  - U: Uremia (Renal Failure)
  - D: Diabetic Ketoacidosis
  - P: Propylene Glycol
  - I: Iron, Isoniazid
  - L: Lactic Acidosis
  - E: Ethylene Glycol
  - S: Salicylates
Decreased Anion Gap
- Rare and typically less clinically significant
- Causes:
  - Hypoalbuminemia: Albumin is a major unmeasured anion, so decreased albumin levels can lower the anion gap
  - Multiple Myeloma: Increased levels of cationic immunoglobulins
  - Bromide Intoxication: Bromide is measured as chloride, leading to an artificially elevated chloride level and a decreased anion gap
  - Lithium Toxicity: Causes \(Cl^-\) retention

Key Terms

Osmolality: Concentration of solute particles in a solution
Osmolal Gap: Difference between measured and calculated osmolality
Anion Gap: Difference between measured cations and anions in serum
Measured Cations: Sodium and Potassium
Measured Anions: Chloride and Bicarbonate
Hypoalbuminemia: Abnormally low levels of protein in the blood
Multiple Myeloma: A cancer of plasma cells
Bromide Intoxication: A condition where a person has ingested a toxic amount of bromide
Normal Saline: Normal Saline (or Saline) is a mixture of sodium chloride (salt) in water. It is used for rinsing wounds, nasal passages, and contact lenses. Intravenous normal saline can be used for fluid replacement in a number of conditions, such as dehydration, hypovolemia, and sepsis
Ischemia: An inadequate blood supply to an organ or part of the body
Hypoxia: An inadequate oxygen supply to the cells and tissues of the body
Hypercapnia: The presence of abnormally high levels of carbon dioxide in the blood
Hypoventilation: The state in which a reduced amount of air enters the lungs
Hyperventilation: The state of breathing too fast or too deeply
Paresthesias: An abnormal sensation, typically tingling or pricking (“pins and needles”), caused chiefly by pressure on or damage to peripheral nerves
Carpopedal Spasm: Cramps in the hands and feet
Enzyme: A substance produced by a living organism which acts as a catalyst to bring about a specific biochemical reaction
In Vitro: Taking place in a test tube, culture dish, or elsewhere outside a living organism
In Vivo: Occurring within a living organism
Homeostasis: The process by which organisms maintain a relatively stable internal environment
Electrolyte: An ion that conducts electrical impulses in solution

Precautions

Result Interpretation