Key Clinical Formulas
Serum Osmolality: 2(Na) + Glucose/18 + BUN/2.8
Calculated Osm = 2(140) + 90/18 + 14/2.8 = 280+5+5 = 290
Calculated Osm = 2(140) + 90/18 + 14/2.8 = 280+5+5 = 290
Anion Gap: Na − (Cl + HCO₃) = 140 − (102 + 24) = 14 (normal 8-12)
Corrected Sodium (hyperglycemia):
Na⁺ corrected = Na⁺ measured + 1.6 × (Glucose − 100)/100
Na⁺ corrected = Na⁺ measured + 1.6 × (Glucose − 100)/100
Free T4 Index: T4 × T3 uptake (estimate of free T4)
TSH Log-Linear: TSH doubles/halves with each ~40% change in free T4
TSH Log-Linear: TSH doubles/halves with each ~40% change in free T4
Core Concepts
1. Hypothalamic-Pituitary Axis
Hypothalamus releases releasing/inhibiting hormones → anterior pituitary → tropic hormones → target glands → hormones. Negative feedback loops maintain homeostasis. Examples: TRH→TSH→T4/T3; CRH→ACTH→cortisol.
Hypothalamus releases releasing/inhibiting hormones → anterior pituitary → tropic hormones → target glands → hormones. Negative feedback loops maintain homeostasis. Examples: TRH→TSH→T4/T3; CRH→ACTH→cortisol.
2. Diabetes Mellitus
Type 1: autoimmune β-cell destruction → absolute insulin deficiency. Type 2: insulin resistance + relative deficiency. Diagnosis: HbA1c ≥6.5%, fasting glucose ≥126, OGTT ≥200, or random ≥200 with symptoms.
Type 1: autoimmune β-cell destruction → absolute insulin deficiency. Type 2: insulin resistance + relative deficiency. Diagnosis: HbA1c ≥6.5%, fasting glucose ≥126, OGTT ≥200, or random ≥200 with symptoms.
3. Thyroid Disorders
Hyperthyroidism: low TSH, high T4/T3. Graves' disease: TSH-receptor antibodies. Hypothyroidism: high TSH, low T4. Hashimoto's: autoimmune thyroiditis — most common in iodine-sufficient areas.
Hyperthyroidism: low TSH, high T4/T3. Graves' disease: TSH-receptor antibodies. Hypothyroidism: high TSH, low T4. Hashimoto's: autoimmune thyroiditis — most common in iodine-sufficient areas.
4. Adrenal Disorders
Cushing's: excess cortisol — moon face, buffalo hump, central obesity, striae. Addison's: adrenal insufficiency — fatigue, hyperpigmentation, hypotension. Pheochromocytoma: episodic hypertension, headache, sweating, palpitations.
Cushing's: excess cortisol — moon face, buffalo hump, central obesity, striae. Addison's: adrenal insufficiency — fatigue, hyperpigmentation, hypotension. Pheochromocytoma: episodic hypertension, headache, sweating, palpitations.
5. Calcium and Bone Metabolism
Parathyroid hormone (PTH) raises calcium: bone resorption, renal reabsorption, vitamin D activation. Calcitonin (thyroid C cells) lowers calcium. Hypercalcemia: stones, bones, groans, psychiatric overtones.
Parathyroid hormone (PTH) raises calcium: bone resorption, renal reabsorption, vitamin D activation. Calcitonin (thyroid C cells) lowers calcium. Hypercalcemia: stones, bones, groans, psychiatric overtones.
Core Definitions
Hormone: A chemical messenger secreted by endocrine glands into the bloodstream, acting on distant target cells via specific receptors. Types: peptides (insulin), steroids (cortisol), amines (thyroxine, epinephrine).
Negative Feedback: The output of a system inhibits its own production. Example: high T4 inhibits TRH and TSH → T4 production decreases. Maintains hormonal homeostasis.
Diabetic Ketoacidosis (DKA): Hyperglycemia (>250), ketonemia, metabolic acidosis (pH <7.3, HCO₃ <18). Treatment: IV fluids, insulin drip, potassium replacement, treat underlying trigger (infection common).
Myxedema Coma: Severe hypothyroidism with altered mental status, hypothermia, hypoventilation, hypotension. Medical emergency — IV thyroid hormone, corticosteroids, supportive care. Mortality 30-50%.
Worked Examples
Example 1: Corrected Sodium
Measured Na⁺ = 132, glucose = 500. Correction: Na⁺ = 132 + 1.6 × (500−100)/100 = 132 + 6.4 = 138.4 mEq/L. Hyponatremia is dilutional — resolves with glucose control.
Measured Na⁺ = 132, glucose = 500. Correction: Na⁺ = 132 + 1.6 × (500−100)/100 = 132 + 6.4 = 138.4 mEq/L. Hyponatremia is dilutional — resolves with glucose control.
Example 2: TSH Interpretation
TSH = 8.0 (high), Free T4 = 0.6 (low) → primary hypothyroidism (thyroid failure). TSH = 0.01 (low), Free T4 = 3.0 (high) → primary hyperthyroidism. TSH = 0.5 (low-normal), Free T4 = 2.5 (high) → secondary (pituitary) hyperthyroidism.
TSH = 8.0 (high), Free T4 = 0.6 (low) → primary hypothyroidism (thyroid failure). TSH = 0.01 (low), Free T4 = 3.0 (high) → primary hyperthyroidism. TSH = 0.5 (low-normal), Free T4 = 2.5 (high) → secondary (pituitary) hyperthyroidism.
Example 3: HbA1c to Average Glucose
ADAG formula: eAG (mg/dL) = 28.7 × HbA1c − 46.7. HbA1c 7% → 28.7 × 7 − 46.7 = 154 mg/dL. HbA1c 8% → 183 mg/dL.
ADAG formula: eAG (mg/dL) = 28.7 × HbA1c − 46.7. HbA1c 7% → 28.7 × 7 − 46.7 = 154 mg/dL. HbA1c 8% → 183 mg/dL.
Practice Problems
Problem 1: Calculate corrected sodium for Na⁺=128, glucose=600.
Answer: 128 + 1.6 × (500)/100 = 128 + 8 = 136 mEq/L — pseudohyponatremia
Answer: 128 + 1.6 × (500)/100 = 128 + 8 = 136 mEq/L — pseudohyponatremia
Problem 2: A patient has TSH 12, Free T4 0.5. What is the diagnosis?
Answer: Primary hypothyroidism. The thyroid is failing (low T4), so the pituitary compensates by producing excess TSH.
Answer: Primary hypothyroidism. The thyroid is failing (low T4), so the pituitary compensates by producing excess TSH.
Problem 3: What are the diagnostic criteria for diabetes mellitus?
Answer: Any one: HbA1c ≥6.5%, fasting plasma glucose ≥126 mg/dL, OGTT 2-hour ≥200 mg/dL, or random glucose ≥200 with classic symptoms.
Answer: Any one: HbA1c ≥6.5%, fasting plasma glucose ≥126 mg/dL, OGTT 2-hour ≥200 mg/dL, or random glucose ≥200 with classic symptoms.
Problem 4: Differentiate primary from secondary adrenal insufficiency.
Answer: Primary (Addison's): high ACTH, hyperpigmentation, hyperkalemia, hyponatremia. Secondary (pituitary): low ACTH, no hyperpigmentation, normal potassium (aldosterone preserved via RAAS).
Answer: Primary (Addison's): high ACTH, hyperpigmentation, hyperkalemia, hyponatremia. Secondary (pituitary): low ACTH, no hyperpigmentation, normal potassium (aldosterone preserved via RAAS).
Problem 5: What is the anion gap and what does an elevated gap indicate?
Answer: AG = Na − (Cl + HCO₃). Normal 8-12. Elevated suggests unmeasured anions: lactate, ketones, toxic alcohols (methanol, ethylene glycol), uremia, or salicylates.
Answer: AG = Na − (Cl + HCO₃). Normal 8-12. Elevated suggests unmeasured anions: lactate, ketones, toxic alcohols (methanol, ethylene glycol), uremia, or salicylates.