Appendix A_ Formulas

Electrolytes 

Na+ (corrected for hyperglycemia): 

  • Corrected Na+ = measured Na+ + [(glucose – 100) x 0.024] 

Ca2+ (corrected for hypoalbuminemia): 

  • Corrected Ca2+ = [(4 – serum albumin) x 0.8] + measured Ca2+ 

Free Water Deficit: 

  • Water deficit = wt (kg) x k x [(plasma Na+ / 140) – 1]; where k = 0.5 for males and 0.4 for females 

Osmolality: 

  • Calculated Osm = (2 x Na+) + (glucose / 18) + (BUN / 2.8) + (EtOH / 4.6)  

  • normal: 270–290 

  • Osm gap = measured Osm – calculated Osm {normal < 10} 

  • >10 is abnormal: caused by renal failure, methanol, ethylene glycol, sorbitol, mannitol, isopropanol, radiocontrast dye 

Anion Gaps: 

  • Serum AG = [Na+] – [Cl-] – [HCO3] {normal 10-14} 

  • Corrected AG (for hypoalbuminemia) 

  • Corrected AG = serum AG + [(4 – serum albumin) x 2.5] 

  • ∆AG = (AG – 12) + HCO3 {normal 23–30}. 

  • ∆AG >30: concomitant metabolic alkalosis (excessively high HCO3). 

  • ∆AG <23: concomitant non-AG metabolic acidosis (excessively low HCO3). 

  • Urine AG = U[Na+] + U[K+] – U[Cl-] 

  • NH4+ is the major unmeasured cation, so a strongly negative UAG suggests high urine NH4+. 

  • Urine AG <0: GI HCO3 loss. 

  • Urine AG >0: Renal HCO3loss (RTA). 

Body Fluid / IV Fluids 

Body fluid composition: 

  • Total Body Water = 0.6 x wt (kg) for males 0.5 x wt (kg) for females 

  • Extracellular fluid (ECF) = 0.2 x wt (kg) 

  • Intravascular: 1/3 ECF  

  • Interstitial: 2/3 ECF 

  • Intracellular fluid (ICF) = 0.4 x wt (kg) 

IVF and tonicity: 

 

 

 

 

 

 

 

 

Plasma 

142 

4 

104 

27 

29 

306 

NS 

154 

- 

154 

- 

- 

308 

D5W 

- 

- 

- 

- 

- 

278 

D5 1⁄2NS 

77 

- 

77 

- 

- 

421 

1 amp NaHCO3 

50 

- 

- 

50 

- 

100 

20 mEq KCl 

- 

20 

20 

- 

- 

40 

  • e.g. 1⁄4NS + 20 mEq KCl + 1⁄2 amp NaHCO3 = (308/4) + 40 + (100/2) = 167 mOsm/L, or roughly equivalent in tonicity to 1⁄2NS 

IVF effect on plasma Na: 

  • ∆Na per liter IVF given = [NaIVF(mEq/l) + KIVF(mEq/l) – Naserum (mmol/l)] / [Total Body Water + 1] 

Renal 

Creatinine Clearance: 

  • Estimated CrCl (Cockcroft-Gault Equation)* = [(140 – age) x (wt in kg)] / [serum Cr x 72] 

  • *multiply by 0.85 for females 

  • {normal 100–125 ml/min (M) or 85–105 ml/min (F)} 

  • Measured CrCl = [urine Cr x urine volume (ml/24hr)] / [serum Cr x 1440 (min/24hr)] 

Fraction Na excretion: 

  • FENa = [(urine Na+ / serum Na+) x 100] / [(urine Cr / serum Cr)] 

  • <1% suggests pre-renal 

  • FENa interpretable only in oliguric states (UOP < 400 cc/day) 

Transtubular Potassium Gradient: 

  • TTKG = (urine K+ / serum K+) / (urine Osm / serum Osm) 

  • With hyperkalemia: 

  • < 7 suggestive decreased aldosterone activity. 

  • > 7 suggestive effective volume depletion with normal aldosterone activity.  

Hemodynamics 

Cardiac Output: 

  • CO = HR x stroke volume 

  • CI = CO / BSA (in m2); where BSA= √([ht (cm) x wt (kg)] / 3600) 

  • Fick Technique: CO estimated O2 consumption or VO2 (ml/min)* / arteriovenous O2 difference**  

Resistance: 

  • SVR = [(MAP – CVP) / CO] x 80  

  • {normal 700–1600 dynes*s/cm5} 

  • PVR = [(MPAP – PCWP) / CO] x 80  

  • {normal 20–120 dynes*s/cm5} 

Pressure: 

  • Pulse Pressure = SBP – DBP 

  • MAP = [SBP + (DBP x 2)] / 3 

Pulmonary 

Alveolar-arterial O2 gradient: 

  • A–a O2 gradient = [FiO2 x (pAtm – pH2O)] – (pCO2 / R) – pO2 

  • = [FiO2 x (760 – 47)] – (pCO2 / 0.8) – pO2 

  • = 150 – (pCO2 / 0.8) – pO2 

  • {normal 5–25 or age/3} *at sea level on RA 

Statistics 

 

 

Disease (+) 

Disease (–) 

Test (+)  

A True Positive 

B False Positive  

Test (–)  

C False Negative  

D True Negative  

  • Sensitivity = A / (A + C) 

  • Specificity = D / (D + B) 

  • Positive Predictive Value = A / (A + B) 

  • Negative Predictive Value = D / (C + D) 

  • Positive Likelihood Ratio = sensitivity / (1 – specificity)  

  • Negative Likelihood Ratio = (1 – sensitivity) / specificity  

  • Number needed to treat (NNT) = 1 / (absolute risk reduction)