Formulas
Na+ (corrected for hyperglycemia):
Corrected Na+ = measured Na+ + [(glucose – 100) x 0.024].
Ca++ (corrected for hypoalbuminemia):
Corrected Ca++ = [(4 – serum albumin) x 0.8] + measured Ca++.
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].
DAG = (AG – 12) + HC03 {normal 23–30}.
DAG >30: concomitant metabolic alkalosis (excessively high HCO3).
DAG <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 HCO3 loss (RTA).
Hillier TA, Abbott RD, Barrett EJ. Hyponatremia: evaluating the correction factor for hyperglycemia. Am J Med. 1999 Apr;106(4):399-403.
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) Intracellular fluid (ICF) = 0.4 x wt (kg)
Intravascular Interstitial
1/3 ECF 2/3 ECF
IVF and tonicity:
|
Fluid |
Na+ (mEq/L) |
K+ (mEq/L) |
Cl- (mEq/L) |
HCO3 (mEq/L) |
Other (mEq/L) |
Osmolality (mOsm/L) |
|
Plasma |
142 |
4 |
104 |
27 |
29 |
306 |
|
NS |
154 |
- |
154 |
- |
- |
308 |
|
D5W |
- |
- |
- |
- |
- |
278 |
|
D5 ½NS |
77 |
- |
77 |
- |
- |
421 |
|
1 amp NaHCO3 |
50 |
- |
- |
50 |
- |
100 |
|
20 mEq KCl |
- |
20 |
20 |
- |
- |
40 |
e.g. ¼NS + 20 mEq KCl + ½ amp NaHCO3 = (308/4) + 40 + (100/2) = 167 mOsm/L, or roughly equivalent in tonicity to ½NS
IVF effect on plasma Na:
DNa per liter IVF given = NaIVF(mEq/l) + KIVF(mEq/l) – Naserum (mmol/l)
Total Body Water + 1
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.
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**
* VO2 can be measured or estimated by 125 ml/min/m2 x BSA (in m2)
** AV O2 diff = 13.4 x hemoglobin (g/dl) x [SaO2(%) – SvO2(%)]
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
Alveolar-arterial O2 gradient:
A–a O2 gradient = [FiO2 x (pAtm – pH2O)] – (pCO2 / R) – pO2 {normal 5–25 or age/3}
= [FiO2 x (760 – 47)] – (pCO2 / 0.8) – pO2
= 150 – (pCO2 / 0.8) – pO2 *at sea level on RA
|
|
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)