CHAPTER 4: Calculations

PAO₂ = Alveolar partial pressure of O₂ [mm Hg]

PaO₂ = Arterial partial pressure of O₂ [mm Hg]

FiO₂ = Fraction of inspired O₂ (0.21 in room air)

P_atm = Atmospheric pressure (about 760 mm Hg at sea level)

$P H 2 O$ = Partial pressure of water vapor (about 47 mm Hg at 37°C)

PaCO₂ = Arterial partial pressure of CO₂ [mm Hg]

R = Respiratory quotient, reflecting basal metabolic rate describing amount of CO₂ production for a given O₂ consumption (ranges from 0.7 to 1; usually 0.8 is used)

• Measure of the efficiency of the oxygenation of blood

• The normal A-a gradient varies with age. A helpful calculation is [age(years)+10]/4

• Normal A-a gradient ranges from 7 to 14 mm Hg when breathing room air; 20–65 mm Hg when on 100% O₂. As the gradient value increases, it is reflective of a worsening condition

• Gradient is affected by ventilation/perfusion (V/Q) or diffusion abnormalities but unaffected by hyper- or hypoventilation

• If PaO₂ corrects with supplemental O₂, consider asthma or other conditions associated with V/Q mismatch

• If PaO₂ does not correct with supplemental O₂, consider shunt

WBC = White blood cell count [cells/mm³]

Polys = Percentage of polymorphonuclear neutrophils

Bands = Percentage of band forms

• Neutropenia generally defined as an ANC less than 1500 cells/mm³

• Severe neutropenia (ANC <500 cells/mm³) is associated with a high risk of infection

AG = Anion Gap

[Na⁺] = Serum concentration of sodium ions [mEq/L]

[Cl⁻] = Serum concentration of chloride ions [mEq/L]

$[ HCO 3 − ]$ = Serum concentration of bicarbonate ions [mEq/L]

• Aids in classifying metabolic acidosis

• Normal anion gap is 8–12 mEq/L

• Elevated anion gap is caused by an increase in unmeasured anions which may be any of the following:

  • “MUD PILES”: M ethanol; U remia; D iabetic ketoacidosis; P araldehyde or P henformin; I ron, I nfection, or I NH; L actic acidosis; E thanol or E thylene glycol; and S alicylates

• Acidosis with a normal anion gap (“non-anion gap acidosis”) is generally caused by a loss of $HCO 3 −$ which can be associated with multiple causes, including the following:

  • “HARD-UP”: H yperalimentation; A cetazolamide; R enal tubular acidosis; D iarrhea; U reteroenteric fistula; P ancreaticoduodenal fistula

Note: Hypoalbuminemia leads to underestimation of the AG and requires the following correction: Corrected AG=AG+0.25(40−Alb)

Hb: Hemoglobin concentration [g/dL]

SaO₂: Saturation of hemoglobin with oxygen [0.99%]

PaO₂: Arterial partial pressure of O₂ [mm Hg]

(1 g Hb can carry 1.36 mL of oxygen [mL/g])

0.0031: Oxygen solubility coefficient [O₂/dL/mm Hg]

• Directly reflects the total number of oxygen molecules in the arterial blood, both bound and unbound to hemoglobin

• The SaO₂, or Pulse oximetry, is reflective of the oxygen bound by hemoglobin

• Note that the contribution of dissolved oxygen (as reflected in the latter portion of the equation [0.0031 × PaO₂]) is very small

• Normal CaO₂ range: 17–24 mL/dL

• Prevalence: Proportion of people with disease in an entire population

  {(TP + FN)/(TP + FP + FN + TN)}

  Remember that “incidence” is the number of new cases in a time frame (often a year) and prevalence is the number of people with disease in the total population at any one time

• Sensitivity: Proportion of people with disease who will have a positive result

  • ✓ Sens = {TP/(TP+FN)}

• Specificity: Proportion of people without the disease who will have a negative result

  • ✓ Spec = {TN/(FP+TN)}

• Positive predictive value (PPV): Proportion of people with a positive test result who actually have the disease

  • ✓ PPV = {TP/(TP+FP)}

• Negative predictive value (NPV): Proportion of people with a negative test result who do not have disease

  • ✓ NPV = {TN/(FN+TN)}

• Odds ratio (OR): Evaluates whether the odds of a certain event or outcome is the same for two groups

  • ✓ OR= (TP×TN)/(FN×FP)

• Relative risk reduction (RRR): Measures how much the risk (rate of some outcome) is reduced in the experimental group compared to the control group

  • ✓ RRR=CER−EER/CER where CER is the control group event rate and EER is the experimental event rate

• Absolute risk reduction (ARR): The difference on outcome rates between the control and the treatment groups

  • ✓ ARR=CER−EER

• Number needed to treat (NNT): The number of patients that would need to be treated to prevent one bad outcome

  • ✓ NNT = 1/ARR or 1/(CER−EER)

• Likelihood ratio for a test result is defined as the ratio between the probability of observing that result in patients with the disease in question, and the probability of that result in patients without the disease

Weight [kg]

Height [m]

• Adult values: Normal is 18–25; overweight is 25–30; obese is greater than 30

• Pediatric norms vary by age and according to growth charts

Body Surface Area [m²]

Weight [kg]

Height [cm] (notice difference from BMI calculation which is in meters)

• Used to calculate dosages for certain medications (e.g., steroids, chemotherapeutic agents)

• Other formulas for BSA have been derived (Boyd, Dubois, and Haycock)

or

CPP: Cerebral perfusion pressure [mm Hg]

CVP: Central venous pressure (direct measure) [mm Hg]

MAP: Mean arterial pressure (calculated or direct measure) [mm Hg]

ICP: Intracranial pressure (direct measure) [mm Hg]

• Maintenance of CPP reduces mortality after severe brain injury

• ICP monitoring is recommended in most comatose patients with severe head injury and is considered a central part of critical care management

• A CPP>60 mm Hg and ICP<20 are desired for patients recovering from a brain injury. Note that in a hypotensive patient even small increases in ICP can be detrimental

• MAP can be calculated by doubling the diastolic blood pressure and then adding it to the systolic blood pressure and dividing that sum by 3 (see MAP calculation)

• If the CPP gets too low, then the brain may not get enough oxygen and the patient can suffer hypoxic brain injury

Infusate Na⁺: Amount of sodium in infusion [mmol/L]

Infusate K⁺: Amount of potassium in infusion [mmol/L]

Serum Na⁺: Serum sodium [mmol]

TBW: Total body water (Liters)

• Calculation of change in serum sodium helps predict sodium changes associated with a given infusion. May be used to limit the risk of demyelinating encephalopathy due to rapid correction of hypo- or hypernatremia

Degrees Fahrenheit = 1.8 × degrees Celsius + 32

1 inch = 2.54 centimeters (cm)

1 teaspoon = 5 milliliters (mL)

1 tablespoon = 15 milliliters (mL)

1 fluid ounce = 30 milliliters (mL)

1 deciliter (dL) = 0.1 liter (L)

1 dry ounce = 30 grams (g)

1 atmosphere = 760 mm Hg = 760 torr (1 torr = 1 mm Hg)

2.2 pounds = 1 kilogram (kg)

1 milligram (mg) = 0.001 gram (g)

1 microgram (mcg or µg) = 0.001 milligrams (mg)

$QT c =QT/√RR$

QT = Measured QT interval [seconds]

RR = Preceding RR interval [seconds]

1 box width = 0.04 seconds (when paper runs at 25 mm/sec)

• QT_c > 0.44 seconds is concerning for long QT syndrome

• Certain electrolyte abnormalities and medications may increase the QT_c

ALB_n = Normal plasma alb = 4.0 g/dL

ALB_p = Measured plasma alb [g/dL]

Ca_p = Measured plasma calcium concentration [ mg/dL]

• Corrects the measured plasma calcium concentration for hypoalbuminemia

• Measuring an ionized calcium level may be more accurate

$Na p +$ = Plasma sodium concentration [mmol/L]

GL_p = Measured plasma glucose concentration [mmol/L]

CrCl = Creatinine clearance [mL/min]

Corrected CrCl = Corrected to a body surface area of 1.73 m² [mL/min/1.73 m²]

U_Cr = Urine creatinine [ mg/dL]

U_vol = Urine volume [mL]

P_Cr = Plasma creatinine concentration [ mg/dL]

T_min = Time of urine collection [minutes]

• Represents the volume of plasma cleared of creatinine per unit time

• Creatinine is freely filtered, not reabsorbed, and minimally secreted by the kidneys. Thus, creatinine clearance is an estimate of glomerular filtration

• Clearance can be normalized to 1.73 m² in order to compare it to reference values

CrCl = Creatinine clearance [mL/min]

K (age-dependent constant) = 0.33 for low birth weight infants; 0.45 for term infants; 0.55 for children; 0.55 for adolescent girls; 0.7 for adolescent boys

Height [cm]

P_Cr = Plasma creatinine concentration [ mg/dL]

• A simple estimate of GFR in children derived from body length and serum creatinine

• GFR can be used to screen for kidney disease, follow disease progression, confirm need for definitive treatment (e.g., dialysis, transplantation), and help determine appropriate medication doses for patients with kidney injury or disease

$FE Na =100×( U Na × P Cr )/( U Cr × P Na )$

U_Na = Urine sodium concentration [mEq/L]

P_Cr = Plasma creatinine concentration [ mg/dL]

U_Cr = Urine creatinine concentration [ mg/dL]

P_Na = Plasma sodium concentration [mEq/L]

• FE_Na < 1.0% concerning for prerenal azotemia

• FE_Na > 2.0% concerning for acute tubular necrosis

$FWD=Coeff×Weight×( Na p /140−1)$

FWD [L]

Weight [kg]

Na_p = Measured plasma sodium concentration [mEq/L]

Coeff: 0.6 for children and nonelderly men; 0.5 for nonelderly women and elderly men; 0.45 for elderly women.

• Provides an adequate estimate of the water deficit in patients with hypernatremia caused by pure water loss. (See Change in Serum Na⁺ formula)

• Used to determine the amount of free water needed to treat hypernatremia (usually corrected over a period of hours to days dependent on the acuity of onset)

Glucose infusion rate (GIR) [ mg/kg/min]

%Glucose = Percent glucose in intravenous fluid (e.g., D10W contains 10% glucose)

Daily Rate = Fluid administration rate [mL/kg/day]

Hourly Rate = Fluid administration rate [mL/h]

Weight [kg]

• Used in the management of hypoglycemia, especially in neonates

• Glucose utilization of healthy neonates is approximately 5–8 mg/kg/min

• Based on assumption that diastole lasts approximately twice as long as systole

Na⁺ = Serum sodium concentration [mEq/L]

GLC = Serum glucose concentration [ mg/dL]

BUN = Serum urea nitrogen concentration [ mg/dL]

• Normal serum osmolality is approximately 285–295 mOsm/L

• Osmolal gap = Measured Osm−Calculated Osm (normal ≤10)

• If the measured serum osmolality is more than 10 mOsm/L above the calculated serum osmolality, consider causes for an osmolal gap due to unmeasured osmotically active substances such as mannitol, ethanol, methanol, and ethylene glycol

PaO₂= Arterial partial pressure of O₂ [mm Hg]

FiO₂= Fraction of inspired oxygen

• Index of severity of hypoxemia; lower number indicates shunt

• Used as part of the definition of Acute Lung Injury (ALI) and Acute Respiratory Distress Syndrome (ARDS)

• For ALI, P/F = 200–300 mm Hg

• For ARDS, P/F <200 mm Hg

PaCO₂ = Arterial partial pressure of CO₂ [mm Hg]

$[ HCO 3 − ]$ = Serum concentration of bicarbonate ions [mEq/L]

• Calculates the expected PaCO₂ in pure metabolic acidosis (respiratory compensation)

• The patient’s actual (measured) PaCO₂ is then compared to this

  • ✓ If the two values correspond, respiratory compensation can be considered to be adequate

  • ✓ If the measured PaCO₂ is higher than the calculated value, there is also a primary respiratory acidosis

  • ✓ If the measured PaCO₂ is lower than the calculated value, there is also a primary respiratory alkalosis