1833

Appendix

EFormulasCerebral/Neurologic Formulas

Intracranial pressure (ICP)[Normal: <20 cm H2O, <15 mmHg]

Cerebral perfusion pressure (CPP) = MAP – ICP

[Normal: 70–100 mmHg]Cerebral vascular resistance (CVR)

[Normal: 1.5–2.1 mmHg/100 g/min/mL]

Cerebral blood flow (CBF) = CPP/CVR

Hemodynamic Formulas

[Normal: 75 mL/100 g gray matter/min][Normal: 45 mL/100 g white matter/min]

Jugular bulb saturation (SjvO2)[Normal: 55–70%]

Cerebral metabolic rate (CMRO2) = (CBF)(CaO2 – CjvO2)

[Normal: 3–3.5 mL/100 g/min]

Cerebral oxygen extraction = CMO

(CBF)(CaO )

CaO C O

CaO2

2 jv 2

2

2 =−

Pulse pressure = systolic BP – diastolic BP

Mean arterial pressure (MAP) = SBP 2(DBP)

3+

[Normal: 70–105 mmHg]

Central venous pressure (CVP)[Normal: 0–8 mmHg]

Pulse pressure variation = PPV = (PPmax – PPmin)/PPmean (Over a respiratory cycle or other period of time; Normal: ≤10%)

Stroke volume variation = SVV = (SVmax – SVmin)/SVmean (Over a respiratory cycle or other period of time; Normal: ≤10%)

Mean pulmonary artery pressure ( )PA[Normal: 10–20 mmHg]

Pulmonary artery occlusion pressure (PAOP)[Normal: 4–12 mmHg]

Cardiac output (CO) = Stroke volume (SV) × Heart rate (HR)[Normal: 4–8 L/min]

Cardiac index (CI) = COBSA

[Normal: 2.5–4.0 L/min/m2]

Pulmonary vascular resistance (PVR) = (PA PAOP)80

CO−

[Normal: 150–250 dyne/s/cm−5]

Pulmonary vascular resistance index (PVRI) = (PA PAOP)80

CI−

[Normal: 100–240 dyne/s/cm−5/m2]

Systemic vascular resistance (SVR) = (MAP CVP)80

CO−

[Normal: 800–1,200 dyne/s/cm−5]

Systemic vascular resistance index (SVRI) = (MAP CVP)80

CI−

[1,300–2,900 dyne/s/cm−5/m2]

Stroke volume index (SVI) = CIHR

[Normal: 40 ± 7 mL/beat/m2]Right ventricular stroke work index (RVSWI)

= SVI( PA – CVP)(0.0136)

[Normal: 6–10 gm.meter/m2 per beat]Left ventricular stroke work index (LVSWI)

= SVI(MAP – PAOP) (0.0136)

[Normal: 43–56 gm.meter/m2 per beat]

Arterial O2 content (CaO2) = O2 combined with hemoglobin + O2 dissolved in the plasma

[1 g Hb binds 1.36 mL O2]

= (1.36)(Hb)(SaO2) + 0.0031(PaO2)

[Normal: 20 mL O2/dL]Mixed venous O2 saturation (SvO2)

[Normal: 75%]

Mixed venous O2 content (CvO2) = (1.36)(Hb)(SvO2) + 0.0031(PvO2)

[Normal: 15 mL O2/dL]

O2 delivery (D.O2) = CO × CaO2 × 10

[Normal: 600–1,000 mL O2/min]

Oxygen delivery indexed (DO2I) = CI × CaO2 × 10

[Normal: 500–600 mL/min/m2]

O2 consumption (V.O2) = CI(CaO2 – CvO2)

[Normal: 110–150 mL/min/m2]

O2 extraction ratio = (CaO CvO )

CaO2 2

2

−

[Normal: 25%]

Respiratory FormulasOxygEnatiOn

Fraction of inspired O2 (FIO2)[Range: 0.21–1.0]

Respiratory quotient (R) = VCO2 expired/VO2 inspired

[Normal: 0.8]Barometric pressure (PB)

[760 mmHg at sea level]

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1834 Appendices CritiCal Care Catalog

Partial pressure of H2O (PH2O)[47 mmHg at 37°C]

Partial pressure of inspired O2 (PIO2) = FIO2 (PB – PH2O)

[150 mmHg at sea level breathing room air (FIO2 = 0.21)]Partial pressure of alveolar O2 (PAO2) (alveolar gas equation)

PAO2 = FIO2 (PB – PH2O) –PaCO

R2

= (FIO2 × 713) – (PaCO2/0.8) (at sea level)= 150 – (PaCO2/0.8) (at sea level on room air)

[Range: 100 mmHg on room air; 673 mmHg on 100% O2]Partial pressure of arterial O2 (PaO2)

[Normal: 70–100 mmHg on room air] Increased: hyperventilation, increased FIO2, contaminated sample Decreased: hypoventilation, decreased FIO2, V

./Q. mismatch, intra-

pulmonary or anatomic R → L shunt, diffusion abnormalities

Alveolar–arterial O2 gradient (P(A – a)O2) = PAO2 – PaO2

[Normal: 3–16 mmHg on room air; 25–65 mmHg on 100% O2]

VEntilatiOnPartial pressure of arterial CO2 (PaCO2)

[Normal: 46 mmHg]Partial pressure of alveolar (expired) CO2 (PetCO2)Dead-space ventilation (VD): Portion of VT that does not par-ticipate in gas exchange

VD = anatomic dead space + physiologic dead space

[Normal: 150 mL]Engelhoff modification of the Bohr formula for dead space

VDVT

= PaCO PetCO

PaCO2 2

2

−

Minute ventilation (VE) = respiratory rate × VT

Pulmonary capillary blood O2 content (CcO2)

= 1.36 (Hb)(SaO2)(FIO2) + 0.003(PBH2O – PaCO2)(FIO2)

Shunt fraction (Q.

s/Q.

t) = CcO CaOCcO CvO

2 2

2 2

−−

Renal Formulas

Toxicology Formulas

lung VOlumEs

Tidal volume (VT): Volume inspired/expired with each breath[Normal: 500 mL; 6–7 mL/kg lean body weight]

Inspiratory reserve volume (IRV): Maximal inspired volume end-tidal inspiration

[Normal: 25% of vital capacity (VC)]Inspiratory capacity (IC): Maximal volume inspired from rest-ing expiratory level

IC = IRV + VT

[Normal: 1–2.4 L]Expiratory reserve volume (ERV): Maximal expired volume from end-tidal inspiration

[Normal: 25% of vital capacity (VC)]Residual volume (RV): Volume remaining in lungs after maxi-mal expiration

[Normal: 1–2.4 L]Functional residual capacity (FRC): Volume remaining in lungs at end-tidal expiration

FRC = ERV + RV

[Normal: 1.8–3.4 L]Vital capacity (VC): Maximal volume expelled by forceful effort after maximal inspiration

VC = IRV + ERV + VT

[Normal: 3–5 L; 50–60 mL/kg lean body weight in females; 70 mL/kg lean body weight in males]

Total lung capacity (TLC): Volume in lungs at end of maximal inspiration

TLC = VC + RV

[Normal: 4–6 L]

Lung Mechanics

Plateau pressure (Pplat)Peak inspiratory pressure (PIP)Esophageal pressure (Pesoph)Transpulmonary pressure = Ptp = Pplat – Pesoph

[Normal: For recruitment Ptp = 25 cm H2O; to set PEEP Ptp – end-exp = 0 – 5 cm H2O; to set Vt or Pinsp Ptp – end-insp = <15 cm H2O]

Positive end-expiratory pressure (PEEP)

Compliance = change in volume/change in pressure

Static compliance (Cst) = VT

Pplat PEEP− [Normal: 70–160 mL/cm H2O (paralyzed/anesthetized and supine)]

Dynamic compliance (Cdyn) = VT

PIP PEEP− [Normal: 50–80 mL/cm H2O (paralyzed/anesthetized and supine)]

Creatinine clearance (ClCreat) = (U )(urine volume)

PCreat

Creat

Fractional excretion of sodium (FeNa+)

= ×+

urine [Na ]plasma [Na ]

plasma [creatinine+ ]]urine [creatinine]

100×

Free water clearance

= −urine volurine osmolality

plasma osmolalityyurine vol×

Serum methanol concentration [MeOH] in mg/dL = 3.2 (Osms – (2 × [Na+]) – ([BUN]/2.8) – ([glucose]/18)

– ([ETOH]/4.6) – 10)

Ethylene glycol concentration = 6.2 (Osms – (2 × [Na+]) – ([BUN]/2.8) – ([glucose]/18)

– ([EtOH]/4.6) – 10)

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Appendix e Formulas 1835

TABLE E.1 Daily Renal Excretion of Cations and Anions in Normals

Electrolyte Urinary Excretion (mmol/d)

CATIONSNa 127 ± 6

K 49 ± 2

Ca 4 ± 1

Mg 11 ± 1

NH4 28 ± 2

total 219 é 3

ANIONSCl 135 ± 5

So4 34 ± 1

Po4 20 ± 1

organic anions 29 ± 1

total 221 é 6

Na, sodium; K, potassium; Ca, calcium; Mg, magnesium; NH4, ammonia; Cl, chloride; So4, sulfate; Po4, phosphate.

TABLE E.2 Use of Urine Electrolytes

Diagnostic Problem Urinary ValuePrimary Diagnostic Possibilities

Volume depletion Na = 0–10 mmol/l extrarenal sodium loss

Na >10 mmol/l renal salt wasting or adrenal insufficiency

acute oliguria Na = 0–10 mmol/l Prerenal azotemia

Na >30 mmol/l acute tubular necrosis

Hyponatremia Na = 0–10 mmol/l Severe volume deple-tion, edematous

Na >dietary intake

inappropriate antidi-uretic hormone secretion; adrenal insufficiency

Hypokalemia K = 0–10 mmol/l extrarenal K loss

K >10 mmol/l renal K loss

Metabolic alkalosis Cl = 0–10 mmol/l Cl-responsive alkalosis

Cl = dietary intake Cl-resistant alkalosis

Na, sodium; K, potassium; Cl, chloride.

TABLE E.3 Interpretation of Urine Electrolytes

Electrolyte Normal Response Patient Response Potential Pitfalls

Na+ reflects diet and eCF volume; <10 mmol if eCF volume contracted

>20 mmol in eCF volume contraction suggests renal tubular damage

Diuretic useNo reabsorbed anionsrecent vomiting, drugs

Cl− reflects diet and eCF volume; <10 mmol if eCF volume contracted

>20 mmol with eCF volume contraction suggests renal damage

DiureticDiarrhea

K+ reflects diet, plasma [K], aldosterone action

if hypokalemia and urine [K]:>20 mM or rate of K excretion>30 mmol/d then K excretion too high

K-sparing diureticslow urine [Na]Water diuresis

pH Depends on acid–base statusUseful for bicarbonaturia

Useful once low NH4+ excretion confirmed to

define cause of low NH4+

Unreliable for urine NH4+

Urinary tract infection

HCo3− Depends on diet and acid–base status;

>10 mM indicates HCo3− load 0 in

acidemia

High urine HCo3− with chronic metabolic

alkalosis indicates vomiting or HCo3− input

High urine HCo3 with acidemia in prta

Urinary tract infectionCarbonic anhydrase inhibitors

(Na+, K+, Cl−) Depends on diet and acid–base status Na + K > Cl = low urine NH4+

Cl > Na + K = high urine NH4+

KetonuriaDrug anionsalkaline urine

Na+, sodium; Cl, chloride; K+, potassium; HCo3−, carbonate; NH4, ammonia; eCF, extracellular fluid; prta, partial renal tubular acidosis.

From Halperin Ml, goldstein MB. Fluid, Electrolyte and Acid-Base Emergencies. Philadelphia, Pa: WB Saunders; 1988.

Infectious Diseases Formulas

antibiOtic KinEticsThe volume of distribution (VD) of an antimicrobial is calcu-lated as:

VA

CDp

=

where A = total amount of antibiotic in the body and Cp = antibiotic plasma concentration.

Repetitive dosing of antibiotics depends on the principle of minimal plasma concentrations (Cmin):

CD

(V )(2 1)minD

=−n

where D = dose and n = dosing interval expressed in half-lives.

The plasma concentration at steady state (Css) of an antimi-crobial can be estimated utilizing the following formula:

CDose per half-life

(0.693)(V )ssD

=

antibiOtic adjustmEntsRenal dysfunction in critically ill patients is common. In those patients receiving aminoglycosides, dosage modification is required according to the aminoglycoside clearance:

Aminoglycoside clearance = (Ccr)(0.6) + 10

where Ccr = creatinine clearance in mL/minute.In order to estimate the creatinine clearance, the Cockcrof

and Gault formula is utilized:

Ccr (mL/min) = (140 age) weight

Cr 72− ×

×

where Cr = serum creatinine in mg/dL. Another modification to this formula is the Spyker and Guerrant method:

Ccr (mL/min) = (140 age) (1.03 0.053 Cr)

Cr− × − ×

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