Hemodynamic Formulae, Calculations, and Charts





Dubois and Dubois [2]:


$$ \mathrm{B}\mathrm{S}\mathrm{A}\;\left({\mathrm{m}}^2\right)=0.007184\times \mathrm{height}\;{\left(\mathrm{cm}\right)}^{0.725}\times \mathrm{weight}\;{\left(\mathrm{kg}\right)}^{0.425} $$



47.2 Derived Hemodynamic Data



47.2.1 Cardiac Output





$$ \mathrm{S}\mathrm{V}=\mathrm{E}\mathrm{D}\mathrm{V}-\mathrm{E}\mathrm{S}\mathrm{V} $$



$$ \mathrm{C}\mathrm{O}=\mathrm{S}\mathrm{V}\times \mathrm{H}\mathrm{R} $$



$$ \mathrm{E}\mathrm{F}=\mathrm{S}\mathrm{V}/\mathrm{E}\mathrm{D}\mathrm{V} $$
where SV = stroke volume, EDV and ESV = end-diastolic and end-systolic volumes, CO = cardiac output, HR = heart rate, and EF = ejection fraction.


47.2.2 The Fick Equation





$$ Q\;\left(\mathrm{l}/ \min \right)=\frac{{\mathrm{VO}}_2\left(\mathrm{ml}\;{\mathrm{O}}_2/ \min \right)}{\mathrm{arterial}\;{\mathrm{O}}_2\;\mathrm{content}-\mathrm{venous}\;{\mathrm{O}}_2\;\mathrm{content}\;\left(\mathrm{ml}\;{\mathrm{O}}_2/\mathrm{l}\right)} $$
where Q is cardiac output expressed in liters per minute (l/min) and VO2 is the oxygen consumption in ml O2/min.

The denominator of the Fick equation is the arteriovenous oxygen content difference (a − v O2 diff) and is expressed as ml O2/l of blood.


$$ \mathrm{Oxygen}\;\mathrm{capacity}\;\left(\mathrm{ml}\;{\mathrm{O}}_2/\mathrm{l}\right)=\mathrm{H}\mathrm{g}\mathrm{b}\;\left(\mathrm{g}/\mathrm{l}\right)\times 1.39\;\left(\mathrm{ml}\;{\mathrm{O}}_2/\mathrm{g}\kern0.24em of\;\mathrm{H}\mathrm{g}\mathrm{b}\right) $$

The oxygen content of the blood is the amount of oxygen in that specific sample (either arterial or venous) and can be estimated by the following formula:


$$ \begin{array}{c}\begin{array}{c}{\mathrm{C}}_{\mathrm{a}}{\mathrm{O}}_2\left(\mathrm{ml}\;{\mathrm{O}}_2/\mathrm{l}\right)=\mathrm{Oxygen}\;\mathrm{capacity}\;\left(\mathrm{ml}\;{\mathrm{O}}_2/\mathrm{l}\right)\\ {}\times \mathrm{arterial}\;\mathrm{oxygen}\;\mathrm{saturation}\;\left(\%\right)\end{array}\\ {}\begin{array}{c}{\mathrm{C}}_{\mathrm{v}}{\mathrm{O}}_2\left(\mathrm{ml}\;{\mathrm{O}}_2/\mathrm{l}\right)=\mathrm{Oxygen}\;\mathrm{capacity}\;\left(\mathrm{ml}\;{\mathrm{O}}_2/\mathrm{l}\right)\\ {}\times \mathrm{venous}\;\mathrm{oxygen}\;\mathrm{saturation}\;\left(\%\right)\end{array}\end{array} $$

If the patient is breathing enriched oxygen (F I O2 > 30 %), the amount of dissolved oxygen must be accounted for in the flow equation. The solubility coefficient of oxygen in plasma is 0.00003 O2 ml/ml plasma/mmHg O2 tension or 0.032/l of plasma.


$$ \begin{array}{c}\begin{array}{c}{\mathrm{C}}_{\mathrm{a}}{\mathrm{O}}_2=\mathrm{Oxygen}\;\mathrm{capacity}\times \mathrm{arterial}\;\mathrm{oxygen}\;\mathrm{saturation}\;\left(\%\right)\\ {}+0.032\times {\mathrm{P}}_{\mathrm{a}}{\mathrm{O}}_2\left(\mathrm{mmHg}\right)\end{array}\\ {}\begin{array}{c}{\mathrm{C}}_{\mathrm{v}}{\mathrm{O}}_2=\mathrm{Oxygen}\;\mathrm{capacity}\times \mathrm{venous}\;\mathrm{oxygen}\;\mathrm{saturation}\;\left(\%\right)\\ {}+0.032\times {\mathrm{P}}_{\mathrm{v}}{\mathrm{O}}_2\left(\mathrm{mmHg}\right)\end{array}\end{array} $$


47.2.3 Assessment of Flows and the Q p:Q s Ratio


Flow calculations are based on the Fick principle and can be applied to both pulmonary (Q p ) and systemic blood flows (Q s).

Q p can be estimated by the following equation:


$$ \begin{array}{l}{Q}_{\mathrm{p}}=\frac{{\mathrm{VO}}_2}{\mathrm{p}\mathrm{ulmonary}\;\mathrm{venous}\;{\mathrm{O}}_2\;\mathrm{content}-\mathrm{pulmonary}\;\mathrm{a}\mathrm{rterial}\;{\mathrm{O}}_2\;\mathrm{content}}\;\mathrm{or}\\ {}{Q}_{\mathrm{p}}=\frac{{\mathrm{VO}}_2\left({\mathrm{ml}\;\mathrm{O}}_2/ \min \right)}{\left(\mathrm{P}\mathrm{V}\;\mathrm{s}\mathrm{a}\mathrm{t}-\mathrm{P}\mathrm{A}\;\mathrm{s}\mathrm{a}\mathrm{t}\right)\times 1.39\times \mathrm{H}\mathrm{g}\mathrm{b}\left(\mathrm{g}/\mathrm{l}\right)}\end{array} $$
where PV is pulmonary vein and PA is pulmonary artery saturation.

Similarly, Q s is estimated as


$$ \begin{array}{c}{Q}_{\mathrm{s}}=\frac{{\mathrm{VO}}_2}{\mathrm{s}\mathrm{ystemic}\;\mathrm{a}\mathrm{r}\mathrm{t}\mathrm{erial}\;{\mathrm{O}}_2\;\mathrm{content}-\mathrm{mixed}\;\mathrm{venous}\;{\mathrm{O}}_2\;\mathrm{content}}\;\mathrm{o}\mathrm{r}\\ {}{Q}_{\mathrm{s}}=\frac{{\mathrm{VO}}_2\left({\mathrm{ml}\;\mathrm{O}}_2/ \min \right)}{\left(\mathrm{A}\mathrm{o}\;\mathrm{s}\mathrm{a}\mathrm{t}-\mathrm{M}\mathrm{V}\;\mathrm{s}\mathrm{a}\mathrm{t}\right)\times 1.39\times \mathrm{H}\mathrm{g}\mathrm{b}\left(\mathrm{g}/\mathrm{l}\right)}\end{array} $$
where Ao is aortic and MV is mixed venous saturation.

Finally, effective pulmonary blood flow (Q ep) is the amount of deoxygenated blood that is pumped to the lungs.


$$ \begin{array}{l}{Q}_{\mathrm{p}}=\frac{{\mathrm{VO}}_2}{\left(\mathrm{pulmonary}\;\mathrm{venous}\;{\mathrm{O}}_2\;\mathrm{content}-\mathrm{mixed}\;\mathrm{venous}\;{\mathrm{O}}_2\;\mathrm{content}\right)}\;\mathrm{or}\\ {}{Q}_{\mathrm{ep}}=\frac{{\mathrm{VO}}_2\left(\mathrm{ml}/ \min \right)}{\left(\mathrm{P}\mathrm{V}\;\mathrm{s}\mathrm{a}\mathrm{t}-\mathrm{M}\mathrm{V}\;\mathrm{s}\mathrm{a}\mathrm{t}\right)\times 1.39\times \mathrm{H}\mathrm{g}\mathrm{b}\left(\mathrm{g}/\mathrm{l}\right)}\end{array} $$



$$ \begin{array}{c}\mathrm{Mixed}\;\mathrm{venous}\;\mathrm{s}\mathrm{a}\mathrm{t}\mathrm{uration}=\frac{\left(3\times \mathrm{S}\mathrm{V}\mathrm{C}\;\mathrm{s}\mathrm{a}\mathrm{t}+\mathrm{I}\mathrm{V}\mathrm{C}\;\mathrm{s}\mathrm{a}\mathrm{t}\right)}{4}\;\mathrm{or}\\ {}=\frac{\mathrm{SVC}\;\mathrm{s}\mathrm{a}\mathrm{t}-\left(\mathrm{S}\mathrm{V}\mathrm{C}\;\mathrm{s}\mathrm{a}\mathrm{t}-\mathrm{I}\mathrm{V}\mathrm{C}\;\mathrm{s}\mathrm{a}\mathrm{t}\right)}{4}\end{array} $$



$$ {Q}_{\mathrm{p}}:{Q}_{\mathrm{s}}=\frac{\left(\mathrm{A}\mathrm{o}\;\mathrm{s}\mathrm{a}\mathrm{t}-\mathrm{M}\mathrm{V}\;\mathrm{s}\mathrm{a}\mathrm{t}\right)}{\left(\mathrm{P}\mathrm{V}\;\mathrm{s}\mathrm{a}\mathrm{t}-\mathrm{P}\mathrm{A}\;\mathrm{s}\mathrm{a}\mathrm{t}\right)} $$
where Ao is the aortic saturation, MV is the mixed venous saturation, and PV and PA saturations are the pulmonary vein and artery, respectively. SVC is superior caval and IVC inferior caval vein saturations.


47.2.4 Oxygen Transport


Global oxygen delivery (DO2), also known as systemic oxygen transport (SOT):

DO2 = Q s × CaO2 expressed in ml/min.

The oxygen extraction ratio (O2ER):


$$ {\mathrm{O}}_2\mathrm{E}\mathrm{R}=\frac{{\mathrm{VO}}_2}{{\mathrm{DO}}_2}. $$


47.2.5 Resistance (Wood Units)


Pulmonary vascular resistance:


$$ \mathrm{P}\mathrm{V}\mathrm{R}=\frac{\left(\mathrm{mPAP}-\mathrm{mLAP}\right)}{Q_{\mathrm{p}}} $$
where PVR = pulmonary vascular resistance, mPAP = mean pulmonary artery pressure, mLAP = mean left atrium pressure (alternatively, pulmonary vein or PCWP may be used), and Q p = pulmonary blood flow.

Similarly, systemic vascular resistance can be calculated as follows:


$$ \mathrm{S}\mathrm{V}\mathrm{R}=\frac{\left(\mathrm{mAoP}-\mathrm{mRAP}\right)}{Q_{\mathrm{s}}} $$
where SVR = systemic vascular resistance, mAoP = mean arterial pressure, mRAP = mean right atrial pressure, and Q s = systemic blood flow.

Wood units × 80 = dyne − sec − cm−5

Normal values:

PVRI: 1–3 Wood units × m2 or 80–240 dyn × s × cm−5 × m2

SVRI: 15–30 Wood units × m2 or 800–1,600 dyn × s × cm−5 × m2


47.2.6 Oxygen Consumption per Body Surface Area (ml/min/m2) by Gender, Age, and Heart Rate [3, 4]


Oxygen consumption (assumed values):



  • Infant <3 months is ~130 ml/min/m2.


  • 2–5 years ~150–200 ml/min/m2.


  • Adolescents ~120–180 ml/min/m2.


  • Adult females ~100 ml/min/m2.


  • Adult males ~110–120 ml/min/m2.


  • 1–2 years ~200 ml/min/m2.
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Related posts:

  1. Pulmonary Artery Branches
  2. The Usual Vascular Access
  3. Creating an Interatrial Communication
  4. Hemodynamics: Pressures and Flows

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Jul 8, 2016 | Posted by in CARDIOLOGY | Comments Off on Hemodynamic Formulae, Calculations, and Charts

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