U01.07.007 Cardiac output equations

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Learning Objectives

By the end of this section, learners will be able to:

  1. Apply the fundamental equations governing stroke volume, ejection fraction, and cardiac output
  2. Interpret ejection fraction as a marker of ventricular function
  3. Explain how heart rate and stroke volume contribute to cardiac output at rest and during exercise
  4. Relate pulse pressure and mean arterial pressure to underlying cardiovascular physiology
  5. Recognize clinical conditions associated with abnormal hemodynamic values

Stroke Volume (SV)

Stroke volume is the volume of blood ejected by the ventricle during each cardiac cycle.

SV = EDV − ESV\textbf{SV = EDV − ESV}

Where:

  • EDV (End-Diastolic Volume): Volume of blood in the ventricle at the end of diastole
  • ESV (End-Systolic Volume): Volume of blood remaining after systole

Stroke volume increases with increased preload or contractility and decreases with increased afterload.

Ejection Fraction (EF)

Ejection fraction represents the fraction of end-diastolic volume ejected with each heartbeat.

EF = SV ÷ EDV = (EDV − ESV) ÷ EDV\textbf{EF = SV ÷ EDV = (EDV − ESV) ÷ EDV}

Clinical Significance:

  • EF is an index of ventricular systolic function
  • Normal EF: 50%–70%
  • Reduced EF: Seen in systolic heart failure
  • Preserved EF: Typically seen in diastolic heart failure, despite impaired filling

Cardiac Output (CO)

Cardiac output is the volume of blood pumped by the heart per minute.

CO = SV × HR\textbf{CO = SV × HR}

Where:

  • SV: Stroke volume
  • HR: Heart rate

Exercise Physiology:

  • Early exercise: CO increases via ↑ HR and ↑ SV
  • Late exercise: CO increases primarily via ↑ HR, as SV plateaus

Fick Principle

The Fick equation calculates cardiac output based on oxygen consumption:

\textbf{CO = \dfrac{\text{Rate of O₂ consumption}}{\text{Arterial O₂ content − Venous O₂ content}}}

This principle is commonly used in cardiac catheterization to obtain accurate CO measurements.

Heart Rate and Diastolic Filling

  • As heart rate increases, diastole shortens disproportionately
  • Very high heart rates (e.g., ventricular tachycardia) lead to:
    • ↓ Diastolic filling time
    • ↓ Stroke volume
    • ↓ Cardiac output

This explains why extreme tachycardia can paradoxically reduce cardiac output.

Pulse Pressure (PP)

Pulse pressure is the difference between systolic and diastolic blood pressure:

PP = SBP − DBP\textbf{PP = SBP − DBP}

Key Relationships:

  • PP is directly proportional to stroke volume
  • PP is inversely proportional to arterial compliance

Increased Pulse Pressure Seen In:

  • Aortic regurgitation
  • Arterial stiffening (isolated systolic hypertension in older adults)
  • Obstructive sleep apnea (↑ sympathetic tone)
  • High-output states (e.g., anemia, hyperthyroidism)
  • Exercise (transient)

Decreased Pulse Pressure Seen In:

  • Aortic stenosis
  • Cardiogenic shock
  • Cardiac tamponade
  • Advanced heart failure

Mean Arterial Pressure (MAP)

Mean arterial pressure represents the average pressure driving blood through the systemic circulation.

MAP = CO × Total Peripheral Resistance (TPR)\textbf{MAP = CO × Total Peripheral Resistance (TPR)}

At resting heart rates:

MAP = ⅔ DBP + ⅓ SBP = DBP + ⅓ PP\textbf{MAP = ⅔ DBP + ⅓ SBP = DBP + ⅓ PP}

MAP is the primary determinant of organ perfusion and is tightly regulated by cardiac output and systemic vascular resistance.

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