Cardiac Output

Fundamentals of Cardiac Output

• Definition of Cardiac Output (CO): Cardiac output is defined as the volume of blood pumped by a single ventricle in the span of one minute.

• The Closed Loop Principle: Because the circulatory system functions as a closed loop, the volume of blood pumped by the right ventricle must be equivalent to the volume pumped by the left ventricle. Consequently, cardiac output remains the same regardless of which ventricle is measured.

• Physics and Flow: In the context of physics, cardiac output is essentially a measure of flow. Flow is frequently represented by the variables $Q$ or $F$.

• Units of Measurement: Because it is a measure of flow, cardiac output is expressed as volume per unit of time, typically in milliliters per minute ($ml/min$) or liters per minute ($L/min$).

The Mathematical Equation for Cardiac Output

• The Basic Formula: Cardiac output is calculated by multiplying the heart rate ($HR$) by the stroke volume ($SV$).     $CO = HR \times SV$

• Heart Rate (HR): This is the frequency of the heart's pumping action, measured in beats per minute ($bpm$).

• Stroke Volume (SV): This is the volume of blood ejected by a ventricle during a single contraction (beat). It is measured in volume per beat.

  • Formula for units: $(beats/min) \times (ml/beat) = ml/min$

• Calculation Variability: Depending on the desired unit, stroke volume can be expressed in liters per beat ($L/beat$) to yield a final result in liters per minute ($L/min$), as the "beat" units cancel each other out during multiplication.

Average Resting Values and Physiological Norms

• Resting Heart Rate: While values vary by textbook and reference, an average resting heart rate is generally considered to be between $65$ and $75$ beats per minute. A common standardized value used for calculations is $75$ beats per minute ($75\text{ beats/min}$).

• Resting Stroke Volume: The average volume of blood pumped by a ventricle in one beat is approximately $70$ milliliters per beat ($70\text{ ml/beat}$).

• Standard Cardiac Output Calculation:     $CO = 75\text{ beats/min} \times 70\text{ ml/beat} = 5250\text{ ml/min}$     $CO = 5.25\text{ L/min}$

• Human Blood Volume Statistics:

  • Females: Average blood volume ranges from $4$ to $5$ liters ($4 \text{ to } 5\text{ L}$).

  • Males: Average blood volume ranges from $5$ to $6$ liters ($5 \text{ to } 6\text{ L}$).

  • General Average: Approximately $5$ liters ($5\text{ L}$).

• Physiological Significance: The calculated resting cardiac output of approximately $5.25\text{ L/min}$ indicates that the heart pumps an amount roughly equivalent to the body's entire blood volume through each circuit (pulmonary and systemic) every single minute. This ensures constant oxygenation of blood in the lungs and constant nutrient delivery/waste removal at the tissue level.

Maximal Performance and Cardiac Reserve

• Exercise and Elevation: Cardiac output can increase significantly during exercise by increasing both heart rate and stroke volume.

• Heart Rate Elevation: Heart rates can reach levels such as $140$, $155$, $165$, or $170$ beats per minute ($bpm$).

• Contractility: Through improved contractility, the heart can eject more than the standard $70$ milliliters of blood per beat.

• Maximal Cardiac Output: In high-performance scenarios, cardiac output can reach or exceed $20$ to $25$ liters per minute ($20 \text{ to } 25\text{ L/min}$). This represents a four-fold to five-fold increase over resting levels.

• Cardiac Reserve: This is defined as the difference between a person's resting cardiac output and their maximal cardiac output.

  • In a healthy individual, the cardiac reserve is approximately $15$ to $20$ liters per minute ($15 \text{ to } 20\text{ L/min}$).

  • This reserve is a built-in mechanism to accommodate the demands of harder-working tissues with adequate blood flow and oxygen delivery.

Components of Stroke Volume: EDV and ESV

• Stroke Volume Components: Stroke volume can be further broken down into two primary volumes related to the cardiac cycle.

• End Diastolic Volume (EDV): This is the volume of blood present in the ventricle at the end of the filling phase (diastole), just before the heart beats.

  • During late diastole, the atria squeeze to fill the ventricle to its maximum capacity.

• End Systolic Volume (ESV): This is the volume of blood remaining in the ventricle at the end of the contraction phase (systole). The ventricle does not eject all of its blood; some remains behind.

• Calculating Stroke Volume: Stroke volume is the difference between the volume before contraction and the volume after contraction.     $SV = EDV - ESV$

Dynamics and Relationships of Cardiac Variables

• EDV and Stroke Volume Relationship: There is a direct relationship between End Diastolic Volume and Stroke Volume. If EDV increases (the ventricle fills more) while ESV remains constant, the SV will increase.

• EDV and Cardiac Output Relationship: Because EDV and SV are directly related, an increase in EDV leads to an increase in cardiac output ($CO$).

• ESV and Stroke Volume Relationship: There is an inverse (indirect) relationship between End Systolic Volume and Stroke Volume. If ESV increases (more blood is left in the heart after contraction) while EDV remains constant, the SV will decrease.

  • Increased Afterload typically results in an increased ESV.

• ESV and Cardiac Output Relationship: Because ESV and SV are inversely related, an increase in ESV leads to a decrease in cardiac output ($CO$).

• Heart Rate and Stroke Volume (at Constant CO): If cardiac output is maintained at a constant level (e.g., $5\text{ L/min}$), then heart rate and stroke volume are inversely related. If heart rate increases ($75\text{ bpm}$ to $100\text{ bpm}$), stroke volume must decrease to keep the output the same.

• Heart Rate/Stroke Volume and CO (General): If one variable increases while the other is held constant, cardiac output will increase (direct relationship). This is because both $HR$ and $SV$ are in the numerator on the same side of the formula.

• Physiological Regulation: The body's primary objective is to maintain a cardiac output consistent with the metabolic demands of the tissues (oxygen and nutrient needs). The system can either "quiet down" cardiac output when cells are at rest or speed up the heart and increase stroke volume when tissues demand high levels of resources.