Function of the Circulatory System

Biology

1. Fundamental Concepts

Definition: The circulatory system is responsible for the transport of blood, nutrients, gases, and waste products throughout the body.
Components: Includes the heart, blood vessels (arteries, veins, capillaries), and blood.
Function: Facilitates the exchange of oxygen and carbon dioxide between tissues and the environment.

2. Key Concepts

Blood Flow Dynamics: $${\text{{Volume}}} \cdot {\text{{Flow Rate}}} = {\text{{Pressure}}}$$

Oxygen Transport: $${\text{{Oxygen Saturation}}} = \frac{{\text{{Oxygen Content}}}}{{\text{{Total Capacity}}}}$$

Cardiac Output: $${\text{{Cardiac Output}}} = {\text{{Heart Rate}}} \cdot {\text{{Stroke Volume}}}$$

3. Examples

Example 1 (Basic)

Problem: Calculate the cardiac output if the heart rate is 70 beats per minute and the stroke volume is 70 mL.

Step-by-Step Solution:

Identify the values: Heart Rate = 70 bpm, Stroke Volume = 70 mL
Apply the formula: $${\text{{Cardiac Output}}} = 70 \cdot 70$$
Calculate: $${\text{{Cardiac Output}}} = 4900 \text{{ mL/min}}$$

Validation: Substitute values → Original: 70 * 70 = 4900; Simplified: 4900 ✓

Example 2 (Intermediate)

Problem: If the total capacity of oxygen in the blood is 200 mL and the oxygen content is 180 mL, calculate the oxygen saturation.

Step-by-Step Solution:

Identify the values: Oxygen Content = 180 mL, Total Capacity = 200 mL
Apply the formula: $${\text{{Oxygen Saturation}}} = \frac{180}{200}$$
Calculate: $${\text{{Oxygen Saturation}}} = 0.9 \text{{ or }} 90\%$$

Validation: Substitute values → Original: 180/200 = 0.9; Simplified: 0.9 ✓

4. Problem-Solving Techniques

Unit Analysis: Ensure all units are consistent before performing calculations.
Dimensional Check: Verify that the units on both sides of an equation match.
Estimation Technique: Use rough estimates to check the reasonableness of your answers.