FS Law, Preload, Afterload

College of Engineering, Department of Biomedical Engineering

Prof. Cathal J. Kearney

Module I: Lecture 5

Topic: Modelling the Cardiovascular System as a Complete Unit

Course: BME330: Quantitative Physiology

Instructor: Prof. Cathal J. Kearney

Figures: All figures are from course textbook unless stated

Learning Outcomes

• Describe the cardiac function curve.
• Define total peripheral resistance (TPR).
• Define mean systemic pressure (PMS).
• Derive the vascular function curve.
• Identify the steady-state operating point.

Cardiac Function Curve Overview

Graphical Representation (Page 3)

• Aortic Valve Activity:
  • Closes at pressures of approx. 80 mmHg.
  • Opens during ventricular ejection when pressure exceeds aortic pressure.
• Pressure Measurements:
  • Aortic pressure, left ventricular pressure, and left atrial pressure are key during different phases of the cardiac cycle.
• Phases of the Cardiac Cycle:
  • Ventricular Filling (Diastole): Heart fills with blood.
  • Isovolumetric Contraction: Ventricles contract, pressure rises with no change in volume.
  • Ventricular Ejection: Blood is expelled into the aorta and pulmonary artery.
  • Isovolumetric Relaxation: Heart relaxes after ejection.

Frank-Starling Law of the Heart (Page 4)

Experimental Setup

• Central Venous Pressure (CVP): Defined as the pressure at the entrance to the right atrium at end diastole.
  • Represented as CVP = PRt. Atr. = PRt. Vent.
• Pressure in Pulmonary Vein: At entrance to the left atrium.
  • Represented as PPulm. V. = PLft. Atr. = PLft. Vent.
• Both CVP and PPulm. V. are referred to as filling pressures.
• F-S Law: Increasing right atrial pressure leads to increased stroke volume of both ventricles.

Definitions of Cardiac Mechanics

Preload and Afterload (Page 5)

• Preload: Amount of stretch placed on cardiac muscle (sarcomere stretch) during diastole.
  • Related to End Diastolic Volume (EDV) and End Diastolic Pressure (EDP).
  • Defined for this class as EDP.
• Afterload: Total force opposing muscle contraction defined as the pressure needed for the heart to eject blood during ventricular contraction.
  • Complex to calculate per individual muscle fibers; arterial pressure (e.g., diastolic, mean, or systolic) commonly serves as a surrogate measure of afterload.

Cardiac Function Curve Dynamics (Page 7)

• Intrinsic regulation of the heart without variable afterload.
• Changes in Ventricular Function Curve:
  • Increased Contractility: Leads to increased heart rate and decreased afterload.
  • Decreased Contractility: Results in decreased heart rate and increased afterload.

Cardiovascular System Dynamics (Page 9)

• Closed System:
  • Venous Return = 7200 L/day = 5 L/min.
  • Right Heart Output: 7200 L/day = 5 L/min.
  • Pulmonary and Systemic Circulation.
  • Fluids in various anatomical regions: kidneys, intestines, skin, lymph, etc.

Derivation of the Vascular Function Curve (Page 10)

• Mean Systemic Pressure (PMS): Defined as pressure when the heart is stopped and blood is instantaneously redistributed.
• Flow Equations:
  • Flow in the vena cava (Qveins).
  • Cardiac Output (C.O.).
  • Compliance equations for veins and arteries.
• Important variables include: Compliance of veins (CV), compliance of arteries (CA), and total peripheral resistance (TPR).

Combining Cardiac and Vascular Function Curves (Page 11)

• Slope Calculation:
  • $Slope = -1 + \frac{C<em>A}{C</em>V} TPR$
• Flow Equation:
  • $Q<em>{veins} = C.O. = -1 + \frac{C</em>A}{C_V} TPR * PMS$

Decision Steps for Cardiovascular Changes (Page 12)

1. Determine if the change affects the heart or peripheral vasculature, or both.
2. Assess if cardiac output increases or decreases.
3. Evaluate heart pump effectiveness using the cardiac function curve.
4. For the vascular function curve:
   • Check if mean systemic pressure changes.
   • Evaluate changes to the slope equation variables.

Hypothetical Scenarios to Discuss (Page 13)

• Scenario 1: Systemic vessels constrict.
  • Impact on both cardiac and vascular function curves, including cardiac output.
• Scenario 2: Patient loses substantial blood.
  • Similar evaluation of effects on cardiac and vascular functions.
• Scenario 3: Patient with heart muscle damage from a heart attack.
  • Expected alterations in cardiac and vascular function curves.

Changing Arteriolar Resistance (Page 14)

• Cardiac output plotted against right atrial pressure.
• Vasodilation vs. Vasoconstriction:
  • Normal operating points analyzed with consideration of compliance (Cv) and afterload (TPR).

Impact of Changing Preload and Afterload (Page 15-21)

• Preload and its effects:
  • Increased preload leads to increased stroke volume (SV).
  • Decreased preload leads to decreased SV.
• Afterload effects:
  • Increased afterload: decreased SV.
  • Decreased afterload: increased SV.
• Diastolic curves monitored during pressure vs. volume analysis.

Changing Contractility (Page 23)

• Sympathetic response factors:
  • Increases heart rate and contractility.
  • Induces vasoconstriction and influences hemodynamic changes.

Effects of Strenuous Exercise (Page 28)

1. Increased heart rate.
2. Increased contractility.
3. Vasoconstriction combined with dominant vasodilation effect.
4. Venoconstriction leading to increased venous return.

Summary and Key Points (Page 29)

• F-S Law: Rising right atrial pressure enhances stroke volume of both ventricles, contributing to the cardiac function curve.
• Effects of preload and afterload precisely detailed:
  • Increasing preload elevates stroke volume.
  • Increasing afterload reduces stroke volume.
• Deriving vascular function curves aids in understanding peripheral flow dynamics.
• Combined cardiac and vascular function curves provide insights for calculating cardiac output.
• Awareness of cardiovascular changes is crucial for interpreting cardiac function, venous function, and pressure-volume loops accordingly.