Cardiovascular Mechanics

Pressure

• Hydrostatic pressure is the pressure present in a fluid at rest due to gravity

$$\Delta P=\rho \cdot g\cdot \Delta h$$ $$\text{MAP}-\text{CVP}=\text{CO}\times \text{SVR}$$

• Mean arterial pressure is the area under the pressure time curve divided by the length of the cardiac cycle
  • It can be estimated by the following equations:

$$\text{MAP}=\frac{1}{3}\text{SBP}+\frac{2}{3}\text{DBP}=\text{DBP}+\frac{\text{Pulse Pressure}}{3}$$

• Determinants of SBP
  • Arterial compliance
  • Stroke volume
  • Systemic vascular resistance
• Determinants of DBP
  • Systemic vascular resistance
  • Arterial compliance
  • Heart rate
• Determinants of pulse pressure:

$$\text{Pulse Pressure}\propto \frac{\text{Stroke Volume}}{\text{Arterial Compliance}}$$

Preload

• Defined as either:
  • Wall tension experienced by the LV at end-diastole (estimated by LV end-diastolic pressure)
  • Sarcomere length in the LV at end-diastole (estimated by LV end-diastolic volume)
• It is influenced by:
  • Total blood volume
  • Ventricular compliance
    • Wall thickness
    • Relaxation (lusitropic) properties
    • Pericardial compliance
  • Rhythm
    • Heart rhythm (as heart rate increases, less time is spent in diastole)
    • Arrythmias where there is no atrial kick (e.g. atrial fibrillation)
  • Intrathoracic pressure (reduces preload)
• Clinical surrogate
  • Central venous pressure

Afterload

• Force opposing ventricular contraction during systole
• It is influenced by:
  • Vascular resistance (e.g. hypertension, vasopressors)
  • Outflow tract obstruction (e.g. aortic stenosis, HOCM)
  • LV chamber size/volume (e.g. heart failure)
  • Arterial compliance
  • Positive pressure ventilation
• Clinical surrogate
  • Systemic vascular resistance

Contractility

• Intrinsic strength of myocardial contraction that is independent of preload and afterload and primarily influenced by the autonomic nervous system’s regulation of cystolic $\mathrm{Ca}{}^{2+}$
• It is influenced by:
  • Sympathetic and parasympathetic activation
  • Ionotropes
  • Beta blockers
  • Calcium channel blockers
  • Pathologic states which interfere calcium handling and ATP generation
    • Ischaemia/infarction
    • Inflammation (e.g. myocarditis)
    • Acid-base derrangements
    • Hypothermia
  • Heart rate (bowditch effect)
• Clinical surrogate
  • Ejection fraction

Stroke Volume and Ejection Fraction

• The volume of blood ejected from the left ventricle during systole

$$\begin{array}{rl}\text{SV}& =\text{EDV}-\text{ESV}\\ \text{EF}& =\frac{\text{SV}}{\text{EDV}}\end{array}$$

Cardiac Output and Cardiac Index

• Cardiac output is volume of blood ejected forward from heart per unit time (L/min)
• Cardiac index is the cardiac output adjusted for estimated body surface area (L/min/m^2)
  • Normal is 2.5-4.0 L/min/m2

$$\begin{array}{rl}\text{CO}& =\text{SV}\times \text{HR}\\ \text{CI}& =\frac{\text{CO}}{\text{BSA}}\end{array}$$

• Oxygen delivery ($D\mathrm{O}{}_2$) is the product of cardiac output and the oxygen content of arterial blood:

$$D\mathrm{O}{}_2=\text{CO}\times \left(\underset{\mathrm{O}{}_2\text{bound to haemoglobin}}{\underbrace{\underset{\text{Hu¨fner’s constant}}{1.34}\times [\mathrm{Hb}]\times \frac{S_{\text{a}}\mathrm{O}{}_2}{100\%}}}+\underset{\mathrm{O}{}_2\text{dissolved in blood}}{\underbrace{\underset{\text{Solubility constant}}{0.023}\times P_{\text{a}}\mathrm{O}{}_2}}\right)$$

• If there is adequate arterial $\mathrm{O}{}_2$ concentration, then cardiac output is the main determinant of $D\mathrm{O}{}_2$
  • Inadequate $D\mathrm{O}{}_2$ defines Shock

Frank-Starling Mechanism

• Stoke volume is dependent upon LV end-diastolic volume

Analogy

• Stoke volume here is how far the rock will travel when released

Viscosity and Turbulence

• Turbulent flow is more likely when Renold’s number (Re) is high
• Renold’s number can be given by (where $\mu$ is the viscosity of fluid)

$$\begin{array}{rl}\text{Re}& =\frac{\rho \cdot v\cdot d}{\mu }\\ & \propto \frac{Q}{d\cdot \mu }\end{array}$$

Sources

Cardiac Mechanics (preload, afterload, contractility, ejection fraction, and cardiac output) - YouTube