Fundamentals of Cardiac Hemodynamics

1. End-Diastolic LV Volume (EDV): The volume of blood in the ventricle at the end of the filling phase (diastole).
2. End-Systolic LV Volume (ESV): The volume of blood remaining in the ventricle after contraction (systole).

The formula for Stroke Volume is:

$$SV = EDV - ESV$$

Cardiac Reserve and Cardiac Index

Beyond simple output, clinicians look at Cardiac Reserve, which is the difference between a patient's normal resting CO and the maximum CO they are capable of pumping during stress. For example, if a patient's resting CO is $5 \text{ L/min}$ but they can reach $20 \text{ L/min}$ during exercise, their cardiac reserve is $15 \text{ L/min}$.

To account for differences in body size, we use the Cardiac Index (CI). This indexes the Cardiac Output to the patient's Body Surface Area (BSA):

$$CI = \frac{CO}{BSA}$$

Preload, Afterload, and Contractility

Hemodynamics are heavily influenced by the mechanical environment of the heart, specifically preload and afterload.

Preload

Preload is the volume load delivered to the ventricle, specifically the amount of blood in the ventricle at the end of diastole. It is heavily influenced by venous return.

Factors that increase preload include:

• Increased blood volume (hypervolemia).
• Increased venous pressure.
• Decreased intrathoracic pressure (e.g., during inhalation).

The Frank-Starling Principle (or length-tension relationship) states that the heart adapts to preload by pumping the volume delivered to it. An increase in preload causes greater stretch of the myocardial fibers, which leads to a greater force of contraction and a higher stroke volume.

Afterload

Afterload is the resistance to ventricular emptying; it is the force the ventricle must overcome to circulate blood. High afterload, caused by conditions like hypertension or valvular stenosis, increases cardiac workload and can decrease both SV and CO.

Contractility

Contractility, also known as inotropic force, is the force of contraction at a given preload and afterload. Unlike the Frank-Starling mechanism, contractility is an intrinsic property of the muscle. The SNS increases contractility, while structural diseases (like an infarct) can cause a negative inotropic response.

Clinical Calculations in Echocardiography

The Bernoulli Equation

In echocardiography, we use the Bernoulli principle to estimate pressure gradients. The principle states that a change in pressure is equal to four times the velocity squared:

$$\Delta \text{Pressure} = 4v^2$$

This is frequently used to calculate the Right Ventricular Systolic Pressure (RVSP) by measuring the velocity of tricuspid regurgitation ($TR_{max\ vel}$). To find the total RVSP, you must add the Right Atrial (RA) pressure to the pressure gradient calculated via Bernoulli:

$$RVSP = 4(TR\ V_{max})^2 + RAP$$

Exam Tip: When using the Bernoulli equation in echo, ensure your Doppler beam is aligned as close to $0^{\circ}$ to the flow as possible. An offset of even $20^{\circ}$ can lead to an underestimation of velocity, which is then squared in the equation, resulting in significant errors.

The Continuity Equation

The Continuity Principle states that the flow rate at any given point must remain constant. In the context of the heart, this means stroke volume must remain constant at any two points.

In clinical practice, we use a modified version of this to calculate valve areas (such as the Aortic Valve Area). This involves using the Velocity Time Integral (VTI), which represents the distance blood travels during one heartbeat:

$$\text{Valve Area}_{(1)} = \frac{0.785 \times d_{(2)}^2 \times VTI_{(2)}}{VTI_{(1)}}$$

Where $d$ is the diameter and $0.785$ is a constant derived from the area of a circle formula ($A = \frac{1}{4}\pi d^2$).