Analog models of blood flow

1. ANALOG MODELS OF BLOOD
FLOW
Gilu Francis

2. Mechanical Models (Windkessel)
• Suggested by Otto Frank (1899)
• The aorta and large blood vessels are represented
by a linear compliant air-cell
• Peripheral vessels are replaced by a rigid tube
with a linear resistance
• V= C. P
• Qout =P/R
• where V, P, and C = volume, pressure, and compliance of the
air-cell and are linearly related
• Qout = outflow of the air-cell
• R = linear resistance of the rigid tube
• Pvenous = 0

3. (a) The Windkessel model of the aorta and peripheral circulation.
(b) Electrical model of the Windkessel model.

4. • Conservation of mass requires that

5. Electrical Models
• In order to investigate linear approximations of
complex blood flow phenomena, electrical analogs,
which result in analogous linear differential equations,
were developed (Dinnar, 1981).
• In these models the vessel resistance to blood flow is
represented by a resistor R, the tube compliance by a
capacitor C, and blood inertia by an inductance L.
Assuming that blood flow and pressure are analogous
to the electrical current and voltage, respectively,
blood flow through a compliant vessel (e.g., artery or
vein) may be represented by an electrical scheme.

6. Following Kirchhoff’s law for currents, the
governing differential equation becomes