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ANALOG MODELS OF BLOOD
FLOW
Gilu Francis
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
(a) The Windkessel model of the aorta and peripheral circulation.
(b) Electrical model of the Windkessel model.
• Conservation of mass requires that
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.
Following Kirchhoff’s law for currents, the
governing differential equation becomes
Analog models of blood flow

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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