FIG 74.1 Windkessel model of the arterial system The Windkessel buffers spurts of water from the pump, while the fire hose functions as a low-resistance conduit (From O'Rourke MF Arterial Function in Health and Disease Edinburgh: Churchill Livingstone; 1982.) FIG 74.2 Electrical analogues of the systemic arterial system (A) Classic two-element Windkessel model with arterial compliance represented by a capacitor (C) and the peripheral resistance by a resistor (R) (B) Modified Windkessel model with addition of a proximal resistor (Zo) to represent characteristic impedance of the proximal aorta (C) Four-element Windkessel model incorporating an inertance element (L) The combination of the cushioning and conduit functions of the arterial tree results in two phenomena: (1) traveling of a pulse wave at a finite speed along the arterial wall and (2) wave reflection at arterial terminations and other discontinuities A more realistic model of a distensible tube with one end receiving pulsatile ejection of blood from the left ventricle and with the other end representing the peripheral resistance has therefore been proposed.140 The pressure wave at any point along the tube represents the result of the incident and reflected waves Elasticity of the tube determines the velocity at which the pulse travels and the timing of arrival of the reflected wave When the tube is distensible, the wave velocity is slow and the reflected wave returns late in diastole With stiffening of the tube, the pulse velocity increases and the reflected wave arrives earlier to merge with the systolic part of the incident wave and results in a higher systolic pressure and a lower diastolic pressure Vascular stiffness is therefore an important mechanical property of the arterial tree and contributes to left ventricular afterload Arterial Impedance as Ventricular Afterload Ventricular afterload can be conceptualized as all the external factors that oppose ventricular ejection and contribute to myocardial wall stress during systole The hydraulic load of the systemic arterial system has therefore been taken to represent the afterload presented to the systemic ventricle.141,142 The total arterial hydraulic load comprises three components: resistance, stiffness, and wave reflection, all of which can be obtained from impedance spectra based on analysis in the frequency domain Vascular Resistance Vascular resistance is commonly used in the clinical setting as an index of systemic ventricular afterload The electrical analogue for vascular resistance is described by the Ohm's law, which applies to direct electric current circuit For a steady flow state, the vascular resistance is derived by dividing pressure gradient by volume flow As the systemic venous pressure is very small when compared with the mean aortic pressure, the systemic arterial resistance can be approximated as mean aortic pressure divided by cardiac output Nonetheless, as arterial blood flow is pulsatile in nature, the use of vascular resistance alone to describe afterload is deemed inadequate Vascular Impedance For pulsatile flow, the corresponding pressure-flow relationship is vascular impedance This is analogous to the voltage-current relationship of an alternating current electrical circuit To analyze the mathematical relationship between pressure and flow waves, Fourier analysis is used to decompose these complex nonsinusoidal waves into a set of sinusoidal waves with harmonic frequencies that are integral multiples of the fundamental wave frequency Vascular input impedance is defined as the ratio of pulsatile pressure to pulsatile flow The aortic input impedance is particularly relevant as it characterizes the mechanical property of the entire systemic arterial circulation and represents the hydraulic load presented by the systemic circulation to the left ventricle.141,142 To obtain the aortic input impedance spectrum, the ascending aortic flow is measured by an electromagnetic flow catheter, while the pressure is measured by a micromanometer mounted onto the catheter Noninvasive determination of aortic input impedance involves the use of Doppler echocardiography to measure flow and tonometry to obtain a carotid, subclavian, or synthesized aortic pressure waveform, the latter based on the radial arterial waveform An example of the human aortic input impedance spectra is shown in Fig 74.3 For a heart rate of 60 beats/min, the fundamental frequency is 1 Hz, the second harmonics is 2 Hz, and so forth The vascular impedance modulus at different harmonics is the ratio of pressure amplitude to flow amplitude The phase difference is the delay in phase angle between the pressure and flow harmonics, which is analogous to time delay in the time domain