Impedance cardiography: Pulsatile blood flow and the biophysical and electrodynamic basis for the stroke volume equations

Impedance cardiography (ICG) is a branch of bioimpedance primarily concerned with the determination of left ventricular stroke volume (SV). As implemented, using the transthoracic approach, the technique involves applying a current field longitudinally across a segment of thorax by means of a constant magnitude, high frequency, low amplitude alternating current (AC). By Ohm’s Law, the voltage difference measured within the current field is proportional to the electrical impedance Z (Ω). Without ventilatory or cardiac activity, Z is known as the transthoracic, static base impedance Z₀. Upon ventricular ejection, a characteristic time dependent cardiac-synchronous pulsatile impedance change is obtained, ΔZ(t), which, when placed electrically in parallel with Z₀, constitutes the time-variable total transthoracic impedance Z(t). ΔZ(t) represents a dual-element composite waveform, which comprises both the radially-oriented volumetric expansion of and axially-directed forward blood flow within both great thoracic arteries. In its majority, however, ΔZ(t) is known to primarily emanate from the ascending aorta. Conceptually, commonly implemented methods assume a volumetric origin for the peak systolic upslope of ΔZ(t), (i.e. dZ/dt_max), with the presumed units of Ω·s^–1. A recently introduced method assumes the rapid ejection of forward flowing blood in earliest systole causes significant changes in the velocity-induced blood resistivity variation (Δρ_b(t), Ωcm·s^–1), and it is the peak rate of change of the blood resistivity variation dρ_b(t)/dt_max (Ωcm·s^–2) that is the origin of dZ/dt_max. As a consequence of dZ/dt_max peaking in the time domain of peak aortic blood acceleration, dv/dt_max (cm·s^–2), it is suggested that dZ/dt_max is an ohmic mean acceleration analog (Ω·s^–2) and not a mean flow or velocity surrogate as generally assumed. As conceptualized, the normalized value, dZ/dt_max/Z₀, is a dimensionless ohmic mean acceleration equivalent (s^–2), and more precisely, the electrodynamic equivalent of peak aortic reduced average blood acceleration (PARABA, d<v>/dt_max/R, s^–2). As necessary for stroke volume calculation, dZ/dt_max/Z₀ must undergo square root transformation to yield an ohmic mean flow velocity equivalent. To compute SV, the square root of the dimensionless ohmic mean acceleration equivalent ([dZ/dt_max/Z⁰]^0.5, s^–1) is multiplied by a volume of electrically participating thoracic tissue (V_EPT, mL) and left ventricular ejection time (T_LVE, s). To find the bulk volume of the thoracic contents (i.e. V_EPT), established methods implement exponential functions of measured thoracic length (L(cm)ⁿ) or height-based thoracic length equivalents (0.01×%H(cm)ⁿ). The new method conceptualizes VEPT as the intrathoracic blood volume (ITBV, mL), which is approximated through allometric equivalents of body mass (aM^b). In contrast to the classical two-element parallel conduction model, the new method comprises a three-compartment model, which incorporates excess extra-vascular lung water (EVLW) as a component of both Z₀ and V_EPT. To fully appreciate the evolution and analytical justification for impedance-derived SV equations, a review of the basics of pulsatile blood flow is in order.