Bernstein-Osypka stroke volume equation for impedance cardiography: citation correction

Sir: Suttner et al. [1] are to be congratulated on a well designed and comprehensive study comparing thermodilution cardiac output (TDCO) to the results obtained from a recently introduced, state-of-the-art, cardiac output computer, utilizing the technology of transthoracic electrical bioimpedance. As correctly stated by the authors, the computer implements the Bernstein-Osypka stroke volume equation. Unfortunately, however, the authors have inadvertently misquoted reference 12 in their paper [2], which they offer as a valid citation for presentation of the Bernstein-Osypka equation and the concept of dZ/dt _max being an ohmic analog of mean aortic blood acceleration. In fact, nowhere in that review paper [2] is the Bernstein-Osypka equation or the acceleratory origin of dZ/dt _max discussed. As correctly cited by Schmidt et al. [3], which is reference 16 in the paper of Suttner et al. the equation was first introduced and published in 2003 as a United States patent (no. 6:511:438 B2, 28 January 2003; D.P. Bernstein, M.J. Osypka, 2003, “Apparatus and method for determining an approximation of the stroke volume and the cardiac output of the heart”). Within the scope of the patent, a variation of the core Bernstein-Osypka equation was published as a peer-reviewed article in July 2005. In that paper the theoretical assumptions, derivation, and rationale for the new equation were presented, including a comparison study with TDCO in post-operative cardiac surgery patients. Shortly after publication of [4] the second peer-reviewed paper, that of Schmidt et al. [3], appeared. As Suttner et al. did not insert the equation into their methods section, the following abbreviated version of the Bernstein-Osypka equation is offered for archival purposes in the journal:

$$ SV_{\text{B}-\text{O}} = \frac{V_{\text{ITBV}}}{\zeta^n} \sqrt{\frac{\text{d}Z/\text{d}t_{\max}}{Z_0 }} T_{\text{LVE(c)}} $$

where V _ITBV = intrathoracic blood volume (ml), ζ = index of transthoracic aberrant electrical conduction, dZ/dt _max = peak rate of change of the blood resistivity (velocity) component of the transthoracic cardiogenic impedance pulse variation (ohmic mean acceleration) (Ω s⁻²), Z ₀ = transthoracic base impedance (Ω), $\sqrt{(\text{d}Z/\text{d}t_{\text{max}})/Z_0} = \text{acceleration}\\ \text{step-down transformation }(\text{s}^{-1})$, T _{LVE (c)} = heart rate-corrected left ventricular ejection time(s) [1, 3]. In [4] T _LVE is implemented without heart rate correction.