Donald P. Bernstein

Stroke volume equation for impedance cardiography

The studys goal was to determine if cardiac output (CO), obtained by impedance cardiography (ICG), would be improved by a new equation N, implementing a square root transformation for dZ/dtmax/Z0, and a variable magnitude, mass-based volume conductor Vc. Pulmonary artery catheterisation was performed on 106 cardiac surgery patients pre-operatively. Post-operatively, thermodilution cardiac output (TDCO) was simultaneously compared with ICG CO. dZ/dtmax/Z0 and Z0 were obtained from a proprietary bioimpedance device. The impedance variables, in addition to left ventricular ejection time TLVE and patient height and weight, were input using four stroke volume (SV) equations: Kubicek (K), Sramek (S), Sramek-Bernstein (SB), and a new equation N. CO was calculated as SV × heart rate. Data are presented as mean ± SD. One way repeated measures of ANOVA followed by the Tukey test were used for inter-group comparisons. Bland-Altman methods were used to assess bias, precision and limits of agreement. P<0.05 was considered statistically significant. CO implementing N (6.06±1.48 l min−1) was not different from TDCO (5.97±1.41 l min−1). By contrast, CO calculated using K (3.70±1.53 l min−1), S (4.16±1.83 l min−1) and SB (4.37±1.82 l min−1) was significantly less than TDCO. Bland-Altman analysis showed poor agreement between TDCO and K, S and SB, but not between TDCO and N. Compared with TDCO, equation N, using a square-root transformation for dZ/dtmax/Z0, and a mass-based VC was superior to existing transthoracic impedance techniques for SV and CO determination.

Estimating Blood Volume in Obese and Morbidly Obese Patients

Preoperative assessment of blood volume (BV) is important for patients undergoing surgery. The mean value for indexed blood volume (InBV) in normal weight adults is 70 mL/kg. Since InBV decreases in a non-linear manner with increasing weight, this value cannot be used for obese and morbidly obese patients. We present an equation that allows estimation of InBV over the entire range of body weights.

Estimating Ideal Body Weight – A New Formula

A simple formula for estimating ideal body weight (IBW) in kilograms for both men and women is presented. The equation IBW = 22 × H2, where H is equal to patient height in meters, yields weight values midway within the range of weights obtained using published IBW formulae.

Electrophysiologic Principles and Theory of Stroke Volume Determination by Thoracic Electrical Bioimpedance

Thoracic electrical bioimpedance (TEB) is a harmless, noninvasive, user-friendly technology with wide patient acceptance. Stroke volume (SV) determination is important because it helps to define oxygen transport. Measurement of SV by TEB is rooted in concrete, basic electrical theory, as well as in theoretical models of electrical behavior of the human thorax and great thoracic vessels. This article is concerned with basic electrical theory as applied to TEB, signal acquisition, and the origin of the thoracic cardiogenic impedance pulse (delta Z). The appendix of the chapter features a more extensive overview of alternating current theory as applied to electrical bioimpedance.

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

Abstract 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/dtmax), 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 (Δρb(t), Ωcm·s–1), and it is the peak rate of change of the blood resistivity variation dρb(t)/dtmax (Ωcm·s–2) that is the origin of dZ/dtmax. As a consequence of dZ/dtmax peaking in the time domain of peak aortic blood acceleration, dv/dtmax (cm·s–2), it is suggested that dZ/dtmax 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/dtmax/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/dtmax/R, s–2). As necessary for stroke volume calculation, dZ/dtmax/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/dtmax/Z0]0.5, s–1) is multiplied by a volume of electrically participating thoracic tissue (VEPT, mL) and left ventricular ejection time (TLVE, s). To find the bulk volume of the thoracic contents (i.e. VEPT), 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 (aMb). 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 VEPT. 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.

Pressure Pulse Contour-derived Stroke Volume and Cardiac Output in the Morbidly Obese Patient

BackgroundThe pressure pulse contour method for measuring stroke volume (SV) and cardiac output (CO) has come of age. Various methods have been proposed, but at this time no single technique has shown clear superiority over the others. This commentary and review discusses the various methods, and particularly the pressure recording analytical method (PRAM). Dissection of the method shows that vascular wall abnormalities, which are not unique to the morbidly obese state, represent one more biophysical perturbation causing inaccuracy in stroke volume and cardiac output determination. As PRAM is an uncalibrated method, its accuracy depends on certain assumptions that may not fully explain the multitude of combinations and permutations that define pulsatile blood flow; specifically, the area under the pressure curve during systole and the morphologic characteristics of the waveform throughout the cardiac cycle. As a result of incomplete theory, referenced specifically to the morbidly obese individual, PRAM does not faithfully mimic established reference standards of flow; it systematically underestimates stroke volume and cardiac output. Field equations, that is, equations that are applicable over the full gamut of hemodynamic conditions and vascular pathology, are analytically derived truisms. They require input variables that satisfy the natural state of affairs. To realize this state of absolute biophysical bliss, these variables should ideally be measured. Unfortunately, because of the constraints of practicality, shortcuts to the absolute truth are obligatorily required. As a result, pressure pulse contour methods have evolved that employ curve analysis and neural networking techniques, providing uncalibrated facsimiles of SV and CO.

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/dtmax being an ohmic analog of mean aortic blood acceleration. In fact, nowhere in that review paper [2] is the BernsteinOsypka equation or the acceleratory origin of dZ/dtmax 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 peerreviewed 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:

Stroke volume obtained by electrical interrogation of the brachial artery: transbrachial electrical bioimpedance velocimetry

The goal of this study is to measure left ventricular stroke volume (SV) from the brachial artery (BA) using electrical bioimpedance. Doppler-derived SV was used for comparison. Twenty-nine healthy adults were recruited for study. Doppler echocardiographic-derived SV was obtained from the product of distal left ventricular outflow tract cross-sectional area and systolic velocity integral. SV from the BA was obtained by transbrachial electrical bioimpedance velocimetry (TBEV). Application of a current field across the left brachium was effected by injection of a constant magnitude, high frequency, low amperage, alternating current. Therein, a static voltage (U(0)) and pulsatile voltage change (ΔU(t)) were measured and converted to their corresponding impedances, Z(0) and ΔZ(t). TBEV-derived SV was obtained by multiplying a square root value of the normalized, acceleration-based, peak first time derivative of ΔZ(t) by a volume conductor and systolic flow time. Inter-method agreement was determined by the Bland-Altman method. To assess the contribution of blood resistivity variations to ΔZ(t), BA diameters were measured at end-diastole and peak systolic expansion. Results indicate that since the BA demonstrates parabolic, laminar flow, with minimal diameter changes, blood resistivity variations are likely responsible for the derived impedance changes. Bland-Altman analysis shows that SV is obtainable by TBEV from healthy humans at rest.

Stroke volume obtained from the brachial artery using transbrachial electrical bioimpedance velocimetry

Stroke volume (SV) is the quantity of blood ejected by the cardiac ventricles per each contraction. When SV is multiplied by heart rate, cardiac output is the result. Cardiac output (CO), in conjunction with hemoglobin concentration and arterial oxygen saturation are the cornerstones of oxygen transport. Measurement of CO is important, especially in sick humans suffering from decompensated heart disease and systemic diseases affecting the contractility or loading conditions of the heart. Although reasonably accurate invasive cardiac output methods are available, their use is restricted to those individuals hospitalized in the intensive care units. Thus, a robust noninvasive alternative is considered desirable. Impedance cardiography (ICG) is one such method, but in patients with severe heart disease and/or excess extravascular lung water, the method is inaccurate. This paper concerns the introduction of a new method, transbrachial electrical bioimpedance velocimetry (TBEV). The technique involves passage of a constant magnitude, high frequency, and low amperage ac from the upper arm to the antecubital fossa. In all other respects, the operational aspects of TBEV are consistent with ICG. There is good evidence suggesting that the TBEV waveform and its derivatives are generated by blood resistivity changes only.

Body-worn, non-invasive sensor for monitoring stroke volume, cardiac output and cardiovascular reserve

Hemorrhagic shock induced by traumatic injury is a leading cause of mortality on the battlefield and in civilian trauma settings. The first hour following injury can be critical to survival, requiring frequent assessment of vital signs and intravascular volume needs. Conventional vital signs, such as heart rate and blood pressure, are generally nonspecific and slow to change until acute blood loss volume nears 25--30% of total blood volume. The lack of specificity associated with these vital signs limits their usefulness in the early detection and monitoring of acute blood loss. In contrast, measurements of cardiac output (CO), stroke volume (SV) and a new parameter termed Cardiovascular Reserve Index (CRI), follow the progression of hemorrhage and response to intravenous fluid therapy. They are superior indicators of blood loss volume and fluid resuscitation needs. We will demonstrate the implementation of all three parameters on a small, noninvasive body-worn device that is wirelessly connected to a central monitoring system.