Page 159 - Computational Modeling in Biomedical Engineering and Medical Physics

148 Computational Modeling in Biomedical Engineering and Medical Physics

resistivity of blood that occurs with its velocity (Moskalenko and Naumenko, 1959; Visser,
1989; Visser, 1992). Within the assumptions and limits of the parallel conductor theory
(Shimazu et al., 1982) for an equivalent cylindrical region of the body, for instance arm or
foot of length L (the distance in between the voltage electrodes), the decrease of the imped-
ance, ΔZ, is related to the blood volume increase, ΔV,through
ρL 2
ΔVtðÞ 52 2 ΔZtðÞ; ð5:3Þ
Z
where ρ is the electrical resistivity of the blood, and Z is the per cycle time-averaged value.
The change in ZtðÞ is supposedly produced only by the change in the blood volume
within the measurement region, which is equated to an equivalent cylindrical region that
is connected, electrically, in parallel with the body segment [forearm in the work by
Shimazu et al. (1982)], and modeled as a series of parallel conductors that represent artery,
tissue, and vein. The time scale of the current source (typically for IPG 1 mA at 50 kHz)
is much smaller than that of the arterial blood flow (60 80 bpm), with which ΔV and
ΔZ fluctuate. The initial splitting of the impedance into two parts (Nyboer et al., 1950)
ZtðÞ 5 ZtðÞ 1 ΔZtðÞ; ð5:4Þ

presents its dynamics as the result of a quasi-periodic drift at the heart frequency, ΔZ
(t), about an average value at the breathing frequency, ZtðÞ, with different magnitudes
and spectra, which bodes the basis to the evaluation of the stroke volume, SV.
The SV usually refers to the left ventricle. It is calculated by subtracting the blood end-
systolic volume (ESV) from its end-diastolic volume (EDV) just preceding the beat, in the
ventricle. The SVs of the ventricles are usually equal, B 70 mL in a healthy 70 kg man. The
SV correlates with the cardiac function: the cardiac output (CO) is calculated by multiplying
SV and heart rate (HR), and the ejection fraction (EF) results by dividing SV through EDV
(Maceira et al., 2006).

Bioimpedance methods and models
On the basis of the plethysmography, Kubicek et al. (1966) proposed a thoracic bioimpedance
method, which evolved later to the ICG. ICG uses four special band electrodes around the
body and utilizes a signal-processing model to estimate SV (Kubicek et al., 1966, 2006;
Vedru, 1994; Woltjer et al., 1997). Later proposed, the integral rheography of the body
(IRB) is considered to be a reliable, not expensive, technically simple method for the assess-
ment of overall hemodynamic features of the body. Its efficiency was proved in massive
examinations of large-scale cohorts of people. It was intensively used in many fields of medi-
cine, for example, surgery, resuscitation, oncology, and dentistry (Misiura, 2017). For model-
ing a perfect contact between the band electrodes and the body, the cylindrical conductor
model SV reduces to Eq. (5.3), which was boldly applied to regions as complex as the thorax.