Techniques for measuring electrical impedance of the human body (bioimpedance) have been devised in bioengineering since the 1960s. These measurements include forcing an AC current through the body (usually at a frequency higher than 10 kHz, to avoid interference with the electrical activity of nervous and muscular tissues), and sensing the voltage drop between two points.
Water and all body fluids (blood, intra and extra cellular fluid, for example) provide the conductive medium of the body. Several measures and studies have been carried on, applying this technique in different parts or regions of the body and using different frequencies, to target different biological information. In numerous applications, only the absolute value of the bioimpedance is to be determined because it is simple to calculate and it provides useful information. In other applications, both amplitude and phase of the complex bioimpedance are measured.
It is relatively difficult to determine precise and reliable mathematical models of bioimpedance, particularly in thoracic regions. The main factors influencing electrical impedance in the chest are the blood in the heart and in the aorta, pleural fluids and pulmonary circulation. Heart pumping, that causes a variable distribution of blood in the heart-aorta region, and respiration are responsible of small variations of thoracic bioimpedance (i.e., the impedance of biologic tissues). From these variations it may be possible to determine heart rate, breath rate, and to evaluate cardiac output (volume of blood pumped by the heart over time).
There is a strong interest in methods of measuring the bioimpedance Zbody, because these measurements typically do not require an invasive technique and the bioimpedance may be correlated to a vast range of physiological parameters. Thus, information from bioimpedance measurements may be seen as potentially useful information in many medical fields.
Furthermore, the simplicity of the measurement, the integrability, reduced size, and low cost of the equipment, make the technique of measuring thoracic bioimpedance particularly suitable to be implemented in wearable or implantable health monitoring systems.
An AC voltage generated by an oscillator is used to control a voltage-to-current converter that delivers a current Iz that is injected through the biologic tissue using two or four electrodes. The voltage on the biologic tissue is sensed, amplified, and AM demodulated for obtaining a base-band signal. The voltage VZ(t) sensed on the electrodes is an AC signal modulated by the bioimpedance Z(t):VZ(t)=|Z(t)|·I0·cos(ωt+Φ(t))
With an AM demodulator it is possible to obtain a base-band signal representing the amplitude |Z(t)| of the impedance, for example, by using the envelope demodulator depicted in FIG. 1, but the phase Φ(t) of Z(t) would be still to be determined.
Another known technique, commonly referred to “synchronous sampling”, for determining the amplitude |Z(t)| and the phase Φ of the impedance, includes sampling the voltage VZ(t) twice in a period: a first sample p being synchronous with the carrier w, and the second sample q being delayed from the first one by one fourth of a carried period T, as schematically shown in FIG. 2. In the hypothesis that the amplitude |Z(t)| is practically constant over each carrier period, the following equations hold:p=|Z|·I0·cos(Φ)q=−|Z|·I0·sin(Φ)from which it is possible to calculate the amplitude and the phase of the impedance.
Unfortunately, these techniques require two sampling channels and relatively onerous calculations that cannot be executed by low cost devices.
An alternative to these onerous calculations includes approximating the amplitude of the bio-impedance with the average of the samples p and q taken into a same period, that is:
                                                      Z                                ≅                                    p              +              q                                      2              ·                              I                0                                                    =                                          Z                                ·                                                    cos                ⁡                                  (                  Φ                  )                                            -                              sin                ⁡                                  (                  Φ                  )                                                                    2              ·                              I                0                                                                        (        1        )            
This technique is suitable for low cost devices, because it may be implemented simply by low-pass filtering the sampled values, though the approximation becomes unacceptably coarse when the phase significantly differs from 0. Moreover, the phase of the bio-impedance is not calculated. A method to estimate the amplitude and the phase of the bio-impedance that may be implemented by low cost devices that have a low computational power may thus be desirable.