

Impedance plethysmography: basic principles.
Correspondence Address:
Impedance Plethysmography technique has been discussed with explanation of two compartment model and parallel conductor theory for the estimation of peripheral blood flow and stroke volume. Various methods for signal enhancement to facilitate computation of blood flow are briefly described. Source of error in the estimation of peripheral blood flow is identified and the correction has been suggested.
The biological tissues show fivehundred fold variation in the values of their electrical resistivity. For instance the electrical resistivity values of urine, plasma, cerebrospinal fluid, blood, skeletal muscle, cardiac muscle, lung tissue, fat and bone are 30, 63, 65, 150, 300, 750, 1275, 2500 and 16600 ohmcm respectively[1]. Though these values are much higher as compared to that of a good conductor of electricity, like copper (1.724 x 106 ohmcm), the wide variation in the values of resistivity from one biological tissue to another makes the measurement of electrical resistance useful in understanding the functioning and viability of internal organs of the body. In practice, measurement of electrical impedance is made in place of resistance due to technical reasons and is carried out by using a sinusoidal current source in the frequency range of 20 KHz to 100 KHz. Some of the physiological quantities estimated from electrical impedance measurement include respiration, blood flow and volume changes, autonomic nervous system activity, muscle contraction, eye movement, endocrine activity and the activity of brain cells[2]. These measurements have led to the introduction of a new technique viz. Impedance Plethysmography in the field of Medicine.
The history of impedance plethysmography (IPG) extends back to 1932 when Atzler and Lehmann observed changes in the capacitance between two parallel plates kept across the human chest. These changes were observed to be synchronous with the activity of the heart. The technique as it exists today was first introduced by Jan Nyboer and coworkers[8] in 1940. In this technique the electrical impedance of any part of the body is measured by either constant current method or bridge method and variations in the impedance are recorded as a function of time. Since blood is a good conductor of electricity, the amount of blood in a given body segment is reflected inversely in the electrical impedance of the body segment. Pulsatile blood volume increase in the body segment caused by systemic blood circulation therefore, causes proportional decrease in the electrical impedance. Variation in the electrical impedance thus yields adequate information about the blood circulation. A typical impedance plethysmograph system is comprised of a sinewave generator followed by voltage to current converter. This current (4 mA r.m.s.) is passed through the body segment of interest with the help of two surface electrodes, called as the current electrodes. These electrodes are made of braided wire and applied in the form of loop around the body segment. Voltage signal developed along the current path is sensed with the help of another pair of electrodes, called as the voltage electrodes. The amplitude of the signal thus sensed is directly proportional to the electrical impedance of the body segment. Thus, amplification and detection of this signal yields instantaneous electrical impedance (Z) of the body segment. Difference between the instantaneous electrical impedance and initial value of electrical impedance (Zo) obtained by sample and hold circuit gives variation in the impedance as a function of time, called the AZ (t) waveform. First time derivative of the impedance (dZ/dt) is also obtained with the help of an electronic differentiator to give the rate of change of impedance as shown in [Figure  1]. How the conductivity changes within a volume conductor are sensed with the help of surface electrodes is illustrated by Baker LE[1]. He has shown that the current density distribution in an isotropic volume conductor is uniform and therefore the equipotential lines which appear on the surface of the conductor are parallel. The current density distribution and the equipotential lines get modified when a sphere of conducting material or that of an insulating material is placed with its centre along the axis of the volume conductor. The potential difference produced by equipotential lines intersecting the voltage electrodes in these cases has been shown to be significantly different[1],[6].
For estimation of blood flow using impedance plethysmography, two compartment model is more closer to practical situation[10]. In this model body segment is considered as a uniform cylinder with a column of blood along its axis and body tissue surrounding the blood column (see [Figure  2]). If L be the distance between the sensing electrodes, the resistance R of the body segment is given as: 1/R = 1/Rt + 1/Rb where Rt is the resistance of the surrounding tissue and Rb is the resistance of the blood column. If At and Ab are the crossectional areas and pt and pb are the resistivities of the surrounding tissue and the blood column respectively, by Ohm's law Rt and Rb are given as: Rt = ?t L/At and Rb = ?b L/Ab. ?t ?b L Therefore R =  ?b At + ?t Ab ?t ?b L2 =  , ?b Vt + ?t Vb where Vt and Vb are the total volume of surrounding tissue and the blood conductor respectively. Assuming that a volume of blood dVb enters the region between sensing electrodes, it results in a small increase in the area of the blood conductor and does not alter the volume of the surrounding tissue. Accepting this fairly reasonable physiological assumption, the expression for the change in resistance (dR) of the body segment in situ can be written as: ?b ?t2 L2 dR =   dVb. (?t Vb + ?b Vt)2 Therefore, the change in blood volume dVb can be written as: (?t Vb + ?b Vt)2 dVb =  dR ?t2 ?b L2 Substituting (?t Vb + ?b Vt)2 = (?t ?b L2/R)2, L2 dVb = ?b  dR.  (1) R2 Keeping in mind the basic assumptions that (a) crosssectional area of the tissue mass remains constant, (b) the area of the blood conductor increases with the entry of the blood in the region between sensing electrodes and (c) the length L remains unchanged, equation (1) can be used for estimation of blood volume dVb entering into the body segment. However, R in equation (1) needs to be replaced by Z as the same is measured using an alternating current. Therefore, L2 dVb =  ?b  dZ  (2) Z2 The negative sign merely signifies that the entry of the blood produces a decrease in the electrical impedance. By convention however, decrease in impedance is recorded as positive deflection by an IPG system.
Equation (2) is in complete agreement with the parallel conductor theory proposed by Nyboer J[7]. According to this theory, assuming Zo to be the impedance of the body segment at the end diastole, the action of systole is to place an additional impedance Z' in parallel with Zo. If Z is the equivalent impedance of Zo and Z’ in parallel, Z’ is given as: Zo. Z Z’ =   Zo Z In paractice Zo and Z differ only by a very small amount (0.4%), so the above equation can be written as: Zo2 Zo2 Z’ =   ZoZ dZ Assuming the volume of blood which corresponds to Z' can be represented as uniform conductor having a length L and area of cross section 'a', Z' can be replaced by pb L/a or pb L2/dV, where pb is the resitivity of blood and dV is the volume of blood entering into the body segment. The above equation therefore becomes: L2 Zo2 pb =   dV dZ. L2 or dV =  ?b  dZ.  (3) Zo2
When equation (2) or (3) is put into practice to calculate the volume of blood ?Vb entering the body segment between the sensing electrodes during one cardiac cycle, both physiological and physical factors come into play. It is important to note that the peak to peak amplitude of AZ(t) waveform is a measure of the difference of the blood flow into and out of the body segment between the sensing electrodes. Therefore, one can either resort to Nyhoer's back projection method[7] or Kubicek's forward slope extension method[4] for measurement of total AZ for the entire systolic period in order to calculate the volume of blood entering the body segment under study. Kubicek et al[5] introduced dZ/dt waveform for the estimation of stroke output of the heart and replaced dZ in equation (3) by the product (dZ/dt)m and T for estimating the stroke volume as follows: L2 [dZ] Stroke volume = ?b  T   (4) Zo2 [dt] m where (dZ/dt)m is the maximum height of the dZ/dt waveform representing the initial rate of change of impedance before any significant runoff has occurred and T is the time for which the aortic valve is open. For accurate estimation of peripheral blood flow, ?Z (t) signal is enhanced using venous occlusion principle [6]. A cuff placed around the proximal part of the limb is inflated (to 5060min Hg) so as to occlude the venous return from the segment but not to impede the arterial flow as shown in [Figure  3] on page 62. With the cuff inflated for Ta seconds the impedance of the limb segment falls by a value of ?Za ohms. If Zo be the initial impedance, C be the mean circumference and L the length of the body segment in question, blood flow into the segment during the time interval Ta seconds is given from equation 3 as follows: L2  ?V (in Ta seconds) = ?b  ?Z?. Zo2 Therefore blood flow into the segment per minute = L2  ?Za ?b   x 60. Zo2 Ta Kubicek et a1[5] and Mohapatra et al[6] substituted Zo C2L/4? in place of pb L2 in this equation in order to eliminate ?b. This gave blood flow into the segment per minute as: C2L 60   ?Za. 4? Ta Since C2L/4? is the volume of the limb segment, it is possible to obtain blood flow in ml per 100 ml of body tissue per minute as: 6000 x ? Za   (5) Zo Ta This method was used for the estimation of peripheral blood flow by most of the investigators. The application of venous occlusion principle was extended to the assessment of venous capacitance and maximum venous outflow in patients with deep vein thrombosis by Wheeler et al[11] and Johnston et al[3]. With the proximal veins occluded, they allowed the arterial inflow into the segment till the AZ (t) waveform saturated. Sudden deflation of the cuff thereafter produced a rapid rise in the impedance as shown in [Figure  3]. This waveform was named as occlusive impedance phlebogram and the upstroke and the downstroke of this waveform were used to obtain proportional values of venous capacitance and maximum venous outflow respectively.
Parulkar et al[9] extended the use of dZ/dt waveform for the assessment of peripheral blood flow. They replaced dZ in equation (3) by the area under the systolic wave of dZ/dt wave from for estimating blood volume change in the limb segment during a cardiac cycle. They further replaced pb L[2]/Zo in equation (3) by volume V of the limb segment. These substitutions and division of both sides of the equation by V gave blood flow into the segment during a cardiac cycle per unit ml of body tissue as: 1 dz  systole  dt. Zo dt Multiplication by 1000 yielded blood flow in ml per 1000 ml of body tissue per cardiac cycle (blood flow index) as 1000 dZ dt.   dt. Zo systole dt For the purpose of simplicity the integration in this equation was approximated by half of the product of (dZ/dt)m and duration of systolic wave (Ts). This simplification yielded blood flow index (BFI) as: 500 Ts (dZ/dt)m / Zo  (6) In view of the authors, while deriving equations (5) and (6) most of the investigators have overlooked the fact that ?b is not the mean resitivity of the body segment under investigation. Assuming p to be the mean resistivity of the body segment, which has person to person variation and also location to location variation even in the same subject, the right hand side of equations (5) and (6) needs to be multiplied by ?b/? in order to have accurate estimation of blood flow.
The authors are thankful to Shri MK Gupta, Asso. Director, E & I Group, BARC, Shri BR Bairi, Head, Electronics Division, BARC and Shri KR Gopalakrishnan, Head, Nuclear Instrumentation Section, BARC for encouraging this work.


