**2. Theoretical and experimental models**

kidney disease.

#### **2.1 Principles of bioimpédance in hemodialysis**

Many different instruments have been marketed using algorithms based on different equations predicting body composition from impedance measurements [22, 23, 24, 25]. The validity of these different equations remains a question of debate since most have been established empirically. Moreover, the equations actually used by the algorithms of commercial microcomputers are not readily accessible, making it rather difficult to discuss their validity or make necessary corrections. The voltage produced by the current is measured to calculate the impedance. The relationships between impedance and other variables such as body water volume have been established using statistical correlations observed in specific populations rather than on a real biophysical basis. Actually, the theoretical basis can be summarized by the following statement: the human body is a complex conductive volume composed of heterogeneous tissues and intra- and extracellular compartments in perpetual movement.

Basically, the algorithms applied are based on regression laws used as a tool predictive of the relationship between two or more body variables constituting a database. Thus for total body water (TBW) the regression equation is written as [26](with H: Height):

$$\text{TBW} = \text{a.} \,\text{H}^2 \,/\text{ R} + \text{b.} \,\text{weight} + \text{c.} \,\text{Age} + \text{d.} \tag{2}$$

TBW is measured in a large population using a gold standard, e.g. isotopic dilution (Fig. 3). The statistical software then uses regression analysis to establish the best fitting equation describing the relationship between TBW and the different measurements, e.g. height, weight, age, gender, resistance… For subsequent resistance measurements, a software inserts the recorded data into the accepted formula and delivers the results as TBW (Fig. 4).

#### **2.1.1 Prediction of total body water**

#### **2.1.1.1 Historical background**

One of the most commonly cited relationship is the cylinder model where the volume of a conductive cylinder is function of its length (L) and its resistance (R). High frequency current penetrates into the cell and runs across body fluids. A TBW value can thus be obtained by modeling the human body as a sum of cylinders. Devices applying this method are calibrated by dilution techniques. These devices rely on the following relationship:

$$\text{TBW} = \text{(a.H2)}/\text{R} + \text{c.}\tag{3}$$

Bioimpedance Measurement in the Kidney Disease Patient 171

Three techniques are generally described, using multiple frequencies, high and low

The multifrequency mode is the most widely studied. It is based on the Cole-Cole model and allows differentiation between intra- and extra-cellular volumes. But the relationship between resistance and water volume is not linear, so that the multifrequency mode is associated with Hanaï theory, which takes into account the non-conductive element, connected in a parallel, to distinguish the different compartments. The parallel model described by Fricke takes into account the conductive elements exhibiting a certain degree of resistance connected in parallel and isolated by a cell membrane. This method has been validated by Van Loan [29, 30, 31]. At high and low frequencies, the Hanaï theory takes into account the presence of non-conductive elements connected in parallel. The measurement improvement mainly concerns the extracellular compartment [32, 33]. At the unique 50 kHz frequency, the theory enables a measurement of TBW (and lean body mass) [28]. Many different formulas have been published, using the term: *H²/R50*, where *H* is the subject's height in cm and *R50* the wrist-ankle resistance. These methods have not been validated and generally cannot detect small volume changes. This limitation may be related to the relative uniformity of tissue elements considered in the formulas which do not take into consideration changes in tissue composition. Simple calculations allow extrapolations for

These different theories can then be applied to measure body segments or the whole body [35, 36, 37, 38]. For segmental measures, the mathematical models remain empirical and actual measures remain dependent on electrode position. Differences appear in comparison with whole body measures with a trend to underestimate water loss during a dialysis session compared with a segmental measurement, particularly in the event of hypotension [39]. One advantage is that the segmental technique would be less sensitive to changes in

The problem is then to transform a resistance measurement into a calculation of body composition. Geometry plays an important role. As seen in Figure 6, three objects with a constant height exhibit the same resistance from top to bottom, despite their different

1 2 8.7

Fig. 6. Complexity of the body geometry-measurement relationship

**2.1.1.2 Theories used** 

extracellular water [34].

**2.1.1.3 From theory to measure** 

volumes [41].

frequencies, and a unique 50 kHz frequency.

patient position from one measure to the next [40].

Fig. 3. Correlation between isotopic dilution and bioimpedance (BIS)

Fig. 4. Exemple of bioimpedance analysis block diagram [23] (R : resistance, X : Reactance)

Thomasset [27, 28] was the first, in 1963, to use two frequencies (1 et 100 kHz), to measure extracellular and total water respectively using the Cole-Cole model (Fig.5). Subsequently, several different formulas have been proposed based on regression equations.

Fig. 5. Cole-Cole model

#### **2.1.1.2 Theories used**

170 Technical Problems in Patients on Hemodialysis

Analyzer

Fig. 4. Exemple of bioimpedance analysis block diagram [23] (R : resistance, X : Reactance) Thomasset [27, 28] was the first, in 1963, to use two frequencies (1 et 100 kHz), to measure extracellular and total water respectively using the Cole-Cole model (Fig.5). Subsequently,

several different formulas have been proposed based on regression equations.

50 kHz

R, X processor equation

Body Composition

Fat Free Mass Body Cell Mass Total Body Water Intra Cellular Water Extra Cellular Water

Phase Angle Capacitance Other Parameters

R

f Increasing frequency

R0

Resistance (

Fig. 3. Correlation between isotopic dilution and bioimpedance (BIS)

Human Body

Body Cell Mass

Extra Cellular Mass

Fat Mass

Fig. 5. Cole-Cole model

X

Reactance (

**Z** 

R50 <sup>R</sup>

Three techniques are generally described, using multiple frequencies, high and low frequencies, and a unique 50 kHz frequency.

The multifrequency mode is the most widely studied. It is based on the Cole-Cole model and allows differentiation between intra- and extra-cellular volumes. But the relationship between resistance and water volume is not linear, so that the multifrequency mode is associated with Hanaï theory, which takes into account the non-conductive element, connected in a parallel, to distinguish the different compartments. The parallel model described by Fricke takes into account the conductive elements exhibiting a certain degree of resistance connected in parallel and isolated by a cell membrane. This method has been validated by Van Loan [29, 30, 31]. At high and low frequencies, the Hanaï theory takes into account the presence of non-conductive elements connected in parallel. The measurement improvement mainly concerns the extracellular compartment [32, 33]. At the unique 50 kHz frequency, the theory enables a measurement of TBW (and lean body mass) [28]. Many different formulas have been published, using the term: *H²/R50*, where *H* is the subject's height in cm and *R50* the wrist-ankle resistance. These methods have not been validated and generally cannot detect small volume changes. This limitation may be related to the relative uniformity of tissue elements considered in the formulas which do not take into consideration changes in tissue composition. Simple calculations allow extrapolations for extracellular water [34].

These different theories can then be applied to measure body segments or the whole body [35, 36, 37, 38]. For segmental measures, the mathematical models remain empirical and actual measures remain dependent on electrode position. Differences appear in comparison with whole body measures with a trend to underestimate water loss during a dialysis session compared with a segmental measurement, particularly in the event of hypotension [39]. One advantage is that the segmental technique would be less sensitive to changes in patient position from one measure to the next [40].

#### **2.1.1.3 From theory to measure**

The problem is then to transform a resistance measurement into a calculation of body composition. Geometry plays an important role. As seen in Figure 6, three objects with a constant height exhibit the same resistance from top to bottom, despite their different volumes [41].

Fig. 6. Complexity of the body geometry-measurement relationship

Bioimpedance Measurement in the Kidney Disease Patient 173

Finally, the superiority of multifrequency impedance over the monofrequency impedance has not been demonstrated. Similarly no one formula has been found superior to the others.

Several studies have been conducted in hemodialysis patients. Three approaches have been particularly fruitful, the nomovolemia/hypervolemia curves established by Chamney [46, 47, 48, 49], the resistance/reactance curves by Piccoli [50, 51, 52] and Zhu's continuous curves [53, 54]. Although essential, these approaches will not be detailed here. Readers may

It has been shown that resistance/reactance curves are modified reversibly by changes in body position (reclining, sitting, upright position). Physical studies have demonstrated a modification in the lines of current passing through the body with changes in body position. In addition, length and resistance measures vary [55]. In the healthy subject, comparison of whole body and segmental measures shows an increase in resistance in all sectors (peripheral and central compartments) when moving from the upright to the reclining position [56, 57]. This is logical for the peripheral sector, related to the decrease in water in this sector which is redistributed to the central sector by cancelation of the gravity effect. However, surprisingly, resistance increases in the trunk, despite the increase in water. One explanation is that impedancemetry poorly evaluates the central sector. In the dialysis patient, and using the segmental mode, resistances vary with electrode position. The volumes calculated using the segmental mode are much higher than with the whole body mode and than with the anthropometric formulas [58]. In conclusion, segmental measures

are insufficient to eliminate artifacts related to changes in body position.

**2.2.1.2 Underestimation of extracellular volume variations in dialysis patients** 

These calculations are made from variations in plasma sodium content, accepting the hypothesis of zero sodium exchange between intra- and extra-cellular compartments or with the dialysis solute (obviously a false assumption). These results show that the contribution of the extracellular volume is superior to that measured by impedancemetry, with certain aberrant results [59, 60]. Conductivity variability is well known in dialysis and is most likely responsible for these problems of fluctuating resistivity for different

Tanita (TBF-300) is a device for measuring body impedance between the two legs. It is simple to use and does not require electrodes. Manufactured in Japan, the devise presents as a weight scale with a built-in body composition analyzer which calculates TBW, total body fat and fat-free body mass [61]. The National Institute of Health has not validated the results. For these measurements, the person stands barefoot on a four-point platform. Impedance measurements are made using a high frequency (50kHz) and low intensity (500

**2.2 Available clinical applications** 

usefully refer to the cited references.

**2.2.1 Problems and solutions 2.2.1.1 Changes of body position** 

compartments during dialysis.

**3.1 Tanita (TBF-300)** 

**3. Experimental materials and methods** 

µA) current between the feet. (formula are not known)

Thus in many models, the human body is considered to be the sum of five compartments (Fig. 7) (the four limbs and the trunk), with a dimension homogeneity factor Kb.

Fig. 7. The 5-compartment human body model

The homogeneity factor is calculated from the resistance of a cylinder (R) which is function of its resistivity (, its length (L) and its cross-section (A) [42]

$$\mathbf{R} = \rho \frac{\mathbf{L}}{\mathbf{A}} \tag{4}$$

Then, by calculating the volume of the cylinder, and separating, arms, legs and trunk, the following formula is established with *l* for leg, *t* for trunk and *a* for arm:

$$\mathbf{R} = \rho \mathbf{4} \pi \mathbf{1} \left( \frac{\mathbf{L\_1}}{\mathbf{C\_1^2}} + \frac{\mathbf{L\_1}}{\mathbf{C\_1^2}} + \frac{\mathbf{L\_a}}{\mathbf{C\_a^2}} \right) \tag{5}$$

This formula, together with the classical formula for the volume of a cylinder, yields the dimension homogeneity constant, KB, which represents a characteristic anthropometric parameter independent of the electrical parameters.

$$\mathbf{V} = \mathbf{K}\_{\text{B}} \rho \frac{\mathbf{L}^2}{\mathbf{A}} \tag{6}$$

$$\mathbf{K\_{b}} = \frac{1}{\mathbf{L}^{2}} \left( \frac{\mathbf{L\_{l}}}{\mathbf{C\_{l}}^{2}} + \frac{\mathbf{L\_{t}}}{\mathbf{C\_{t}}^{2}} + \frac{\mathbf{L\_{a}}}{\mathbf{C\_{a}^{2}}} \right) \left( 2\mathbf{L\_{a}}\mathbf{C\_{a}^{2}} + 2\mathbf{L\_{1}}\mathbf{C\_{1}^{2}} + \mathbf{L\_{t}}\mathbf{C\_{t}^{2}} \right) \tag{7}$$

#### **2.1.1.4 Formula validity and limitations**

When these formulas are applied to measure body composition, the result is always significantly different from gold standard measurements. Thus Fenech [43] and Jaffrin [44] proposed a direct calculation of TBW using the same method as for extracellular water, assuming that TBW is a homogeneous quantity of fluid. The mean resistivity of this TBW was validated by comparison with body composition data obtained using the DEXA method. Jaffrin then raised the question of extrapolating total body resistance from the resistance value measured at 50 kHz [45], using a proportional intermediary multiplier.

Finally, the superiority of multifrequency impedance over the monofrequency impedance has not been demonstrated. Similarly no one formula has been found superior to the others.

### **2.2 Available clinical applications**

172 Technical Problems in Patients on Hemodialysis

Thus in many models, the human body is considered to be the sum of five compartments

**Z <sup>Z</sup> <sup>Z</sup>**

**Z Z**

The homogeneity factor is calculated from the resistance of a cylinder (R) which is function

<sup>L</sup> <sup>R</sup>

Then, by calculating the volume of the cylinder, and separating, arms, legs and trunk, the

<sup>L</sup> L L R 4.

This formula, together with the classical formula for the volume of a cylinder, yields the dimension homogeneity constant, KB, which represents a characteristic anthropometric

> B <sup>L</sup> V K

b aa 11 tt 2222

When these formulas are applied to measure body composition, the result is always significantly different from gold standard measurements. Thus Fenech [43] and Jaffrin [44] proposed a direct calculation of TBW using the same method as for extracellular water, assuming that TBW is a homogeneous quantity of fluid. The mean resistivity of this TBW was validated by comparison with body composition data obtained using the DEXA method. Jaffrin then raised the question of extrapolating total body resistance from the resistance value measured at 50 kHz [45], using a proportional intermediary multiplier.

1 L L L K . (2L C 2L C L C ) LC C C

lta

l t a 222 lta

2

l t a 2 22

CCC 

<sup>A</sup> (4)

<sup>A</sup> (6)

(5)

(7)

, its length (L) and its cross-section (A) [42]

following formula is established with *l* for leg, *t* for trunk and *a* for arm:

Fig. 7. The 5-compartment human body model

parameter independent of the electrical parameters.

**2.1.1.4 Formula validity and limitations** 

of its resistivity (

(Fig. 7) (the four limbs and the trunk), with a dimension homogeneity factor Kb.

Several studies have been conducted in hemodialysis patients. Three approaches have been particularly fruitful, the nomovolemia/hypervolemia curves established by Chamney [46, 47, 48, 49], the resistance/reactance curves by Piccoli [50, 51, 52] and Zhu's continuous curves [53, 54]. Although essential, these approaches will not be detailed here. Readers may usefully refer to the cited references.
