**1. Introduction**

164 Technical Problems in Patients on Hemodialysis

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7757.

#### **1.1 The problematic of hydration status in the kidney disease patient**

Dry weight corresponds to the body weight of a person with normal extracellular fluid volume [1]. In the context of hemodialysis, dry weight is the weight reached at the end of the dialysis session by patients who will remain free of orthostatic hypotension or hypertension until the next session. Clinicians are thus obliged to estimate the appropriate dry weight each individual patient should reach at the end of a dialysis session. If this weight is underestimated, the patients are at risk of various incidents ranging from simple yawning to death. Low dry weight also carries a permanent risk of hypotension, cramps, nausea, vomiting or ischemia. If this weight is overestimated, chronic hyperhydration can cause acute events including pulmonary edema, or hypertension, but also long-term consequences affecting cardiovascular morbidity and mortality [2]. This important notion of dry weight is however quite problematic because it corresponds to a transient state, making it necessary to anticipate weight gain between two dialysis sessions and thus to reach a certain degree of dehydration at the end of each hemodialysis session.

The many methods proposed for measuring dry weight and body composition are still under investigation. The difficulty encountered in establishing a reliable comparative tool for measuring these parameters arises from inevitable physiological, anatomical and physical variability. Most approaches remain empirical, relying on feedback from trial and error [3].

In practice, dry weight is estimated clinically [4]. Physical examination is a classic but limited tool. Solid evidence-based analysis of specific physical findings such as systolic blood pressure, orthostatic blood pressure, or the presence or not of edema is lacking. Such clinical symptoms can also be related to conditions other than a dry weight or body composition problem. Several tests have been proposed to assess the dry weight of hemodialysis patients [5]. Echocardiographic inferior vena cava diameter and biochemical markers are available but results exhibit high variability and poor correlation with extracellular volume; there are also unserviceable in detecting volume depletion.

Bioimpedance spectroscopy measurement has been demonstrated as a potentially useful method to determine the physiological status of living tissues [6]. Disease-related alterations are associated with variations in essential tissue parameters such as physical structure or ionic composition that can be detected as changes in passive electrical properties.

Bioimpedance Measurement in the Kidney Disease Patient 167

The impedance of a biological medium is thus the relationship between the voltage

**U** = **Z I** where **Z** is the complex impedance expressed in Ohms (). In Cartesian form this gives **Z** = R + jX where R is the resistance, X is the reactance, both expressed in Ohms, and j

The bioelectric impedance **Z** describes the inertia of a biological medium opposing passage of a sinusoidal current with intensity **I** and pulsation (rad/s). Along the lines of the electrical current, this impedance generates a difference of potential **U**. Bioelectrical impedance can be represented in a complex plane. It is perfectly defined by knowledge of either its real and imaginary components (R and X), or by its module and its argument, Z

For an isotropic, homogeneous, linear medium, impedance is a function of the medium's electrical properties, conductivity and permitivity, but also depends on the geometric features of the measurement cell. This so-called bioimpedance is a well-known tool for characterizing different physiological water compartments [7]. Because of the complexity and highly heterogeneous nature of living tissues, a global approach is used, considering the

Biological tissues cannot be considered as ideal conductors. They are ionic conductors with heterogeneous structures. If we limit our considerations to the sole electrical aspect of interest here, biological tissues can very schematically be considered as a combination of two components: *i*) a free water medium called the extracellular fluid, within which are suspended *ii*) cells surrounded by a membrane containing and thus limiting a volume of intracellular fluid (Fig. 2). The cell concentration can vary greatly, depending on the nature

The fluid components (extracellular fluid, plasma and intracellular fluid) can be considered as electrolytic suspensions of ions whose concentration, electrical charge and mobility, taking into account the viscosity of the medium, will essentially determine the impedance of the suspension, mainly arising from resistive type resistance. Cell membranes however constitute a more complex component. Cole demonstrated that cell membranes can be likened to capacitors [9, 10, 11]. This divides biological media into two basic components, resistors (R) and capacitors (C), which when connected in parallel produce an electrical equivalent model as described by Fricke [13] (Fig. 2). This simplified model (Re, Ri and C are not ideal) enables an interpretation of observed biophysical

Theoretically, tissue impedance, like any electric impedance, can be measured. The mass of tissue to study simply has to be delimited and linked to a measurement device via a system of electrodes. In practice however, measuring the electrical characteristics of biological tissues raise many specific problems. It is useful to recognize the electrical properties of

difference across the medium and the current amplitude as described by Ohm's law:

Setting Z = 2 2 R X and = arctg (X/R) gives the polar form **Z** = Z ej

whole body as a suspension of cells in water and electrolytes [8].

<sup>j</sup> <sup>t</sup> j( t ) U Uo e ; Io e **I** (1)

**U** and **I** are sinusoidal quantities with phase shift

the imaginary unit, j = 1

**1.2.2 Biological basis** 

of the tissue.

phenomena.

and .

Bioimpedance spectroscopy can be used as a diagnostic tool reflecting the overall status of a patient or of an individual organ. The range of applications derived from this method is wide making this non-destructive and non-invasive approach a promising technique for the characterization of the physiological status of the human body.

This chapter presents the use of bioimpedance spectroscopy as a tool for measuring the dry weight of the hemodialysis patient. The first part summarizes the basic fundamentals of the method, describing the underlying electrical and biological principles and the potential interest for applications in hemodialysis. Techniques and models are presented and discussed. The second part discusses clinical results obtained at the hemodialysis center of the Nancy University Hospital, with focus on patient-related parameters influencing or limiting measurements and their interpretation.

#### **1.2 Basic principles of bioimpedance spectroscopy**

#### **1.2.1 Physical principles**

The bioelectrical properties of the human body depend on the nature of the biological tissues composing it and their relative conductivities. These properties lead to the notion of impedance of a biological medium which varies as a function of the frequency of an electrical current applied across it. This in turn leads to the notion of bioimpedance spectroscopy.

Impedance is a complex quantity (**Z)** describing, in compliance with Ohm's law (assuming sinusoidal voltage), the relationship between the voltage difference across the medium and the amplitude of the electrical current. Because of the capacitive nature of biological media, all impedance measurements of the human body involve a phase shift between the voltage and the current, yielding complex values. Biological media are weak conductors due to the dissipation (or loss) of energy in the media and can be considered as energy-loosing dielectrics. The quantities of interest can thus be defined using a schematic representation of a biological suspension placed between two electrodes (Fig. 1).

Fig. 1. Basic principle of bioimpedance spectroscopy

Bioimpedance spectroscopy can be used as a diagnostic tool reflecting the overall status of a patient or of an individual organ. The range of applications derived from this method is wide making this non-destructive and non-invasive approach a promising technique for the

This chapter presents the use of bioimpedance spectroscopy as a tool for measuring the dry weight of the hemodialysis patient. The first part summarizes the basic fundamentals of the method, describing the underlying electrical and biological principles and the potential interest for applications in hemodialysis. Techniques and models are presented and discussed. The second part discusses clinical results obtained at the hemodialysis center of the Nancy University Hospital, with focus on patient-related parameters influencing or

The bioelectrical properties of the human body depend on the nature of the biological tissues composing it and their relative conductivities. These properties lead to the notion of impedance of a biological medium which varies as a function of the frequency of an electrical current applied across it. This in turn leads to the notion of bioimpedance

Impedance is a complex quantity (**Z)** describing, in compliance with Ohm's law (assuming sinusoidal voltage), the relationship between the voltage difference across the medium and the amplitude of the electrical current. Because of the capacitive nature of biological media, all impedance measurements of the human body involve a phase shift between the voltage and the current, yielding complex values. Biological media are weak conductors due to the dissipation (or loss) of energy in the media and can be considered as energy-loosing dielectrics. The quantities of interest can thus be defined using a schematic representation of

**U**

Electrodes

characterization of the physiological status of the human body.

limiting measurements and their interpretation.

**1.2.1 Physical principles** 

spectroscopy.

**1.2 Basic principles of bioimpedance spectroscopy** 

a biological suspension placed between two electrodes (Fig. 1).

**I**

Biological medium

Fig. 1. Basic principle of bioimpedance spectroscopy

**U** and **I** are sinusoidal quantities with phase shift

$$
\underline{\mathbf{U}} = \mathbf{U} \mathbf{o} \text{ e}^{[\text{tot}}; \underline{\mathbf{I}} = \mathbf{I} \mathbf{o} \text{ e}^{[(\text{tot} + \phi)} \tag{1}
$$

The impedance of a biological medium is thus the relationship between the voltage difference across the medium and the current amplitude as described by Ohm's law:

**U** = **Z I** where **Z** is the complex impedance expressed in Ohms (). In Cartesian form this gives **Z** = R + jX where R is the resistance, X is the reactance, both expressed in Ohms, and j the imaginary unit, j = 1

Setting Z = 2 2 R X and = arctg (X/R) gives the polar form **Z** = Z ej

The bioelectric impedance **Z** describes the inertia of a biological medium opposing passage of a sinusoidal current with intensity **I** and pulsation (rad/s). Along the lines of the electrical current, this impedance generates a difference of potential **U**. Bioelectrical impedance can be represented in a complex plane. It is perfectly defined by knowledge of either its real and imaginary components (R and X), or by its module and its argument, Z and .

For an isotropic, homogeneous, linear medium, impedance is a function of the medium's electrical properties, conductivity and permitivity, but also depends on the geometric features of the measurement cell. This so-called bioimpedance is a well-known tool for characterizing different physiological water compartments [7]. Because of the complexity and highly heterogeneous nature of living tissues, a global approach is used, considering the whole body as a suspension of cells in water and electrolytes [8].

#### **1.2.2 Biological basis**

Biological tissues cannot be considered as ideal conductors. They are ionic conductors with heterogeneous structures. If we limit our considerations to the sole electrical aspect of interest here, biological tissues can very schematically be considered as a combination of two components: *i*) a free water medium called the extracellular fluid, within which are suspended *ii*) cells surrounded by a membrane containing and thus limiting a volume of intracellular fluid (Fig. 2). The cell concentration can vary greatly, depending on the nature of the tissue.

The fluid components (extracellular fluid, plasma and intracellular fluid) can be considered as electrolytic suspensions of ions whose concentration, electrical charge and mobility, taking into account the viscosity of the medium, will essentially determine the impedance of the suspension, mainly arising from resistive type resistance. Cell membranes however constitute a more complex component. Cole demonstrated that cell membranes can be likened to capacitors [9, 10, 11]. This divides biological media into two basic components, resistors (R) and capacitors (C), which when connected in parallel produce an electrical equivalent model as described by Fricke [13] (Fig. 2). This simplified model (Re, Ri and C are not ideal) enables an interpretation of observed biophysical phenomena.

Theoretically, tissue impedance, like any electric impedance, can be measured. The mass of tissue to study simply has to be delimited and linked to a measurement device via a system of electrodes. In practice however, measuring the electrical characteristics of biological tissues raise many specific problems. It is useful to recognize the electrical properties of

Bioimpedance Measurement in the Kidney Disease Patient 169

consists in placing electrodes conveniently on the arms and legs in order to impose an electrical current and measure the voltage it induces across the body. For a reasonable current density, the behavior is linear so that Ohm's law remains valid. Intra- and extracellular fluids are mainly resistive, whereas cell membranes act as an insulator between these two compartments. Rare bioimpedance spectroscopy studies conducted in kidney graft recipients have shown a trend towards improved hydration after transplantation. We have been unable to find any study evaluating hydration changes in patients with acute

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 extra-

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

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).

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:

<sup>2</sup> TBW a . H / R b . wei ght c . Age d (2)

TBW a.H² /R c (3)

body water (TBW) the regression equation is written as [26](with H: Height):

kidney disease.

**2. Theoretical and experimental models 2.1 Principles of bioimpédance in hemodialysis** 

cellular compartments in perpetual movement.

**2.1.1 Prediction of total body water** 

**2.1.1.1 Historical background** 

biological tissues and their components because of their interest both in medicine, where many diagnostic methods are based on electrical principles, and in fundamental physiology, where these same properties contribute to the structural analysis of cell organization, the study of cell excitation mechanisms, or to the analysis of protein molecules. Debye, Cole-Cole and Maxwell-Wagner models have been developed to represent the theoretical interpretations of these phenomena. These models can be used to demonstrate important factors characterizing biological tissues [12].

Fig. 2. Electrical equivalent model (Fricke's model) of a biological cell in suspension in the extracellular fluid. Ri : intra-cellular resistance, Re : extra-cellular resistance, Ce : capacitance

Capacitance and resistance can be combined either in series or in parallel, leading to several variants of the Fricke model. Resistivity (charge accumulation) and conductivity (conduction of electrical current) are however two independent processes for which the parallel model has been found to be more representative. Formulas used for biological tissues are thus all based on the Fricke model [13]. Applying these models to bioimpedance spectroscopy curves allows a quantification of value differences corresponding to the intracellular fluid and the extracellular fluid and thus their corresponding masses. The interest for hemodialysis is obvious.

#### **1.3 Usefulness of bioimpedance for the kidney disease patient**

Much research has been devoted to the determination of body hydration status and fluid compartments, particularly in hemodialysis patients [14]. Work has focused on various physiological parameters with different modalities to study individual segments of the body or the whole body [15, 16, 17] using multiple or unique frequencies [18]. One of the goals is to improve predictive equations and to identify the effect of different parameters on the measures obtained [19, 20]. In dialysis for example, it has been shown that fluid is removed predominantly from the extracellular and peripheral (arms, legs) compartments [21]. Thus, different biofluid models have been proposed to describe the whole body or individual organs. Basically, applying the bioimpedance method to determine body composition

biological tissues and their components because of their interest both in medicine, where many diagnostic methods are based on electrical principles, and in fundamental physiology, where these same properties contribute to the structural analysis of cell organization, the study of cell excitation mechanisms, or to the analysis of protein molecules. Debye, Cole-Cole and Maxwell-Wagner models have been developed to represent the theoretical interpretations of these phenomena. These models can be used to demonstrate important

Cellular Membrane

Extracellular medium

Ce

Ri

Re

Intracellular medium

Fig. 2. Electrical equivalent model (Fricke's model) of a biological cell in suspension in the extracellular fluid. Ri : intra-cellular resistance, Re : extra-cellular resistance, Ce : capacitance Capacitance and resistance can be combined either in series or in parallel, leading to several variants of the Fricke model. Resistivity (charge accumulation) and conductivity (conduction of electrical current) are however two independent processes for which the parallel model has been found to be more representative. Formulas used for biological tissues are thus all based on the Fricke model [13]. Applying these models to bioimpedance spectroscopy curves allows a quantification of value differences corresponding to the intracellular fluid and the extracellular fluid and thus their corresponding masses. The

Much research has been devoted to the determination of body hydration status and fluid compartments, particularly in hemodialysis patients [14]. Work has focused on various physiological parameters with different modalities to study individual segments of the body or the whole body [15, 16, 17] using multiple or unique frequencies [18]. One of the goals is to improve predictive equations and to identify the effect of different parameters on the measures obtained [19, 20]. In dialysis for example, it has been shown that fluid is removed predominantly from the extracellular and peripheral (arms, legs) compartments [21]. Thus, different biofluid models have been proposed to describe the whole body or individual organs. Basically, applying the bioimpedance method to determine body composition

factors characterizing biological tissues [12].

High frequency current

Low frequency current

interest for hemodialysis is obvious.

**1.3 Usefulness of bioimpedance for the kidney disease patient** 

consists in placing electrodes conveniently on the arms and legs in order to impose an electrical current and measure the voltage it induces across the body. For a reasonable current density, the behavior is linear so that Ohm's law remains valid. Intra- and extracellular fluids are mainly resistive, whereas cell membranes act as an insulator between these two compartments. Rare bioimpedance spectroscopy studies conducted in kidney graft recipients have shown a trend towards improved hydration after transplantation. We have been unable to find any study evaluating hydration changes in patients with acute
