Metrological characterization of instruments for body impedance analysis ACTA IMEKO ISSN: 2221-870X September 2022, Volume 11, Number 3, 1 - 7 ACTA IMEKO | www.imeko.org September 2022 | Volume 11 | Number 3 | 1 Metrological characterization of instruments for body impedance analysis Valerio Marcotuli1, Matteo Zago2, Alex P. Moorhead1, Marco Vespasiani3, Giacomo Vespasiani3, Marco Tarabini1 1 Department of Mechanical Engineering, Politecnico di Milano, via Privata Giuseppe La Masa 1, 20156 Milan, Italy 2 Faculty of Exercise and Sports Science, Università degli Studi di Milano, Via Festa del Perdono 7 - 20122 Milan, Italy 3 Technical Department, Metadieta s.r.l., Via Antonio Bosio, 2, 00161 Rome, Italy Section: RESEARCH PAPER Keywords: Bioimpedance; body composition; measurement uncertainty; calibration; multivariate linear regression Citation: Valerio Marcotuli, Matteo Zago, Alex P. Moorhead, Marco Vespasiani, Giacomo Vespasiani, Marco Tarabini, Metrological characterization of instruments for body impedance analysis, Acta IMEKO, vol. 11, no. 3, article 14, September 2022, identifier: IMEKO-ACTA-11 (2022)-03-14 Section Editor: Francesco Lamonaca, University of Calabria, Italy Received October 7, 2021; In final form August 31, 2022; Published September 2022 Copyright: This is an open-access article distributed under the terms of the Creative Commons Attribution 3.0 License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Corresponding author: Valerio Marcotuli, e-mail: valerio.marcotuli@polimi.it 1. INTRODUCTION Body composition describes the main components of the human body in terms of free fat mass (FFM), fat mass (FM) or their ratio FFM/FM. The analysis of body composition is used in different fields such as biology and medicine to estimate the nutritional status, muscular volume variations and potentially event pathological status. For example, physiological aging leads to a reduction of FFM and muscular mass, while fat increases and is redistributed over the body areas [1]. Different levels of body composition, atomic, molecular cellular, tissular and global, can be analyzed depending on the measurement methods [2]. Body mass index (BMI) is a generic indicator of the body composition, but it tends to give inaccurate information when subjects are highly overweight or obese; in fact, it is possible that malnutrition exists yet is masked by the high amount of fat mass [3]. A solution for measuring body composition is represented by the Dual-energy X-ray Absorptiometry (DXA). This is an imaging technique, similar to Magnetic Resonance Imaging (MRI), which scans the patient with two beams of x-rays with different energy (usually 40 and 70 kV). In recent years, DXA has become recognized as the “gold standard” for measuring body composition [4]. It evaluates both the global and the regional distribution of the three main body components: bone mineral content (BMC), FM and FFM. The accuracy of DXA makes it very effective in studying patient composition within specific body regions and evaluating their effect on the patient health [5]. Unfortunately, a DXA machine is expensive ($20,000+) making it typically available only at big infrastructure such as clinics and hospitals. An alternative technique is the Bioelectrical Impedance Analysis (BIA): this employs a low alternate current (AC) with high frequency at 50 kHz transmitted across the body to estimate its composition based on the hydration level of tissues [6]. BIA allows for quick examinations, and it is much less expensive than DXA. Additionally, BIA is less dangerous than DXA as it does ABSTRACT Body impedance analysis (BIA) is used to evaluate the human body composition by measuring the resistance and reactance of human tissues with a high-frequency, low-intensity electric current. Nonetheless, the estimation of the body composition is influenced by many factors: body status, environmental conditions, instrumentation, and measurement procedure. This work studies the effect of the connection cables, conductive electrodes, adhesive gel, and BIA device characteristics on the measurement uncertainty. Tests were initially performed on electric circuits with passive elements and on a jelly phantom simulating the body characteristics. Results showed that the cables mainly contribute to increase the error on the resistance measurement, while the electrodes and the adhesive introduce a negligible disturbance on the measurement chain. This paper also proposes a calibration procedure based on a multivariate linear regression to compensate for the systematic error effect of BIA devices. mailto:valerio.marcotuli@polimi.it ACTA IMEKO | www.imeko.org September 2022 | Volume 11 | Number 3 | 2 not use x-rays, meaning it can be also repeated several times with no contraindications. Nevertheless, BIA can be highly affected by many factors such as altered hydration of the subject, measurement conditions, ethnic background, and health conditions [7]. BIA devices measure the magnitude of the impedance opposed to the current that varies with respect to the body anatomy. Specifically, the physical principle assumes that the body is made up of tissues with different composition. Some tissues are good conductors due to their water content while others are insulators. The water content is inversely related to the resistance that opposes the current flow. On the other hand, cellular membranes, able to accumulate electrical loads, can be considered capacitors. The presence of capacitors is directly proportional to reactance and introduces an observable delay on the current flow. The sum of the resistance and reactance defines the impedance. Its evaluation indicates the body hydration and provides an estimate of the nutritional state equivalent to the cellular amount. Since water is the main component of the cells and it is almost absent in fat, it is possible to deduce the amount of FFM from the water content. Consequently, FM is evaluated by simply subtracting the FFM to the total weight [8]. 1.1. Fricke’s Circuit: a human body electrical model The human body can be modeled as a set of resistance and capacitance connected in parallel or in series. The most common body model used in the field of BIA is the Fricke’s circuit, whose two parallel branches represent the intracellular and extracellular components. In this model, a high-frequency current passes through the intracellular water, while at low frequencies through the extracellular space. This is because at zero or low frequency, the current does not penetrate the cell membrane (acting as an insulator), while it passes through the extracellular medium made of water and sodium [9]. The intracellular behavior, in turn, can be modeled as a resistance Ri (due to the water and potassium content) and a capacitance 𝑋𝑐 of the cell membrane, while the extracellular behavior is described by a single resistance Re as shown in Figure 1. The total body resistance R measured by a BIA instrument is in turn a combination of the two resistances Ri and Re which indicate the real part of a complex number [10]. Generally, the phasor and other indices such the ratio Ri/Re can be good estimators of diseases presence, nutritional status, and hydration condition [11]. 1.2. The calibration plots The Cole-Cole plot is commonly used to visualize the electrical response of body measurements with the resistance R on the x-axis and the negative reactance 𝑋𝑐 on the y-axis. At extremely high or ideally infinite frequency, the intracellular branch is the only one with the minimum resistance value Ri. At low or zero frequency, the current passes only in the extracellular space since the cell membranes act as insulators. Consequently, Re is the maximum value of resistance. The relationship between the capacitance 𝑋𝑐 and the total resistance R of a body can be expressed by a phase angle φ [12]. Therefore, the resulting phasor ranging from Ri and Re describes an arc segment as shown in Figure 2 and all the measured values would lie below it. This plot can be standardized with respect to height, gender, and ethnicity, to form a calibration model divided into adjacent areas contained in tolerance ellipses at 50 %, 75 %, and 95 % belonging to a certain population group (as seen in Figure 3, which shows an example of a calibration model standardized by the height, h) [13]. The plot is used as a calibration map by companies for converting a measurement performed by means of a device into a body status information [14]. If the BIA device displays a low measurement accuracy, measurement results could be misleading. 1.3. Measurement uncertainty The biasing factors on bioimpedance estimation can be attributed to the subject (the measurand is not constant), to the measurement protocols, and to the instrumentation [15]. In this Figure 1. Fricke's circuit model for body composition consisting into two branches related to the intracellular and extracellular behaviors. Figure 2. Example of Cole-Cole plot of the Fricke's circuit. Figure 3. Example of a calibration model standardized by the height (h). ACTA IMEKO | www.imeko.org September 2022 | Volume 11 | Number 3 | 3 study we investigate the possible source of errors of the BIA instrumentation, consisting in a control unit, cables, and electrodes. The control unit is composed of electronic circuitry placed in a case with one or more ports for connecting the cables. Even if protected, the circuitry is subjected to thermal, electrical, and magnetic disturbances [16], [17]. The identification of these disturbances is essential for the performances of the devices and to improve competitivity in the market. For this reason, the control unit and the accessories should be metrologically characterized through a specific test for each possible sources of error [18], [19]. Moreover, if the disturbances are properly identified, a corrective calibration strategy can be applied [20], [21]. 2. MATERIALS AND METHODS 2.1. Instrumental equipment The instrumentation selected for this study consists of a BIA device (Metadieta Bia), three sets of cables, three sets of electrodes of different manufacturers, a series of resistances and capacitors, and a breadboard. Metadieta Bia (Figure 4) is an electromedical device for the evaluation of the corporal composition manufactured by the company Meteda S.r.l. (Rome, Italy). The bioimpedance is measured by placing four electrodes on the hands and feet, with a single cable connected to the main unit. The impedance value is computed from the response to a sinusoidal current of 350 μA with a frequency of 50 kHz (a standard de facto for most BIA devices with a single frequency). The device has a size of 43 × 43 × 12 mm3 and a mass of 50 g; a lithium battery can supply the device up to 14 hours in working conditions. It does not have a screen on the control unit, but it can be managed by an application running on phones, tablets, and computers with a Bluetooth connection. The device is designed to be used in clinics by physicians, nutritional biologists and qualified sanitary personnel but also by consumers in home environment. The application provides the user with information about the preparation and the execution of the test measurement, then it sends and stores the data on the cloud for later analyses. Data measurements are processed on the cloud application and the results can be either quantitative for clinical personnel or qualitative with displayed information in graphs along with the tendencies for individual users. The additional equipment for the test is represented by three cables of the same model between the main unit and the four electrodes clamps and a series of electrodes of three producers: Biatrodes® by Akern slr (Firenze, Italy), BIA Electrodes by RJL Systems Inc (Clinton Twp, MI, USA), and Regal™ resting ECG by Vermed® Inc (Bells Falls, VT, USA). 2.2. Proposed method The first operation to perform with a measurement device regards the metrological characterization in terms of repeatability and reproducibility after the identification of the possible sources of error [22]. Generally, this kind of device makes use of empirical equations whose parameters are established by means of a calibration operation performed in laboratory [23]. Since the calibration curves can assume a large set of values, a simplification of the process can rely on the study of a group of key values. This research proposes a data selection based on six values of resistance between 200 Ω and 900 Ω with a step of 140 Ω, combined with six values of reactance between 15 Ω and 115 Ω with a step of 20 Ω. These values are represented in the grid in Figure 5. To assemble a physical circuit starting from the reactance values, suitable capacitors can be identified by converting 𝑋𝑐 into a capacitance C with the formula: 𝐶 = 1 2 ∙ 𝜋 ∙ 𝑓 ∙ 𝑋𝑐 , (1) where f is the frequency of AC generated by the Metadieta Bia device, i.e. 50 kHz. The capacitance values obtained after the conversion are therefore: 212 nF, 91 nF, 58 nF, 42 nF, 34 nF, and 28 nF. By combining the values of resistance and capacitance, we defined a grid of 36 combinations and we evaluated the measurements’ repeatability and reproducibility in each condition. The procedure also allows identifying compensation functions allowing to reduce the systematic errors affecting the reading [24]. 2.3. Experimental design The Metadieta Bia is turned on when the cables are inserted in the miniUSB port and the connection is initiated by the application on a master device. Measurements are typically performed by placing four electrodes on the hands and feet. The electrodes are silver plated for a low resistance and attached to the skin using an adhesive gel. However, for consistency, all the experiments were performed on laboratory instrumentation with electric circuits Figure 4. Picture of the Metadieta Bia control unit. Figure 5. Calibration grid with 36 combinations of the key values selected. ACTA IMEKO | www.imeko.org September 2022 | Volume 11 | Number 3 | 4 representing the body composition through the Fricke’s model, so the electrodes were included only in specific tests. The tests were performed in MetroSpace Lab of Politecnico di Milano and can be divided into: 1. Preliminary tests for the metrological characterization of Metadieta Bia device, cables, electrodes, and adhesive gel. 2. Test for systematic error compensation based on the calibration grid in Figure 5. A high precision LCR meter, model LCR-819 GW Instek (Good Will Instrument Co., Ltd, Taiwan), was used as a reference system for measuring the impedance of the test components, while a multimeter, model Agilent 34401A, was used for the only resistance measurements of the electrical components. 2.4. Preliminary tests First, the measurement repeatability of the control unit was tested by performing 30 measurements of the resistance R and reactance 𝑋𝑐 repeated on five different electric circuits connecting the cable clamps directly to the circuit with no other modifications between each test and the next. The three different cables of the same model were tested with 30 measurements each with the LCR meter, on the same electric circuit directly connecting the clamps of the cables. Keeping the same configuration, the effect of the electrodes was studied applying these components without the adhesive material between the clamps and the electric circuit with passive elements. A total of 30 different sets of electrodes of the three manufacturers were tested, 4 electrodes for each set. At the same time, the resistance R of the cables and the electrodes was measured 30 times for each component through the multimeter. The variability of electrical resistance of the electrodes was estimated by placing the multimeter terminals in two positions, on the tab and on an opposite area far from it (circled in Figure 6). The effect of the adhesive gel, which determines the interaction with the BIA device and a biological tissue, was simulated by means of a jelly phantom (Figure 7) with nominal resistance of 𝑅𝑝ℎ = (571.2 ± 1.2) Ω (C.I. = 68 %) and nominal reactance of 𝑋𝑐 𝑝ℎ = (75.1 ± 1.9) Ω (C.I. = 68 %) [25]. For this test, 30 measurements for each manufacturer’s electrode were performed to calculate the mean value of the resistance �̅� and reactance �̅�𝑐 and the relative standard deviation. The four electrodes were positioned at the edges of the container, one couple on the left side and the other couple on the right side with a distance of about 30 cm. The distance between the two electrodes of each couple was of about 10 cm as recommended by the manufacturer. This configuration with the dominant distance (30 cm > 10 cm) between the two couples of electrodes aimed to replicate the measurement behaviour on a human body, avoiding uncontrolled dispersion of the electric charge. 2.5. Tests for systematic error compensation A set of 36 circuits with passive elements was built by combining selected components with the resistance and capacitance collected in Table 1, to the key values of the calibration grid in Figure 5. Table 1 also includes the reactance values after the conversion obtained by inverting the Eq.1. The resistances components have a manufacturing tolerance of 0.1%, whereas the capacitors have a value of 1%. The circuits were mounted on a breadboard and the values read by Metadieta Bia device were compared to the values read by the LCR meter as references [26]. The differences between the measured and the reference allowed to calculate the RMSE and control for the presence of defined patterns related to systematic disturbances. Part of these disturbances was removed by adding two corrections terms 𝑅𝑎 and X𝑐 𝑎, obtained by a least square minimization of a multivariate linear model, to the generic measurements R and 𝑋𝑐 in the form: 𝑅𝑎𝑑𝑗 = 𝑅 + 𝑅𝑎 (2) and 𝑋𝑐 𝑎𝑑𝑗 = 𝑋𝑐 + X𝑐 𝑎 , (3) where 𝑅𝑎𝑑𝑗 and 𝑋𝑐 𝑎𝑑𝑗 are the compensated results. Figure 6. Area of the electrode for measuring the resistance. Figure 7. Preliminary test of the electrodes on a jelly phantom. Table 1. Resistances and capacitances of the selected components and the reactance values after conversion for the calibration map experiments. Component 1 2 3 4 5 6 R in Ω 200 330 470 615 780 910 C in nF 225 92 51 36 32 27 Xc in Ω 14 35 56 89 99 120 ACTA IMEKO | www.imeko.org September 2022 | Volume 11 | Number 3 | 5 3. RESULTS 3.1. Preliminary tests The results of the repeatability test of the control unit on the 5 electric circuits with 30 measurements performed on each circuit are shown in Table 2: R and 𝑋𝑐 are the key values chosen for the experiments, 𝑅𝑟𝑒𝑓 and 𝑋𝑐 𝑟𝑒𝑓 are the reference values read by the LCR meter, �̅� and �̅�𝑐 are the mean values read by the Metadieta Bia device with 𝜎𝑅 and 𝜎𝑋𝑐 the relative standard deviations. The three tested cables showed a standard deviation of the resistance of 𝜎𝑅 = 1.8 Ω, while the standard deviation of the reactance is 𝜎𝑋𝑐 = 0.1 Ω. From these values it was possible to evaluate the uncertainty values 𝑢𝑅 = 𝜎𝑅 √30 =⁄ 0.33 Ω and 𝑢𝑋𝑐 = 𝜎𝑋𝑐 √30 =⁄ 0.018 Ω (C.I. = 68 %). The electrode without the adhesive gel were tested on a circuit with the nominal resistance R = (617.812 ± 0.011) Ω (C.I. = 68 %) and the equivalent reactance 𝑋𝑐= (90.137 ± 0.019) Ω (C.I. = 68 %) with the Metadieta Bia device. The mean and the standard deviation of the resistance and the reactance are reported in Table 3. The maximum standard deviation values were reported by the RJL systems electrodes equal to 𝜎𝑅 = 0.5 Ω and 𝜎𝑋𝑐 = 0.1 Ω with the correspondent uncertainties equal to 𝑢𝑅 = 𝜎𝑅 √30 =⁄ 0.091 Ω and 𝑢𝑋𝑐 = 𝜎𝑋𝑐 √30 =⁄ 0.018 Ω (C.I. = 68 %). The resistance-only measurements of the same electrodes performed through the multimeter are reported in Table 4. In this case both RJL systems and Vermed® electrodes reported a maximum standard deviation of 𝜎𝑅 = 0.4 Ω and an uncertainty of 𝑢𝑅 = 𝜎𝑅 √30 =⁄ 0.073 Ω (C.I. = 68 %). The last experiment of the preliminary test on the jelly phantom are reported in Table 5. All three electrode samples showed a standard deviation of 𝜎𝑅 = 0.1 Ω with an uncertainty of 𝑢𝑅 = 𝜎𝑅 √30 =⁄ 0.018 Ω (C.I. = 68 %), whereas Akern and Vermed® electrodes reported a standard deviation different from zero and equal to 𝜎𝑋𝑐 = 0.1 Ω corresponding to an uncertainty of 𝑢𝑋𝑐 = 𝜎𝑋𝑐 √30 =⁄ 0.018 Ω (C.I. = 68 %). 3.2. Systematic error compensation The measurements on 36 electric combinations with the Metadieta Bia device and the reference values are depicted in Figure 8. From these data, the RMSE of the 36 configurations resulted 𝑅𝑅𝑀𝑆𝐸 = 4.17 Ω and 𝑋𝑐,𝑅𝑀𝑆𝐸 = 7.28 Ω. The minimization of the least square on the multivariate linear regression returned the following correction terms: 𝑅𝑎 = −1.592 + 0.994 ∙ 𝑅 + 0.002 ∙ 𝑋𝑐 + 2.45 ∙ 10−5 ∙ 𝑅 ∙ 𝑋𝑐 (4) and X𝑐 𝑎 = −3.412 + 0.010 ∙ 𝑅 + 1.079 ∙ 𝑋𝑐 − 2.19 ∙ 10−5 ∙ 𝑅 ∙ 𝑋𝑐 . (5) with R and 𝑋𝑐 the actual values read by the BIA device. Furthermore, the multivariate linear regression reported the Table 2. Results of the repeatability test of the control unit on 5 electric circuits. R in Ω Xc in Ω Rref in Ω Xcref in Ω �̅� in Ω σR in Ω �̅�𝐜 in Ω σXC in Ω 200 15 200.1 17.9 202.7 0.0 18.9 0.1 200 75 191.4 92.3 193.5 0.1 88.7 0.1 340 115 330.5 124.4 333.4 0.1 116.1 0.0 620 75 617.8 90.1 622.1 0.0 80.2 0.0 900 95 910.9 101.1 916.9 0.0 98.3 0.0 Table 3. Results of the repeatability test of the three producer’s electrodes without the adhesive gel by the Metadieta Bia device. Manufacturer �̅� in Ω σR in Ω �̅�𝐜 in Ω σXC in Ω Akern 619.2 0.2 91.4 0.0 RJL Systems 619.5 0.5 91.4 0.1 Vermed® 619.4 0.1 91.5 0.0 Table 4. Results of the repeatability test of the three producer’s electrodes without the adhesive gel by the multimeter Agilent 34401A. Manufacturer �̅� in Ω σR in Ω Akern 1.6 0.3 RJL Systems 2.1 0.4 Vermed® 2.1 0.4 Table 5. Results of the repeatability test of the three producer’s electrodes with the adhesive gel on the jelly phantom by the Metadieta Bia device. Manufacturer �̅� in Ω σR in Ω �̅�𝐜 in Ω σXC in Ω Akern 573.2 0.1 79.1 0.1 RJL Systems 573.3 0.1 78.5 0.0 Vermed® 573.2 0.1 78.9 0.1 ACTA IMEKO | www.imeko.org September 2022 | Volume 11 | Number 3 | 6 adjusted R2 values of �̅�𝑅 2 =0.947 for the resistance and �̅�𝑋𝑐 2 = 0.696 for the reactance. Compensating for the values in Figure 8 with the terms 𝑅𝑎 and X𝑐 𝑎, the values of RMSE decrease to 𝑅𝑅𝑀𝑆𝐸 =1.16 Ω and 𝑋𝑐,𝑅𝑀𝑆𝐸 =1.28 Ω. 4. DISCUSSION The tests on the Metadieta Bia device revealed that the cables, the silver-plated electrodes, and the gel have a negligible influence on the overall measurement chain: the cables showed an uncertainty of 𝑢𝑅 = 3.3 ∙ 10 -1 Ω (C.I. = 68 %) and 𝑢𝑋𝑐 = 1.8 ∙ 10-2 Ω (C.I. = 68 %), while the maximum uncertainties introduced by the electrodes were 𝑢𝑅 = 8.6 ∙ 10 -2 Ω (C.I. = 68 %) and 𝑢𝑋𝑐 = 1.7 ∙ 10 -2 Ω (C.I. = 68 %). The comparison between the three electrode models also showed that these elements have the same electric characteristics for which the device performance does not change, as proved by Sanchez et Al. [27]. Also, the tests for the gel on the jelly phantom did not report any significant influence since the maximum uncertainties were 𝑢𝑅 = 1.7 ∙ 10-2 Ω (C.I. = 68 %) and 𝑢𝑋𝑐 = 1.7 ∙ 10 -2 Ω (C.I. = 68 %). This means that the adhesive gel is essential for keeping the contact between the electrodes and the skin but it does not add any relevant disturbance to the measurement process [28]. The comparison between the reference values and the measurements with the BIA device in Figure 8 showed that the uncertainties of the reactance and resistance tend to increase for the combinations with higher values. Nonetheless, the trend was corrected effectively by the multivariate linear regression. In fact, the two terms 𝑅𝑎 and X𝑐 𝑎 can decrease the uncertainties to 𝑅𝑅𝑀𝑆𝐸 =1.16 Ω and 𝑋𝑐,𝑅𝑀𝑆𝐸 =1.28 Ω. Moreover, by observing the expressions of 𝑅𝑎, it is evident that the read reactance contribution is negligible. Conversely, the read resistance value has a relevant influence on the compensation procedure. 5. CONCLUSIONS BIA is an effective and valid tool to estimate body composition from a fast and safe single measurement. Nonetheless, the estimation can fail when the measurement conditions change or if there is a poor calibration of the BIA device. In this paper, we evaluated the causes of variability of bioimpedance measurements. First, the equipment was metrologically characterized showing that it does not influence the measurements significantly with uncertainties lower than 0.35 Ω (C.I. = 68 %) for both resistance and reactance. For what concerns the validation of BIA equations, it must be carried out against gold standards, even though they exhibit limitations due to hydration conditions, age, and ethnicity. 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