A Plethysmography Capacitive Sensor for Real-Time Monitoring of Volume Changes in Acute Heart Failure

Depósito de investigación de la Universidad de Sevilla https://idus.us.es/ This is an Accepted Manuscript of an article published by IEEE in IEEE Transactions on Instrumentation and Measurement on 23 June 2021, available at: https://doi.org/10.1109/tim.2021.3091483 “© 2021 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other Works” IEEE Transactions on Instrumentation and Measurement 1  Abstract— A small, wearable, low-weight and low-power - consumption device for plethysmography capacitive sensing is proposed herein. The device allows to carrying out real-time monitorization monitoring of the leg volume changes in patients suffering from Heart Failure (HF) conditions. The dynamic of fluid overload in patients with acute HF serves as a prognosis marker for this kind type of severe disease and, consequently, these patients can benefit from a wearable monitorization monitoring system to measure their body volume evolution during and after hospitalization. Our approach is based on contactless capacitive wearable structures implemented by two different approaches of sensorssensor realizations located in the ankle: 180o -parallel capacitor plates (two modes of operations are compared, with the patient’s body connected to ground and connected to the average voltage between plates), and planar-parallel capacitor plates in which theirwhose overlapped surface varies depending onwith the volume of the patient’s leg. Both systems realizations exhibit good sensitivity to leg volume changes. The acquisition of the capacitance values is performed via a quite simple proposed circuit, proving worthy results that achieves notable performance in simulated volume analysis. A preliminary pilot clinical prototype is described as well. Index Terms—heart failure (HF), plethysmography capacitive sensor, real-time monitorizationmonitoring, wearable I. INTRODUCTION EART Ffailure (HF) is the final outcome of numerous heart -diseases. It is detected by measuring several indicators and signs (e.g., dyspnea, and leg swelling) resulting from deviations in the cardiac structure and/or function [1][1]. Cardiac failure may generate a fluid overload, with the consequent accumulation of pulmonary and systemic liquids. The aAcute decompensated HF is a potentially life-threatening condition requiring hospitalization and emergency treatments, to manage the liquid excess [1][1]. The aAcute HF is also a common and costly disease:, it is the leading the cause of hospitalization in people over 65 years in most European countries, which and is responsible for 2% of healthcare costs This work was supported in part by the Spanish Government’s, Ministerio de Ciencia, Innovación y Universidades, Plan Estatal 2017-2020 Retos: Real time monitoring of hemodynamic variables using intelligent stents (iSTENT) with capacitive sensors and bioimpedance, under the project RTI2018-093512-B- C21, and also by the grants: Real-time monitoring prognostic value of volume with BI test in patients with acute HF. (HEART-FAIL VOLUM). 2019: Instituto San Carlos III. DTS19/00134 and DTS19/00137. E. Rando, P. Pérez, S. F. Scagliusi, G. Huertas and A. Yúfera belong to Instituto de Microelectrónica de Sevilla, IMSE, CNM (Universidad de Sevilla (US), CSIC), Av. Américo Vespucio, SN, 41092 Sevilla, Spain. [2][2],. Besides, it presents with worse prognosisesults worse than breast, prostate and intestine cancers [3][3]. The main factor leading to HF decompensation [1][1] is the body volume excess (liquid overload) due to the neuro-hormonal activation. This is the reason because ofwhy body volume changes continuous-time monitoring of body volume changes allows a potential and early detection of a worsening progress in patients with acute HF. The HF standard evaluation (signs and symptoms, medical imaging and natriuretic peptides analysis) does not consistently predict its time evolution and clinical outcomes after hospitalizations. HF is a clinical entity with a modifiable course and a high potential for control and improvement of health status. Several studies havePrevious studies demonstrated the potential utility of natriuretic peptides as a prognostic marker of acute HF. However, their low sensitivity limits their clinical use, and further studies are needed to assess the correct cut-off points to assist in clinical decisionmaking [4][4]. Other peptides play an important role in physiological and pathological conditions related to the cardiovascular system. Urotensin II has beenwas shown to promote the proliferation of vascular smooth muscle cells [5][5], and could now be considered as a new biomarker in patients with left ventricular hypertrophy [6][6]. of This may be possible interesting for application in HF with preserved ejection fraction. Currently, more thanOver 100 prognostic models for HF have been described so far, although a meta-analysis revealed only moderate accuracy ofthat these models achieve moderate accuracy in predicting mortality, and even less ability precision to in predicting hospitalization [7][7]. In 2012, the IBiS-HUVR team described the first model (PREDICE score) to predict mortality in hospitalized patients with recent HF. The variables included in this score were non-invasive, easy to collect, and widely available, and the model showed a C statistic of 0.763 [8][8]. However, its short-term performance is was also limited. F. J. Medrano is with Instituto de Biomedicina de Sevilla, (IBiS-US, CSIC, Junta de Andalucía), Medicine Dpt., US and Hospital Universitario Virgen del Rocío (HUVR) at Sevilla (Spain). (email: f[email protected]) E. Rando and G. Huertas are also with the Electronic and Electromagnetism Dpt., Physics Faculty, US. Av. Reina Mercedes sn, Sevilla (Spain). (email: [email protected], [email protected]) P. Pérez, S. F. Scagliusi, and A. Yúfera are also with the Electronic Technology Dpt., Escuela Técnica Superior de Ingeniería Informática, US, Av. Reina Mercedes, SN, 41012 Sevilla, Spain. (email: {pablopg, sanfersca, yufera}@imse-cnm.csic.es) Enrique Rando, Pablo Pérez, Santiago F. Scagliusi, Francisco J. Medrano, Gloria Huertas, and Alberto Yúfera A Plethysmography Capacitive Sensor for Real- Time Monitoring of Volume Changes in Acute Heart Failure H Con formato: Color de fuente: Automático Código de campo cambiado Código de campo cambiado Código de campo cambiado Código de campo cambiado Código de campo cambiado Código de campo cambiado Código de campo cambiado Código de campo cambiado Código de campo cambiado Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Código de campo cambiado Con formato: Español (España) IEEE Transactions on Instrumentation and Measurement 2 Despite all these resources, acute HF still has a mortality of 15 %, and more thanover 30 % of patients are readmitted to hospital within 30 days of discharge [9][9]. This outcome could potentially be avoided if through early detection of changes in hemodynamics related to HF are detected early. The Bio-Impedance (BI) has been commonly used to describe cells [10][10], tissues, and organs [11][11], since thegiven that biological electrical properties (conductivity and permittivity) are confident ofsuitable indicators of the biological matter physics. SoThus, BI represents an excellent bio-marker in medical diagnosis [12][12][13][13][14][14]. Frequency spectroscopy techniques can be widely applied also to test BI (e.g., Electrical Impedance Spectroscopy, EIS). Besides, BI tests are noninvasive, cheap, and easy to build. A simple, non-invasive, and very sensitive volume measurement that could help identify high-risk HF patients is bioelectrical BI analysis. These This measurements includes bioelectrical BI vector analysis performed with a singlefrequency [15][15] device and with multi-segment and multi-frequency [16][16] measurement equipment, which can be used to accurately measure intracellular and extracellular water components [17][17]. A large comprehensive recent study showed that point measurement of BI in the leg is inversely associated with the incidence of (Chronotropic Incompetence) (CI) in H HF in the general population [18][18]. The IBiS-HUVR team has recently developed a low-cost portable BI device with four electrodes placed on the skin aboutabove four wires crossed over the ankle. After calibration, the prototype was validated in a clinical trial of comprising 80 hospitalized patients with decompensated CI [19][19]. This preliminary study showeds that the daily measurement of the BI located daily during the hospitalization of HF patients is useful to alert about fluid retention, allowing early detection of decompensation and treatment. Humanbody studies focused to on acute HF diagnosis reported, evaluated the BI of the whole body [12][12][17][17], or some parts, delivering conducting the so-called segmented BI test: arms, legs, and intrathoracic [20][20][21][21] parts. These studies are based on the inverse relationship between body impedance and volume [12][12][22][22], which allows to BI systems the to estimate volumes estimation or edemas, by placing electrodes on the adequate body part. The equipment employed by doctors in BI tests are includes relatively complex electronic systems, generally based on commercial equipment components that lead toresulting in nonportable and heavy devices. There are several examples of BI devices on the market;, however, these devices are not useful suitable for real-time continuous BI monitoring in daily clinical practice., This is the case ofe.g. Medtronics (Optivol), RJL Systems (Quantum/S Analyzer) or SFB7 (Impedimed). Some approaches have triedaimed to evolve toward portable devices [12][12], but they are not comfortable enough for continuous BI monitoring of BI, sincebecause it employsthey employ wet electrodes placed over the chest during an one-hour test. AlsoIn addition, a partially portable BI system for knee edema test has beenwas reported in [23][23]., for knee edema test, withIt makes use of wet electrodes; and some of the its test circuits (the iInstrumentation amplifier and demodulator) are located in a small PCB, using a standard Data Acquisition (DAQ) for signal acquisition at 50- kHz frequency point. An Iimpedance cardiography test is was proposed in [24][24]., It compriseswith a small device of 85x56x45 mm3 and a four-wires setup implemented with Ag/AgCl electrodes. Reference In [16][16], reports a BI analysis is was employed to calculate the edema index as the relationship between extracellular body water and total body water, using a commercial multi-frequency analyzer and wet electrodes. In [18][18], the leg impedance is was identified as the most relevant parameter for acute HF prediction in patients. A wearable device for shorttime hydration assessment has been was developed in [25][25]., It is based on a four-wires BI test, able for measuringthat can measure eight frequencies with a sensitivity of 700- ml TBW (Total Body Water) volume increments. AlsoIn addition, for bladder filling evaluation, a proposal based on the AD5933 chip for BI test is described in [26][26]. The device is was fabricated on a small PCB, and includes wireless connectedconnectivity. Again, in this last proposal, a short -time test is performed and wet electrodes are employed. Similarly, the AD5340 chip iswas employed in [27][27] within a device for wide -scope applications based on body BI measurements (as e.g., TBW), requiring wet electrodes. However, tThese previous studies are made based on tests performed in a short time: some minutes or hours at most,. while However, fluids in humans follow a dynamic process with daily circadian changes and, in patients with HF, this process may depend on the stage, degree of (de)compensation and treatment; the dynamics of fluid overload in patients with acute HF during hospitalization and after discharge have not been previously described yet. An alternative BI measurement technique oriented towards the development of wearable bodyfluid sensors, and capable of performing volume change monitorization monitoring to analyze leg fluid accumulation, should enable continuous time monitoring of acute HF patients. In this approach, dry or non-contact electrodes are required to avoid skin damage in long-term time (one or more days) monitoring. All in all, Tthis article study proposes an alternative and new method to evaluate the prognostic value in acute HF patients by continuously monitoring body volume changes continuously with non-contact capacitive non-contact measurements. The objective is to early prediction early of the clinical outcome of for patients with acute HF by evaluating their leg volume. The here presented work herein presented has beenwas in partpartially described in [28][28], as a wearable device based on capacitive sensing located on the ankle., Here,being here we extended withreport a more detailed theoretical analysis for the proposed capacitive sensing structure proposed, with the incorporation of a second proposal for capacitive sensing. In Section II, the models for the proposed capacitive sensors are described and developed in detail. In Section III, a possible circuit option for electrical test is proposed and evaluated its feasibility to as a capacitive test is evaluated. In Section IV, finiteelement analysis of the sensors are is shown described together with electrical simulations of the measurement circuit using as a guide real experimental data extracted from [29][29] as a guide for Código de campo cambiado Código de campo cambiado Código de campo cambiado Código de campo cambiado Con formato: Color de fuente: Automático Código de campo cambiado Código de campo cambiado Código de campo cambiado Código de campo cambiado Código de campo cambiado Código de campo cambiado Código de campo cambiado Código de campo cambiado Código de campo cambiado Código de campo cambiado Código de campo cambiado Código de campo cambiado Código de campo cambiado Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Código de campo cambiado Código de campo cambiado IEEE Transactions on Instrumentation and Measurement 3 both capacitive approaches. A test example is also described for an experimental venous-occlusion plethysmography assay. Finally, the results are discussed in Section V a discussion of the results is set. II. MATERIALS AND METHODS In this section, both proposed capacitive sensors and their principle of operation will beare comprehensively defined and explained in depth. Analytical results based on principles of electromagnetism are also studied; and they will serve set the basis foras comparison with the simulations and laboratory results. AfterwardsSubsequently, design rules for a first prototype and laboratory characterization are presented and explained. Lastly, the sensor circuitry of the sensor will also be is defineddescribed. A. First approach: A 180º -parallel- plate sensor model A.1 Analytical solution of Pparallelplate electrodes analytical solution. The proposal of bBoth devised sensors is toaim at measuringe the change in ankle radius by varying theaccording to the capacitance variation that occurs when the space between the electrodes and the limb is increased by due to swelling. The sensors would be located in a “wearable” on the lower part of the leg, just above the ankle;, this is one of the areas where more fluid accumulates in the event of HF. (Fig. 1). In this first case, the dimensions of the plates are 2.5x2.5 cm2, separated by 0.5 cm. Fig. 11. Proposed sensor in the patient's leg. To provide a more intuitive explanation of the working principle of the sensor, a parallelplate sensor equivalent will beis briefly explained. Later on, tThe connection between both sensors will become transparent apparent as one of the followingin a subsequent subsections will be dedicated tofocused on it. If we place the surface electrodes, S, in parallel planes (Fig. 2) and at a distance. 𝑑0, the capacitance between them has the expressioncan be expressed as follows: Fig. 22. Rectangular electrodes (the width is denoted by t0). 𝐶 =𝜖0𝑆 𝑑0 eq. 11 In this case, rectangular electrodes are used (Fig. 2);, so thatthus, (eq. 1) is expressed as: 𝐶 =𝜖0𝑙0𝑡0 𝑑0 eq. 22 where 𝑙0 and 𝑡0 are the length and width of the plate, respectively. Fig. 33: Rectangular electrodes (the width of the electrode and the dielectric are t0 and  1=  0  r., respectively). With tThe insertion of a part of the human body with permittivity 𝜖1 of and the proportions indicated in the Fig. 3, the causes a capacitance changes. In this distribution, a parallelcapacitor schemea (Fig. 4) arises from the combination of the empty path and the human -body path., The first path is defined by the capacitor of surface 𝑡0(𝑙0−𝑙1) and length 𝑑0 of length, with permittivity 𝜖0: 𝐶1=𝜖0(𝑙0−𝑙1)𝑡0 𝑑0 eq. 33 The Ssecond contribution is formed by two capacitors aligned in series, both of with surface 𝑙1𝑡0, one of with length 𝑑1 and permittivity 𝜖1=𝜖0𝜖𝑟, and another ofthe other with length 𝑑0−𝑑1 and permittivity 𝜖0: C21 =ϵ0ϵrl1t0 d1 eq. 44 C22 =ϵ0l1t0 d0−d1 eq. 55 𝐶2= ( 1 𝐶21 +1 𝐶22)−1 =𝜖0𝑙1𝑡0𝜖𝑟 𝑑0𝜖𝑟+𝑑1(1−𝜖𝑟) eq. 66 The capacitance of the whole system (Fig. 3) is: 𝐶 =𝐶1+𝐶2=𝜖0(𝑙0−𝑙1)𝑡0 𝑑0+𝜖0𝑙1𝑡0𝜖𝑟 𝑑0𝜖𝑟+𝑑1(1−𝜖𝑟) eq. 77 Con formato: Color de fuente: Automático Código de campo cambiado Con formato: Superíndice Con formato: Espacio Después: 6 pto Código de campo cambiado Código de campo cambiado Con formato: Espacio Después: 6 pto Código de campo cambiado Código de campo cambiado Código de campo cambiado Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Con formato: Espacio Antes: 6 pto Código de campo cambiado Código de campo cambiado Código de campo cambiado Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Código de campo cambiado Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático IEEE Transactions on Instrumentation and Measurement 4 Fig. 44. Equivalent circuit of the system. The permittivity of the skin, blood and muscles is much higher than that of air,; 2 two or 3three orders of magnitude higher indeed, according to [30][30], for frequencies not exceedingbelow 106 Hz. Thus, we can estimate that 1−𝜖𝑟≃−𝜖𝑟 if the human body does not occupy all the volume between the electrodes, that is, 𝑑0 ≠𝑑1. Rewriting (eq. 7eq. 7), we have: 𝐶 ≃𝜖0𝑡0(𝑙0−𝑙1 𝑑0+𝑙1 𝑑0−𝑑1) eq. 88 If the equation is observed,According to this equation, the contribution to the capacitance of the space occupied by the air (eq. 3eq. 3) becomes significantly less smaller than the contribution of the space occupied by the human body (eq. 6eq. 6) when the volume occupied by the human body is comparable to the volume between the electrodes., In such cases, so the first term can be neglected for these cases: 𝐶 ≃𝜖0𝑡0𝑙1 𝑑0−𝑑1 eq. 99 In At this point, one can go from the scenario of parallel - plate electrodes scenario to the that of 180º- parallelplate electrodes. The configuration of the electrodes in this situation changes, with both being located in the same plane and separated by a fixed distance. The dimensions of the plates are still 𝑡0𝑙0 (Fig. 5). Fig. 55. Scheme of the leg with the electrodes at 180º. The part of the human body to be measured is the ankle, which is modeled as a cylinder instead of a cube. This cylinder has a variable radius r, which is the radius of the ankle crosssection, a length much greater than 𝑡0, and is at presents a distance 𝑟0, which is the distance between the electrodes and the centre center of the ankle cross-section (Fig. 5). The hypothesis to evaluate the capacitance between the electrodes is that, in following a similar approximation to the one previously made appliedpreviously, the expression of the capacitance has the same form as (eq. 9eq. 9), and the variables 𝑑0, 𝑑1 and 𝑙1 have a relationare related with the ankle radius r. An intuitive justification for this hypothesis may be that if the capacitor at 180𝑜 if it were folded so that its plates were planeparallel, the dielectric in at the center would flatten out, so that it resemblinged a cube (Fig. 6). Fig. 66. Intuitive extrapolation from the parallel-plate model to the plate model at 180º. The problem in obtainingto obtain an expression of for 𝑙1 is that the width of the leg that occupies the space between the plates is not constant (as it is modeled as a cylinder) and that the closest part of the leg to the sensor has a greater contribution, as given that the electric field is more intense. As forConcerning 𝑑0−𝑑1, the expression is much simpler. We can estimate that it will be the distance between the electrodes and the periphery of the ankle, i.e., 𝑑0−𝑑1=𝑟0−𝑟 eq. 1010 However, the problem can be simplified in the following wayas follows: • It can be considered assumed that there is symmetry exists in most of 𝑡0, so wethereby reducinge the problem to two2 dimensions. There would remain aA crosssection of itwould still remain, as shown in the Fig. 7. • The area to be studied is reduced to the one between a circle whose radius is half the distance between the electrodes (𝜌𝑚𝑖𝑛) and a circle whose radius is half the distance between the electrodes plus the length of the electrodes (𝜌𝑚𝑎𝑥); and the edge effects are neglected (Fig. 7). Fig. 77. Region of study in 2D extrapolation. The potential has radial symmetry., whose A formula can be obtained by solving its lLaplacian in polar coordinates: 𝑉(𝜙)=𝑉0 𝜋𝜙 eq. 1111 where 𝑉0 is the potential between electrodes. The Eelectric field can be calculated with the formula 𝐸 󰇍 = −𝛻 󰇍 𝑉 in polar coordinates: 𝐸(𝜌)=𝑉0 𝜋𝜌 eq. 1212 being 𝜌 the distance from the midway point between the plates to any point in the region of study. As Given that the ankle has a very high permittivity, the internal electric field will be negligible inside it;, so (a) side view (b) top view Código de campo cambiado Código de campo cambiado Con formato: Color de fuente: Automático Código de campo cambiado Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Código de campo cambiado Código de campo cambiado Código de campo cambiado Código de campo cambiado Código de campo cambiado Código de campo cambiado Código de campo cambiado Código de campo cambiado Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Código de campo cambiado Código de campo cambiado Código de campo cambiado Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Con formato: Sangría: Primera línea: 0 cm IEEE Transactions on Instrumentation and Measurement 5 consequently, the potential in itinside the ankle will be constant. Thus, the expression of the potential is: 𝑉(𝜌,𝜙)= 𝑉0 2 𝜙𝑐𝑜𝑟𝑡𝑒(𝜌)𝜙 𝜙 ∈ [0,𝜙𝑐𝑢𝑡(𝜌)] eq. 1313 where 𝜙𝑐𝑢𝑡 is the angle at which the air meets the ankle for a particular 𝜌. The formula for an ankle with a radius R located 5.5 cm away from the electrodes is as follows: 𝜙𝑐𝑢𝑡 =𝑡𝑎𝑛−1 (4𝜌2−4𝑟2+121 √𝑟2(968−16𝑟2)+𝜌2(968−16𝜌2)+32𝑟2𝜌2−14641) eq. 1414 As Given that we are only interested in the field at the electrode to calculate the charge, and as given that the field is perpendicular to its surface, the field there will be onlyfield only in the direction of 𝑒𝜙 󰇍 󰇍 󰇍 󰇍 : 𝐸𝜙(𝜌)= 𝑉0/2 𝜙𝑐𝑢𝑡(𝜌)𝜌 eq. 1515 • The electric field must be continuous on the surface of the electrode, since because 𝜎(𝜌)=𝜖0𝐸𝜙(𝜌), where 𝜎 is the charge surface density. For 𝜌>5.5−𝑟, the equation (𝐸𝜙(𝜌) = 𝑉0/2 𝜙𝑐𝑢𝑡(𝜌)𝜌 Eϕ(ρ)= V0/2 ϕcut(ρ)ρ) can be used. For a lower value of 𝜌, this expression makes no sense, because the field lines do not cross the ankle. Therefore, we use the (𝐸(𝜌)=𝑉0 𝜋𝜌𝐸(ρ)=V0 πρ) by , adding a constant to make the field constant. Thus, the expression of the field would bebecomes as follows: 𝐸𝜙(𝜌)= 𝑉0 𝜋𝜌+𝐾 𝜌 ∈ [𝜌𝑚𝑖𝑛,5.5−𝑟] 𝐸𝜙(𝜌)= 𝑉0/2 𝜙𝑐𝑢𝑡(𝜌)𝜌 𝜌 ∈ [5.5−𝑟,𝜌𝑚𝑎𝑥] eq. 1616 Once these approximations have been made and the electric field has been calculated, the charge density can be calculated with as 𝜎(𝜌)= 𝜖0𝐸𝜙(𝜌) and integrated with respect to the variable 𝜌 to obtain the charge per unit length. Dividing the this charge per unit length by the difference in electrode potential (𝑉0) gives the capacity per unit length measured by the sensor. Multiplying The multiplication of the result obtained by 𝑡0=2.5 cm the result obtained, that would beconstitutes the result outcome for the 3D sensor (Fig. 8). Fig. 88. Estimated capacitance of the sensor based on analytical calculations. Adjusting the curve (Fig. 8), we can see that, in fact, 𝑙1 is proportional to 𝑟2. It is also verified that 𝑙0−𝑙1 is equal to 𝑟0− 𝑟, although 𝑟0 seems to be a bitslightly higher greater than 5.5 cm. An offset need tomust be added to the formula (r0 = 5.577 cm, a = 0.1642 pF, b = 0.005789 pF.cm-1, adjusted R- square:0.9999): 𝐶(𝑝𝐹)= 𝑎+𝑏 𝑟2 𝑟0−𝑟 eq. 1717 Until now, the leg was considered as a dielectric whose voltage can be changed easily by the plates. However, this is not the case. The human body usually sits at a few mV, pretty muchbasically equivalent to ground for this matter. Consequently, let us studywe must compare the leg at ground voltage vs. leg at intermediate voltage. As it will be explained below, the negative plate of the capacitor will be connected to ground., so Thus, if the voltage of the body is not corrected, the results of this section change drastically. A simple analytical solution (yet accurate enough for this study) is obtained by considering assuming that the field lines that are cut by the leg collapse there and do not count at all for the calculation of the total charge of the plate. Then, the analytical result for the 3D sensor case is: 𝐸𝜙(𝜌)= 𝑉0 𝜋𝜌 𝜌 ∈[𝜌𝑚𝑖𝑛,5.5−𝑟] 𝐸𝜙(𝜌)=0 𝜌 ∈[5.5−𝑟,𝜌𝑚𝑎𝑥] eq. 1818 Performing the integration in on its surface (𝜌 and 𝑡0), the total charge and, therefore, the capacitance is calculated as follows: 𝐶 =𝜖0⋅𝑡0⋅𝑙𝑜𝑔(5.5−𝑟 𝜌𝑚𝑖𝑛 ) eq. 1919 Results of tThis formula equation can be seenis depicted in (Fig. 9). In this condition, the sensor is not useful for the target application due to its low small change in capacitance. Consequently, a system will be described in next sections to that changes the voltage of the human body in order to maintain it at the middle point between both plates. This is equivalent as to the assumption made in this section to estimate the capacitance analytically. Fig. 99. Capacitance versus vs. radius of the leg if the voltage of the leg is close to (or equal to) ground. Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Código de campo cambiado Con formato: Fuente: Times New Roman, Sin Cursiva, No revisar la ortografía ni la gramática Con formato: Fuente: Sin Cursiva Con formato: Fuente: Sin Cursiva Con formato: Fuente: Sin Cursiva Con formato: Fuente: Sin Cursiva Con formato: Fuente: Sin Cursiva Código de campo cambiado Con formato: Fuente: Sin Cursiva Con formato: Fuente: Sin Cursiva Con formato: Fuente: Sin Cursiva Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Código de campo cambiado Código de campo cambiado Código de campo cambiado Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Código de campo cambiado Código de campo cambiado IEEE Transactions on Instrumentation and Measurement 6 On other hand, in order to chooseConcerning the choice of the material for the sensor plates of the sensor, some factors must be taken into account: lightness, high conductivity, corrosion resistance, non-toxicity, and low price. A.2 Model of Sensor Plates model. Considering According to these aspects, aluminum is the perfect candidate for the electrodes: • The Llightness requisite is fulfilled for by all types of aluminum, as given that its density is around approximately 2.7 g/cm3. • It is the fourth most conductive metal (2.8⋅10−8𝛺⋅m). Only silver, gold and copper have better performance. • It is commonly used for food storage and even implants, so the toxicity is not an issue. • Due to its abundancy, recyclability, and mass production, it is one of the most affordable metals at the moment. • Corrosion resistance is not as simplea more involved aspect: It varies a lotsignificantly depending onwith the environment and the type of aluminum alloy. AlsoMoreover, the mechanism of protection is achieved through passivation, that is, a layer of oxide is depositeds on the surface of the material, for isolationng it. This layer can have different lengths and permittivity, depending on the alloys, thereby affecting the capacitance to different extents. Al 1XXX series (Pure Aluminum 99.0%) has excellent corrosion resistance, the best conductivity, and is generally one of the cheapest in the market. The only oxide produced is Aaluminum Ooxide (Al2O3), whose relative permittivity is 𝜖𝑜𝑥 ≃15, and the thickness (𝑡𝑜𝑥) is, in the worstcase scenario, 1 nm (Fig. 10). If we calculate the capacitance of the layer for a 2.5x2.5 cm2 sensor: 𝐶𝑜𝑥 = 𝜖𝑜𝑥𝜖0𝑆𝑢𝑟𝑓𝑎𝑐𝑒 𝑡𝑜𝑥 =83.0⋅106 pF eq. 2020 Fig. 1010. Aluminum -oxide layer on the plate. The Lleg capacitance measured by the sensor is between 1-2 pF. There will be a layer in each electrode;, and theythe electrodes are in series with the capacitance (C≃1 pF) that we want to measure: 𝐶𝑠𝑒𝑛𝑠𝑜𝑟 =( 1 𝐶𝑜𝑥 +1 𝐶+1 𝐶𝑜𝑥)−1 eq. 2121 The thickness of the oxide layer is not big large enough to affect the measurement. A specific superficial or heat treatment is not needed, as because there are no demanding mechanical specifications for this use. Another advantage of using aluminum is it’s aits magneticity:, as magnetic fields will not interfere with the sensor. Some oOther materials were not considered for different reasons: • Copper: Its absorption through human skin makes it toxic, so it would only be valid for an early prototype that is not going expected to be used a very long timeduring a long period. • Silver and gold: Their price make them unaffordable. The dimensions of the sensor are: 2.5x2.5 cm2 of surface, separated by 0.5 cm, as it has beenwas used for previous calculations. There are three main capacitors in this configuration. Two of them are formed by the 2.5x2.5 cm2 surfaces, one on each side of the plate. One of them will vary depending onwith the radius of the leg (𝐶𝑠𝑒𝑛𝑠𝑜𝑟), whereas the other one is constant and unwanted (𝐶𝑏𝑎𝑐𝑘). The side face of the plates forms an unwanted third capacitor, whose capacitance (𝐶𝑠𝑖𝑑𝑒) depends on the thickness (𝑡𝑝𝑙𝑎𝑡𝑒) of the plate: 𝐶𝑠𝑖𝑑𝑒 =𝜖0⋅2.5⋅𝑡𝑝𝑙𝑎𝑡𝑒 0.5 eq. 2222 An acceptable offset caused by this fact foron the total capacitance of the sensor is 0.02 pF, which is achieved with 𝑡𝑝𝑙𝑎𝑡𝑒 = 0.5 mm (𝐶𝑠𝑖𝑑𝑒 =0.022 pF). A.3 Chassis model. Regarding to the chassis model, the plates of the sensor are attached to a cylindrical strip that will be placed around the leg. The materials for the chassis and the glue to attach the electrodes must be insulating and with low permittivity, in order not to electrically connect the electrodes or cause a high offset in the capacitance. The chassis must also be strong enough not to preclude toany deformation. The ABS polymer is flexible and resistant enough to perform this task., It is also very convenient because it is 3D printable. Its relative permittivity is around approximately 3.5. On the other hand, In addition, the Epoxy bicomponent is one of the best glues to joint metal and plastic, it is insulating, and its permittivity depends on the hardener, but will not be higher thannever exceeding 5. Its thickness will be 200-500 𝜇m. The space between the leg and the sensor is filled with polymeric foam. Its contribution to the capacitance of the sensor is not that easy to predict. Its relative permittivity will vary depending onwith the air/polymer ratio from 1.2 to 3 (no compression to maximum compression with no air between the polymer). When the leg swells, the foam will be compressed, increasing its permittivity. A very simple model, yet with verythat provides similar results similar to other more complex onesmodels, is considering based on a capacitor filled with foam whose transverse section (equipotential surface) is occupied by 𝛼⋅𝑆 of polymer and (1−𝛼)𝑆 of air, where 𝑆 is the area of the surface and 𝛼 is the volume fraction of polymer in the foam. Then, the differential capacitance of this section of distance 𝛿𝑑 is: Con formato: Color de fuente: Automático Código de campo cambiado Código de campo cambiado Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Con formato: Superíndice Con formato: Superíndice Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático IEEE Transactions on Instrumentation and Measurement 7 𝛿𝐶𝑓𝑜𝑎𝑚 = 𝛿𝐶𝑝𝑜𝑙𝑦𝑚𝑒𝑟 +𝛿𝐶𝑎𝑖𝑟 eq. 2323 𝛿𝐶𝑓𝑜𝑎𝑚 =𝜖0𝜖𝑝𝛼𝑆 𝛿𝑑 +𝜖0(1−𝛼)𝑆 𝛿𝑑 eq. 2424 𝛿𝐶𝑓𝑜𝑎𝑚 =𝜖0𝑆 𝛿𝑑 [(𝜖𝑝−1)⋅𝛼+1] eq. 2525 All the sections along the distance 𝑑 have, in on average, the same differential capacitance. As Given that they are in series, the sum of the inverse of all the differential capacitances gives the total capacitance: 𝐶𝑓𝑜𝑎𝑚 =𝜖0𝑆 𝑑[(𝜖𝑝−1)⋅𝛼+1] eq. 2626 Then, the relative permittivity of the foam is: 𝜖𝑓𝑜𝑎𝑚(𝛼) = (𝜖𝑝−1)⋅𝛼+1 eq. 2727 A typical 𝛼 for non-compressed foam is 0.1, which gives 𝜖𝑓𝑜𝑎𝑚 =1.2, a usual permittivity value for this kind type of materials. However, a 40% foam compression of the foam will lead to a 𝛼 = 0.5 and, therefore, 𝛼 will be 2. In what followsNext, the first prototype and the setup for the experimental characterization will beare reported. A two-layer PCB were was used without mask will be used to make the plates (Fig. 11). A.4 Prototype and setup for experimental characterization. Although Copper, instead of these are not made of aluminum, but of copperwas employed in this test,; the difference will not be appreciable in this test is not significant in practical terms and copper is more convenient to implement a prototype (Fig. 11). The dimensions of the plates are wereof 2.5x2.5 cm2 and separated by 0.5 cm. Two layers are were used to remove so the unwanted 𝐶𝑏𝑎𝑐𝑘 is annihilated: One layer is was used as an electrode, and the field lines from his its back collapsed in the other, so the no parasitic 𝐶𝑏𝑎𝑐𝑘 actually does not formwas formed. As forConcerning the leg, it will bewas substituted for a flexible metallic plate of with a much higher greater length than the sensor. and will beIt was placed so that it formssuch that a cylinder of with different radii was implemented. It will have iIts voltage changed according to what is defined abovethe previous explanations. The mechanical design must had to be robust enough to avoid a relative variation from the center of the leg to the sensor. The value of the dielectric constant of the medium between plates can had to minimally vary with humidity, in a range that does not affect in which the performance of the sensor was not affected. The pPhysical activity is also not expected to affect the behavior of the sensor, since because there are no relevant changes in the radius of the leg during exercise. However, prolonged standing or sitting usually causes increased edema in declining areas due to the effect of gravity, and, therefore, leading to causes an increase in the radius of the leg. Nevertheless, in clinical practice, most measurements of biological parameters are performed under baseline conditions first thing in the morning., which This could allow us to minimizinge this possible limitation of our device. Fig. 1111. Plates of the 180º sensor before being mounted in for the setup. The dimensions are 2.5x2.5 cm2. B. Second approach: Parallelplate sensor by overlap B.1 Analytical solution. The second version of the sensor consists of two parallel plates at a certain mutual distance between them. One of the plates is fixed at a distance to the center of the leg, and the other one is fixed to the perpendicular leg perpendicular to it, as shown in Fig. 12. Both plates are barely overlapped when the leg radius is under healthy conditions (which is considered,assumed to be 4 cm), so the capacitance of the sensor is minimal. A higher greater radius would translate in more a greater overlap and, therefore, the an increased capacitance of the sensor rises up. Therefore, tThis is the working principle of this kind type of sensing. When the leg swells, the plate attached to the leg overlaps more than the other plate, rising the sensor capacitance (Fig. 13). Let us, now, extract derive an analytical solution of the sensor. As in any regular parallel -plate capacitor, the capacitance provided by the overlapped surface is as follows: 𝐶1=𝜖0𝑆 𝑑 eq. 2828 𝐶1=𝜖0⋅𝑡0𝑟−𝑟0 𝑑 eq. 2929 in whichwhere 𝑑 is the distance between the plates and 𝑆 is the overlapped surface. For the domain 𝑟 > 𝑟0 (in whichwhere 𝑟0 is the radius of the leg in which the overlap is zero, and 𝑟 is the actual radius oif the leg), 𝑆 = 𝑡0⋅(𝑟−𝑟0) (𝑡0 is the width of the plate, as in previous sections). Then, Fig. 1212. Scheme of the sensor plates and the leg when the leg radius is 4 cm. Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Código de campo cambiado Con formato: Color de fuente: Automático Con formato: Superíndice Con formato: Color de fuente: Automático Código de campo cambiado Con formato: Color de fuente: Automático Código de campo cambiado Con formato: Color de fuente: Automático Código de campo cambiado Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Con formato: Sangría: Primera línea: 0 cm IEEE Transactions on Instrumentation and Measurement 8 Fig. 1313. Scheme of the sensor plates and the leg when the leg radius swallows from 4 to 4.5 cm, so there is moreresulting in a greater overlap, and the increased capacitances rises up. The non-overlapped surface also contributes to the capacitance. This surface is ofpresents a length 𝑙0−(𝑟−𝑟0) and thickness 𝑡0. The closest distance of this surface to the closer end of the other plate is 𝑑, and the furthest distance to the closer end is √(𝑙0−(𝑟−𝑟0))2+𝑑2. We can say, at first glance, that the average distance of this surface to the other plate is approximately (√(𝑙0−(𝑟−𝑟0))2+𝑑2+𝑑)/2. Then, its contribution to the total capacitance is: 𝐶2= 2𝜖0𝑡0𝑙0−(𝑟−𝑟0) √(𝑙0−(𝑟−𝑟0))2+𝑑2+𝑑) eq. 3030 The total capacitance of the sensor is the sum of 𝐶1 and 𝐶2: 𝐶 =𝜖0𝑡0𝑟−𝑟0 𝑑+2𝜖0𝑡0𝑙0−(𝑟−𝑟0) √(𝑙0−(𝑟−𝑟0))2+𝑑2+𝑑) eq. 3131 The curve of the capacitance versus vs. radius is represented in Fig. 14. It shows a highly linear region until reaching the last millimeters of the range, which makes it ideal to be used as a sensor. Fig. 1414: Capacitance versus vs. the radius of the leg for r0 = 4 cm, l0 = 1 cm and d = 0.1 cm. B.2 Model of Ssensor plates model. Regarding the sensor plates model, the same considerations as in the previous section can be applied for this sensor as well., although hereHowever, an exhaustive study of the parasite capacitances is not necessary in this case, as given that the only significant capacitance that will be appreciated will be caused by the circuit, not by the sensor itself. ThenTherefore, the same material (Aluminum 1XXX) with the same thickness (0.5 mm) can be used. The dimensions in this case, will beare 𝑡0= 2.5 cm and 𝑙0= 1 cm. B.3 Chassis model. Concerning to the chassis model, unlike in the previous section, one of the plates must be attached perpendicularly to the cylindrical strip, and the other one to the leg, perpendicularly as well. The same considerations aspects as in the previous section must be considered to choose the chassis material of the chassis, but now the foam will does not interfere in with the capacitance as because it is not placed between the plates. B.4 Prototype and setup for experimental characterization. With reference regard to the prototype and the setup for experimental characterization, the same two-layer PCB as in the previous section will bewas transformed into the electrodes (Fig. 15). The dimensions of the plates are were 1.25x2 cm2. The separation between plates will be of aroundwas approximately 0.06 mm. Only a fine plastic will bewas placed between them to increase the capacitance as much as possible. Fig. 1515. Plates of the sensor by overlap before being mounted to for the setup. The dimensions are 1.25x2 cm2. One of the plates will bewas fixed and the other one will bewas placed from no overlap to almost full overlap in order to study the whole range of operation. As Given that the distance between plates (𝑑) is was very small compared to 𝑙0−(𝑟−𝑟0) in almost 100% of the range, the second term of the equation of the capacitance versus vs. the radius will becomes simplifyied, leaving a linear relation between the capacitance and the radius of the leg: 𝐶 =𝜖0𝑡0𝑟−𝑟0 𝑑+2𝜖0𝑡0𝑙0−(𝑟−𝑟0) √(𝑙0−(𝑟−𝑟0))2+𝑑2+𝑑) ≈𝜖0𝑡0𝑟−𝑟0 𝑑+2𝜖0𝑡0 eq. 3232 III. MEASUREMENT CIRCUITS There are countless many ways to measure capacitance. In this case, a system is needed that allows measurements of in the order of picofarads with an accuracy of 0.1 𝑝𝐹. The frequency passing through the sensor should not exceed 106 Hz, as because this would cause a decrease in the permittivity of the human body and, consequently, in the capacitance measured by the sensor, so it would make the measurement more difficulthindering the measurement process. A suitable way approach to measure the capacitance at low frequencies is through a differentiating circuit where in which the output is the derivative of the input, as shown in Fig. 16. Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Código de campo cambiado Código de campo cambiado Con formato: Color de fuente: Automático Con formato: Color de fuente: Automático Código de campo cambiado Con formato: Superíndice Código de campo cambiado Código de campo cambiado