# Portable Knee Health Monitoring System by Impedance Spectroscopy Based on Audio-Board

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## Abstract

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## 1. Introduction

## 2. Design and Implementation of the Knee Impedance Measurement System

_{K}is the impedance of the knee, and Z

_{AB}and Z

_{CD}are the parasitic impedances between electrodes A and B and C and D, respectively. The resistances with the dashed lines (R

_{xSI}) can be inserted (snapped in, hence the subscript SI) or removed from the circuit in order to change gains and ranges, as it will be discussed in the following. In the prototype used in this work, these changes must be made manually, and this fact allows to employ an extremely simple electronic board. Manual switches can be used, of course, or programmability can be added if required. It must be noted, however, that changing the resistances in the field is seldom required, since, as it will be discussed in the following, the expected range of possible values for Z

_{K}can be easily managed with a fixed setting. Indeed, all testing on actual subjects reported in the following sections have been performed in a fixed configuration with all the R

_{xSI}(with R

_{xSI}= 10 kΩ) inserted.

_{I}, in Figure 1 is used to limit the maximum current sent toward the patient. When performing bioimpedance measurements, it is preferable to use current signals rather than voltages because the safety of applying electrical signals in vivo is limited by the magnitude of applied current, and therefore a better control is possible. Assuming R

_{ISI}removed from the circuit, with a maximum value of the voltage at the output OUTL of 1 Vrms, the maximum current toward the patient is limited to 10 μA rms (R

_{I}= 100 kΩ). A resistance (R

_{ISI}) can be snapped in to increase the level of the current. Typically, we employed R

_{ISI}of 10 kΩ that, in parallel with R

_{I}, allows for a maximum current of about 110 μA, that is still well within the safe range for the patient [24]. As we have noted before, the resistance R

_{ISI}, if present, is installed during initial system configuration and it is never accessible to the operator when performing measurements on a patient. Note that the maximum current can only be obtained if the impedance between nodes A and D (|Z

_{AD}| = |Z

_{AB}+ Z

_{K}+ Z

_{CD}|) is negligible with respect to R

_{I}(or to R

_{I}in parallel to R

_{ISI}). This is indeed the case in impedance measurements on a knee, where |Z

_{AD}| is typically in the order of 100 Ω or below, as we shall discuss in the following. The current exiting node A reaches node D (virtual ground) at the input of a trans-resistance amplifier (OP 27 and R

_{R}or R

_{R}//R

_{RSI}) with a trans-resistance gain G

_{R}= −R

_{R}(or G

_{R}= −R

_{R}//R

_{RSI}). The trans-resistance amplifier is used to send a voltage proportional to the actual current through the circuit to the right input INR of the audio board. Clearly, for aligning the output dynamic of the output OUTL with the input dynamic of INR (1 V rms in both cases), we have R

_{I}= R

_{R}, and, if snap-in resistances are used, they also must match, that is R

_{ISI}= R

_{RSI}. In order to measure the impedance Z

_{K}between nodes B and C, the voltage between these nodes must be detected and amplified. The values of |Z

_{K}| typically range from few tens of ohms up to about 100 Ω. When working with a maximum current of 10 μA, a gain of about 1000 is required to take advantage of the full dynamic range of the input INL of the audio board (1 V rms), while when operating with R

_{ISI}= 10 kΩ in place, a gain of 100 is sufficient. To reach a large bandwidth, so that accurate measurements above 50 kHz can be made, we divided the voltage-amplifying chain into two stages. The first stage is a large bandwidth, JFET input instrumentation amplifier LTC1167, that provides for an amplification of 10 of the differential voltage across the impedance Z

_{K}with a −3 dB bandwidth of 800 kHz. The second stage is a voltage amplifier based on an OP37 operational amplifier. In its default configuration (R

_{2SI}not present), the voltage gain of the second stage is 101 with a −3 dB bandwidth in excess of 600 kHz. When the 10 kΩ snap-in resistance (R

_{2SI}) is in place, the gain reduces to 10.1 with a −3 dB bandwidth in excess of 5 MHz. The AC coupling stage R

_{A}, C

_{A}is used to reject the DC component at the output of the instrumentation amplifier. With R

_{A}= 10 kΩ and C

_{A}= 3.3 μF, the low corner frequency is about 5 Hz, well below the frequency range in which bioimpedance measurements are usually carried out (above a few kHz [25]).

_{XSI}removed from the circuit (maximum test current about 10 μA rms). We can resort to SPICE simulation to verify what would be the result of measurements in the particular simple case of Z

_{K}= R

_{K}= 100 Ω, Z

_{AB}= R

_{AB}= 10 Ω and Z

_{CD}= R

_{CD}= 10 Ω. The resulting estimated impedance (Z

_{M}) according to such a simulation is reported in Figure 2, where the grey area indicates the frequency region outside the measuring capability of the audio board being used (f > 80 kHz).

_{M}| = 100 Ω and ∠Z

_{M}= 0 at low frequencies (f < 500 Hz) is due to the presence of the high pass filter C

_{A}R

_{A}in Figure 1. The effect of the high pass filter could be reduced by decreasing the cut-in frequency (by increasing C

_{A}) but, since, as we will discuss presently, we need a calibration procedure for correcting the error at high frequencies, this is not really necessary. Moreover, bioimpedance measurements are rarely performed below a few kHz.

_{C}(f), defined as follows:

_{K}is the actual true value of the impedance and Z

_{M}is the impedance as obtained from the measurement with the circuit in Figure 1. Suppose now we can ensure that the correction function H

_{C}is essentially the same regardless of the actual Z

_{K}(in a reasonable and useful range): if this is the case, we can obtain H

_{C}(f) from an actual measurement on an actual test impedance (a known calibration impedance Z

_{C}) and then obtain the actual value of any impedance by multiplying the measured value Z

_{M}at any frequency by H

_{C}, as suggested by Equation (1).

_{ext}and R

_{int}, whose physical meaning will be discussed in the following sections, are expected to range between 30 and 100 Ω and the capacitance C in the range between 10 and 15 nF.

_{K}in the form of Figure 3 with random and uncorrelated values, within the expected ranges, for R

_{in}, R

_{ext}and C for each run. The correction function H

_{C}was evaluated for each set of values in order to check how much it changed depending on the actual Z

_{K}being tested. In a first simulation set-up, we performed the test in the same conditions in which Figure 2 was obtained, that is with all snap-in resistances removed from the circuit. The results are summarized in Figure 4. All curves representing the modulus and the phase of the correction functions lie inside two limiting curves: the deviation is however so small that the limiting curves can be distinguished, with the scale used for the figure, only in the case of the modulus and only for frequencies above about 20 kHz. It can be noticed that in the entire frequency range that can be explored (outside the gray areas), the deviation in the modulus of the correction function is expected to be less than 0.2% and, more importantly, the deviation in the phase is expected to be less than 0.03 degrees. This means that any calibration curve obtained from a calibrated impedance (in the possible range for Z

_{K}) can be used to obtain a calibration function H

_{C}that can be used for all actual measurements with small errors in the estimation of the modulus (less than 0.2%) and an almost negligible error in the phase.

_{C}and the reason why such spread increases for increasing frequency. It is clear that for H

_{C}to change as a function of Z

_{K}, either the gain of the voltage amplification chain (from V

_{BC}to the input INL in Figure 1) or the gain of the current amplification chain (from I

_{IN}to the input INR in Figure 1), or both, should depend on the value of Z

_{K}. We clearly expect the gain of these two chains to depend on the frequency, but the reason why we observe a dependence, at the same frequency, on the value of Z

_{K}and the reason why this change increases with frequency (with Z

_{K}changing in the same predefined range) are not obvious. There is certainly no reason, as can also be easily verified through simulation, for the gain of current amplification chain to depend on Z

_{K}or in any circuit component to the left of node D in Figure 1. Similarly, if the inverting input of the instrumentation amplifier was actually grounded, there would be no reason for the gain of the voltage amplification chain to depend on Z

_{K}. The fact is, however, that the non-inverting input of the instrumentation amplifier is not grounded, and this is indeed the reason why we may obtain a gain that changes with the value of the impedance. In order to understand why, let us assume, for the sake of simplicity, that the impedance Z

_{CD}be completely negligible. In this case, we observe that node C is “virtually” grounded through the input of the trans-resistance stage. More in detail, the impedance from node C toward ground (with Z

_{CD}= 0) is the input impedance of the trans-resistance stage. Whereas in most applications we may assume this impedance to be negligible, in our particular case in which |Z

_{K}| is at most 100 Ω, this is not true in the entire frequency range in which we are interested. In order to estimate such an impedance in our operating conditions, we can safely assume the OP27 to be described by a single pole frequency response with a DC gain A

_{V}

_{0}and a pole frequency f

_{op}. Since we typically operate at frequencies, f, above 100 Hz (hence f >> f

_{op}) and well below the gain bandwidth product of the operational amplifier, we can estimate the modulus of the input impedance Z

_{IT}of the transresistance stage to be:

_{R}= 100 kΩ and typical values for A

_{V}

_{0}and f

_{OP}(A

_{V}

_{0}× f

_{OP}= 8 MHz for the OP27), at the frequency of 10 kHz we have |Z

_{IT}|≈125 Ω, that is an input impedance larger than the typical Z

_{K}on which we want to perform measurements. The result of this situation is that the common mode voltage at the input of the instrumentation amplifier can be larger than the differential voltage across Z

_{K}. More in general, at low frequencies, |Z

_{IT}| is small, hence the common mode voltage at the input of the LT1167 is small compared to the differential voltage, and this fact, combined with the high value of the CMRR (105 dB for f < 100 Hz), results in the almost complete rejection of the contribution of the common mode input voltage to the output voltage at node INL in Figure 1. As the frequency increases, however, the common mode input voltage for the same differential voltage across Z

_{K}increases because |Z

_{IT}| increases (by 20 dB/decade), and, at the same time, the CMRR decreases (−20 dB/decade above 100 Hz). These two effects both cause a larger and larger contribution of the common mode input voltage to the output voltage at INL as the frequency increases. The contribution of the common mode input voltage to the output voltage introduces an error, and we can reasonably expect this error to change as Z

_{K}changes and to be larger and larger as the frequency increases. This fact is indeed nicely confirmed by the result of the Monte Carlo simulations reported in Figure 5, where the maximum deviation (∆) in the modulus of the correction function H

_{C}is reported vs. frequency in the very same conditions used to obtain Figure 5 (empty squares) and in the case in which 10 kΩ snap-in resistances are inserted in parallel to R

_{I}, R

_{2}and R

_{R}. We can clearly see that the maximum deviation (∆) increases at a rate of about 40 dB/decade, which can be directly correlated to the increase by 20 dB/decade of the input impedance of the trans-resistance stage and the decrease of the CMRR of the instrumentation amplifier by −20 dB/decade, as discussed above. As a further evidence of the correctness of our interpretation, it can be noticed that when the snap-in resistances are inserted, this causes a reduction by a factor of about 10 in the input impedance of the trans-resistance stage, and this, according to the mechanism discussed above, causes in turn a decrease of the maximum deviation (∆) by the same factor at all frequencies, as can be seen in Figure 5. Since there is not much that can be done about the CMRR of the instrumentation amplifier, it is clear that the only way to further reduce the maximum deviation would be to design a trans-resistance amplifier with a much smaller equivalent input impedance. On the other hand, especially when the snap-in resistances are present, the maximum deviation is sufficiently small and there is no need to increase the complexity of the circuit. With the snap-in resistances in place, the maximum deviation in the modulus of H

_{C}at 50 kHz is about 0.05 × 10

^{−3}and, at the same frequency, the maximum deviation in the phase can be estimated to be below 10

^{−3}degrees.

_{K}with Z

_{AB}= Z

_{CD}= 10 Ω. Using a single resistor greatly simplifies performing the calibration measurement while remaining effective. To demonstrate this fact, we first extracted the calibration function H

_{C}from actual measurements on the 100 Ω resistor, and then used H

_{C}for correcting the actual measurements on a test impedance in the form of Figure 3, with R

_{ext}= 100 Ω, C = 10 nF, R

_{in}= 100 Ω. The results of such procedure are summarized in Figure 6. The measurements obtained without correction (black dots) are shown together with the measurement modified using the correction function H

_{C}obtained from a previous measurement on the calibration impedance (empty squares) and with the calculated values for the modulus and the phase of the impedance being tested (continuous black line). As it can be noticed, after correction, the measured values are essentially coincident with the expected ones.

## 3. Knee Impedance Measurement System: Software

_{O}(t) given by:

_{O}, we obtain a sinusoidal current i

_{k}(t) through the impedance chain Z

_{AB}, Z

_{K}and Z

_{CD}that, in turn, results in a sinusoidal voltage drop v

_{k}(t) across the impedance of interest Z

_{K}. The board in Figure 1 amplifies both signals to produce the voltages V

_{V}and V

_{I}at the left and right input of the audio board:

_{R}by −1 so that we obtain the same phase for the voltage and the current in the case of a pure resistance for Z

_{K}and we have assumed, for the sake of simplicity, real gains independent of the frequency. We have, however, explicitly noted the fact that both the amplitude and the phase of the signals can depend on the time as a result of physiological causes, such as the cardiac activity. Both amplitude and phase changes are expected to be small and occurring over a time much longer than the signal period. After analog to digital conversion, each of the input signals is sent to a coherent demodulator implemented in software, so that their amplitude and phase can be extracted. The cut-off frequency of the fourth-order IIR low pass filters (LPF in Figure 7) is set in such a way that, besides eliminating the high-frequency components at the output of the multipliers, the numerical signal can be decimated by a factor M = 16, thus reducing the data rate from 192 down to 12 kHz. This sampling frequency is largely sufficient to retain the information due to the possible modulation in the amplitudes and phases of the detected signals. At the outputs of the decimation stages, the in-phase and in-quadrature components can be further low pass filtered in order to reduce noise before the estimation of the impedance. Depending on whether or not we want to retain information on the amplitude and phase fluctuations due to physiological activities, we may have to employ different cut-off frequencies to distinguish phenomena occurring in different frequency bands. In order to simplify such a process and to maintain high flexibility in the data elaboration process, we resorted to the QLSA public domain library [26]. While QLSA is mainly intended for multi-channel spectral analysis, as part of its inner working operation, it performs multi-stage low pass filtering and decimation on the incoming signal stream. More precisely, for each input signal sequence, QLSA is used to perform the filtering operations schematically shown in Figure 8.

_{R}corresponding to the input sampling rate and with an attenuation larger than 70 dB above f

_{R}/4 [26]. In this way, we can obtain several low pass filtered outputs with geometrically decreasing bandwidth limits (by a factor of 4 at each step) and correspondingly lower sampling rate, thus lowering the load for analysis algorithms at lower sampling rates.

_{K}at any given time from the knowledge of the quantities A

_{V}cos(Φ

_{V}), A

_{V}sin(Φ

_{V}), A

_{I}cos(Φ

_{I}), A

_{I}sin(Φ

_{I}) and from the knowledge of the voltage and trans-resistance gains G

_{V}and G

_{R}.

## 4. System Testing

_{ext}models the extracellular liquids, R

_{in}the intracellular liquids and C the capacitance of the cellular membrane [16,28]. The ratio R

_{ext}/R

_{in}was found to be an important indicator for identifying osteoarthritis or cartilage damage [16,17]. Moreover, the ratio of the intracellular resistances of the two knees allows to identify the dominant leg (if any). In addition to this term, the real part (RE) and the imaginary part (X) of the impedance were also discriminating factors for determining the health status of the knee, and their value at 50 kHz [29] was used. Parameters R

_{ext}, R

_{in}and C (not used for the study) where extracted by fitting the experimental data (using OriginPro 8 by OriginLab Corporation) against the real (RE) and imaginary (X) parts of the impedance in Figure 3:

## 5. Results and Discussion

_{ext}/R

_{in}is the ratio between the extracellular and the intracellular resistances and R

_{inr}/R

_{inl}is the ratio between the intracellular resistances of the right and of the left knee.

#### 5.1. Data Discussion: ∆R and ∆X

#### 5.2. Data Discussion: Rext/Rin

_{ext}/R

_{in}lower than one. The only subject who has the R

_{ext}/R

_{in}> 1 (for both right and left knee) belongs to group 1 (subject E1 in Table 2) and is an elderly subject (woman, 77 years old) who has been diagnosed with advanced osteoarthritis. None of the other subjects had a diagnosis of osteoarthritis. This first observation is in accordance with what is reported in References [16,17]. Indeed, in healthy knees, the resistivity of the extracellular environment is lower than that of the intracellular. Since R

_{ext}is associated with the extracellular liquids, its increase in osteoarthritic knees is justified by an increase of apatite crystals and pyrophosphate of calcium (that can be considered as non-conductive particles) in the synovial fluid due to disease [32,33]. Moreover, an increase of the number of leucocytes (size of 10–20 μm) in the synovial liquid of an osteoarthritic knee has been observed [34] and this can contribute to the increase of R

_{ext}. Finally, when the knee is in an inflammatory status, cytokines are released into the synovial fluid [35], thus resulting in a further increase of the extracellular resistance. For non-osteoarthritic knees, a mean value of R

_{ext}/R

_{in}= 0.63 has been registered, with a minimum value of 0.3 and a maximum of 0.82. The variations of R

_{ext}/R

_{in}are due to inflammatory states (different values of R

_{ext}) or to different values of R

_{in}. This topic will be discussed in more detail in the next subsection.

#### 5.3. Data Discussion: R_{inl}/R_{inr}

_{in}is mainly associated to the articular cartilage cells’ metabolism [36] (chondrocytes are the only cell type in the cartilage tissue [37]). This metabolism is stimulated by mechanical loading, detected by the mechanoreceptors on the cell surface [38]. In Reference [36], it is explained that through the process of mechanotransduction: mechanical signals modulate the biochemical activity of chondrocytes, regulating metabolic activities by influencing the state of the knee joints. In particular, dynamic compressions during moderate exercise generate mechanical stimuli that can regulate the metabolic balance, thus preventing the progression of cartilage damage [38]. A proper mechanical loading is crucial for the health of knee joints, as it has been demonstrated that insufficient biomechanical stimuli, due, for example, to a forced immobilization, can lead to reduced thickness and softening of the cartilage [39], whereas, conversely, an excessive load can inhibit the articular cartilage regenerative capacity, leading to damage or, in extreme cases, to irreversible destruction [38]. In the case of high load, cytokines are released in the intracellular fluid. Based on these considerations, we have chosen to identify the dominant leg as the one with a higher R

_{in}value, because it seems legitimate to correlate, for the same subject, the higher R

_{in}value with a higher load condition for the relative knee joint.

_{in}of at least 10% compared to the other. If this difference is not noticed, it is assumed that there is no dominant leg. The resistance R

_{in}is related to the intracellular fluid and to the metabolic activity of the knee cells, therefore it is reasonable to assume that a higher value of this resistance indicates a greater workload for the knee. Among the examined subjects, four of them show a dominant leg. Among the subjects of group 2 (group of people who regularly practice sport), subjects S1 and S4 show the right leg and the left leg to be dominant, respectively. This result has been verified. In fact, S1 is a (woman, 43 years old) fitness coach with a meniscus problem causing inflammation and edema in the left knee (as also discussed in Section 5.1). Therefore, during workouts, the subject loads on the right knee to avoid making the injured knee problem worse. Subject S4 is a young right-handed basketball player not yet very skilled in the use of his left hand and who consequently mainly jumps on the left leg (think of the lay-up movement in the basketball game).

_{in}of the left knee may not only be due to a greater load but also to a decrease in the pH of the knee. Indeed, a strong negative correlation between the pH variations and the quantity of intracellular liquid has been observed in References [40,41], and in the case of osteoarthritic knees (or with damage to cartilage), the concentration of hyaluronic acid decreases and the pH of the synovial fluid increases, which could be an explanation for a higher intracellular resistance.

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Nicolini, A.P.; de Carvalho, R.T.; Matsuda, M.M.; Sayum, J.F.; Cohen, M. Common injuries in athletes’ knee: Experience of a specialized center. Acta Ortop Bras.
**2014**, 22, 127–131. [Google Scholar] [CrossRef] [Green Version] - Resta, P.; Presti, D.L.; Schena, E.; Massaroni, C.; Formica, D.; Kim, T.; Shin, D. A wearable system for knee flexion/extension monitoring: Design and assessment. In Proceedings of the IEEE International Workshop on Metrology for Industry 4.0 & IoT, Roma, Italy, 3–5 June 2020; pp. 273–277. [Google Scholar]
- Hootman, J.M.; Macera, C.A.; Ainsworth, B.E.; Addy, C.L.; Martin, M.; Blair, S.N. Epidemiology of musculoskeletal injuries among sedentary and physically active adults. Med. Sci. Sports Exerc.
**2002**, 34, 838–844. [Google Scholar] [CrossRef] [PubMed] - Calmbach, W.L.; Hutchens, M. Evaluation of patients presenting with knee pain: Part I. History physical examination radiographs and laboratory tests. Am. Fam. Physician
**2003**, 68, 907–912. [Google Scholar] [PubMed] - Friedman, L.; Finlay, K.; Jurriaans, E. Ultrasound of the knee. Skelet. Radiol.
**2001**, 30, 361–377. [Google Scholar] [CrossRef] - Tsai, B.; Xue, H.; Birgersson, E.; Ollmar, S.; Birgersson, U. Dielectrical properties of living epidermis and dermis in the frequency range from 1 khz to 1 mhz. J. Electr. Bioimpedance
**2019**, 10, 14–23. [Google Scholar] [CrossRef] [Green Version] - Rodríguez Timaná, L.C.; Castillo García, J.F. Characterization of people with type II diabetes using electrical bioimpedance. In AETA 2019—Recent Advances in Electrical Engineering and Related Sciences: Theory and Application. AETA 2019; Cortes Tobar, D., Hoang Duy, V., Trong Dao, T., Eds.; Lecture Notes in Electrical Engineering; Springer: Cham, Switzerland, 2019; Volume 685. [Google Scholar]
- Arpaia, P.; Cesaro, U.; Frosolone, M.; Moccaldi, N.; Taglialatela, M. A micro-bioimpedance meter for monitoring insulin bioavailability in personalized diabetes therapy. Sci. Rep.
**2020**, 10, 13656. [Google Scholar] [CrossRef] [PubMed] - Coates, J.; Chipperfield, A.; Clough, G. Wearable Multimodal Skin Sensing for the Diabetic Foot. Electronics
**2016**, 5, 45. [Google Scholar] [CrossRef] [Green Version] - Nuñez, C.; Gallagher, D.; Visser, M.; Pi-Sunyer, F.X.; Wang, Z.; Heymsfield, S.B. Bioimpedance analysis: Evaluation of leg-to-leg system based on pressure contact footpad electrodes. Med. Sci. Sports Exerc.
**1997**, 29, 524–531. [Google Scholar] [PubMed] [Green Version] - Kubicek, W.G.; Patterson, R.P.; Witsoe, D.A. Impedance cardiography as a noninvasive method of monitoring cardiac function and other parameters of the cardiovascular system. Ann. N. Y. Acad. Sci.
**1970**, 170, 724–732. [Google Scholar] [CrossRef] - Zink, M.D.; König, F.; Weyer, S.; Willmes, K.; Leonhardt, S.; Marx, N.; Napp, A. Segmental bioelectrical impedance spectroscopy to monitor fluid status in heart failure. Sci. Rep.
**2020**, 10, 3577. [Google Scholar] [CrossRef] - Jotta, B.; Coutinho, A.B.B.; Pino, A.V.; Souza, M.N. Lactate threshold by muscle electrical impedance in professional rowers. Rev. Sci. Instrum.
**2017**, 88, 045105. [Google Scholar] [CrossRef] [PubMed] - Morais, A.P.; Pino, A.V.; Souza, M.N. Detection of questionable occlusal carious lesions using an electrical bioimpedance method with fractional electrical model. Rev. Sci. Instrum.
**2016**, 87, 084305. [Google Scholar] [CrossRef] [PubMed] - Cheng, Y.T.; Tai, C.C.; Chou, W.; Tang, S.T.; Lin, J.H. Analyzing the audio signals of degenerative arthritis with an electronic stethoscope. Rev. Sci. Instrum.
**2018**, 89, 085111. [Google Scholar] [CrossRef] - Neves, E.B.; Pino, A.V.; Almeida, R.M.V.R.D.; Souza, M.N.D. Knee bioelectric impedance assessment in healthy/with osteoarthritis subjects. Physiol. Meas.
**2010**, 31, 207–219. [Google Scholar] [CrossRef] - Alvarenga, R.L.; Souza, M.N. Assessment of knee osteoarthritis by bioelectrical impedance. In Proceedings of the 25th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Cancun, Mexico, 17–21 September 2003; pp. 3118–3121. [Google Scholar]
- Hersek, S.; Töreyin, H.; Inan, O.T. A robust system for longitudinal knee joint edema and blood flow assessment based on vector bioimpedance measurements. IEEE Trans. Biomed. Circuits Syst.
**2016**, 10, 545–555. [Google Scholar] [CrossRef] - Shandhi, M.M.H.; Hersek, S.; Inan, O.T. A finite element model of knee electrical bioimpedance for facilitating edema quantification. In Proceedings of the IEEE EMBS International Conference on Biomedical & Health Informatics, Orlando, FL, USA, 16–19 February 2017; pp. 73–76. [Google Scholar]
- Hersek, S.; Toreyin, H.; Teague, C.N.; Millard-Stafford, M.L.; Jeong, H.-K.; Bavare, M.M.; Wolkoff, P.; Sawka, M.N.; Inan, O.T. Wearable vector electrical bioimpedance system to assess knee joint health. IEEE. Trans. Biomed. Eng.
**2017**, 64, 2353–2360. [Google Scholar] [CrossRef] - MP150 System, Biopac Systems Inc. Available online: https://www.biopac.com/wp-content/uploads/MP150-Systems.pdf (accessed on 17 November 2020).
- USB Audio Board Behringer U-PHORIA UMC202HD. Available online: https://www.behringer.com/behringer/product?modelCode=P0BJZ (accessed on 17 November 2020).
- PortAudio Libraries. Available online: www.portaudio.com (accessed on 11 January 2021).
- Olson, W.H. Electrical safety. In Medical Instrumentation: Application and Design, 5th ed.; Wiley: New York, NY, USA, 2020; pp. 803–847. [Google Scholar]
- Kyle, U.G.; Bosaeus, I.; De Lorenzo, A.D.; Deurenberg, P.; Elia, M.; Gomez, J.M.; Heitmann, B.L.; Kent-Smith, L.; Melchior, J.-C.; Pirlich, M.; et al. Bioelectrical impedance analysis—Part I: Review of principles and methods. Clin. Nutr.
**2004**, 23, 1226–1243. [Google Scholar] [CrossRef] - Ciofi, C.; Scandurra, G.; Giusi, G. QLSA: A software library for spectral estimation in low-frequency noise measurement applications. Fluct. Noise Lett.
**2019**, 18, 1940004-1–1940004-12. [Google Scholar] [CrossRef] - McAdams, E.; Jossinet, J.; Lackermeier, A.; Risacher, F. Factors affecting electrode-gel-skin interface impedance in electrical impedance tomography. Med. Biol. Eng. Comput.
**1996**, 34, 397–408. [Google Scholar] [CrossRef] [PubMed] - Cole, K.S. Membranes Ions and Impulses: A Chapter of Classical Biophysics; University of California Press: Berkeley, CA, USA, 1968. [Google Scholar]
- Lukaski, H.; Moore, M. Bioelectrical impedance assessment of wound healing. J. Diabetes Sci. Technol.
**2012**, 6, 209–212. [Google Scholar] [CrossRef] [Green Version] - Gabriel, S.; Lau, R.W.; Gabriel, C. The dielectric properties of biological tissues: II. Measurements in the frequency range 10 Hz to 20 GHz. Phys. Med. Biol.
**1996**, 41, 2251–2269. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Janssen, G. Die Chondropathia patellae als Prägonarthrose-Zur Atiologie und Therapie anhand von Ergebnissen nach Abrasio patellae [Chondropathy of the patella as pre-arthrosis of the knee. Its causes and treatment, based on results after “abrasio patellae” (author’s transl)]. Z. Orthop. Ihre Grenzgeb.
**1974**, 112, 1036–1044. [Google Scholar] [PubMed] - Nero, P.; Nogueira, I.; Vilar, R.; Pimentão, J.B.; Branco, J.C. Identificação de cristais no líquido sinovialpor por microscopia eletrônica. Acta Reum. Port.
**2006**, 31, 75–81. [Google Scholar] - Doherty, M.; Belcher, C.; Regan, M.; Jones, A.; Ledingham, J. Association between synovial fluid levels of inorganic pyrophosphate and short term radiographic outcome of knee osteoarthritis. Ann. Rheum. Dis.
**1996**, 55, 432–436. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Melo, R.G. O l’ıquido Sinovial. Acta Reum. Port.
**2003**, 28, 249–266. [Google Scholar] - Webb, G.R.; Westacott, C.I.; Elson, C. Osteoarthritic synovial fluid and synovium supernatants up-regulate tumor necrosis factor receptors on human articular chondrocytes. Osteoarthr. Cartilage
**1998**, 6, 167–176. [Google Scholar] [CrossRef] [Green Version] - Primorac, D.; Molnar, V.; Rod, E.; Jeleč, Ž.; Čukelj, F.; Matišić, V.; Vrdoljak, T.; Hudetz, D.; Hajsok, H.; Borić, I. Knee Osteoarthritis: A Review of Pathogenesis and State-Of-The-Art Non-Operative Therapeutic Considerations. Genes
**2020**, 11, 854. [Google Scholar] [CrossRef] - Goldring, S.R.; Goldring, M.B. Changes in the osteochondral unit during osteoarthritis: Structure, function and cartilage bone crosstalk. Nat. Rev. Rheumatol.
**2016**, 12, 632–644. [Google Scholar] [CrossRef] [PubMed] - Musumeci, G. The Effect of Mechanical Loading on Articular Cartilage. J. Funct. Morphol. Kinesiol.
**2016**, 1, 154–161. [Google Scholar] [CrossRef] [Green Version] - Vanwanseele, B.; Eckstein, F.; Knecht, H.; Spaepen, A.; Stüssis, E. Longitudinal Analysis of Cartilage Atrophy in the Knees of Patients with Spinal Cord Injury. Arthritis Rheum.
**2003**, 48, 3377–3381. [Google Scholar] [CrossRef] - Mohan, K.R.; Raymer, G.H.; Moran, G.R.; Marsh, G.; Thompson, R.T. Changes in tissue water content measured with multiple-frequency bioimpedance and metabolism measured with 31P-MRS during progressive forearm exercise. J. Appl. Physiol.
**2006**, 101, 1070–1075. [Google Scholar] - Damon, B.M.; Gregory, C.D.; Hall, K.L.; Stark, H.J.; Gulani, V.; Dawson, M.J. Intracellular acidification and volume increases explain R(2) decreases in exercising muscle. Magn. Reson. Med.
**2002**, 47, 14–23. [Google Scholar] [CrossRef] [PubMed]

**Figure 1.**Circuit schematic of the proposed system. Z

_{K}is the impedance of the knee, and Z

_{AB}and Z

_{CD}are the parasitic impedances between electrodes A and B and C and D, respectively.

**Figure 2.**Simulation of the measurement results with Z

_{k}= 100 Ω. The grey area indicates the frequency region outside the measuring capability of the audio board being used.

**Figure 3.**Equivalent circuit of a knee. R

_{ext}models the extracellular liquids, R

_{in}the intracellular liquids and C the capacitance of the cellular membrane.

**Figure 4.**Modulus and the phase of the correction functions. The deviation is so small that the limiting curves can be distinguished, with the scale used for the figure, only in the case of the modulus and only for frequencies above 20 kHz.

**Figure 5.**Maximum deviation of the modulus of the correction function H

_{C}vs. frequency. The empty squares refer to the same simulation condition in which Figure 4 has been obtained. In the case of the empty circles, the only change was the presence of 10 kΩ snap-in resistances in parallel to R

_{I}, R

_{2}and R

_{R}in Figure 1.

**Figure 6.**Measurements on a test impedance as in in Figure 3 with R

_{ext}= 100, C = 10 nF and R

_{in}= 100. The black dots are the measurement results when no correction is applied. The empty squares are the measurement results corrected with the calibration function H

_{C}obtained from a previous measurement on a single 100 Ω resistor. As it can be noticed, after correction, the measurement essentially coincides with the nominal value of the tested impedance at each frequency (black line).

**Figure 7.**Schematic diagram of the operation of the Digital Signal Processing (DSP) section of the system software.

**Figure 11.**Reactance vs. resistance for left (injured) knee and right (healthy) knee. (

**a**) Acute phase of injury, (

**b**) situation after two weeks from (

**a**), during which the subject performed heavy sport activity, (

**c**) situation after another 10 days of training, during which the subject tried to load less on the leg in pain, (

**d**) situation after about 3 months of less stressful activity for the joints (walking and swimming) and ice therapy.

**Table 1.**Medical diagnosis and related investigation techniques for all the examined subjects. Subjects S3 and S4 do not suffer from any knee-related medical condition.

Group | Subject | Diagnosis | Medical Investigation |
---|---|---|---|

1 | E1 | High-grade osteoarthritis | NMR (Nuclear Magnetic Resonance), X-Ray |

E2 | mild cartilage problems due to age | orthopedic medical examination | |

2 | S1 | Meniscus inflammation | NMR |

S2 | Meniscus inflammation | NMR | |

S3 | - | - | |

S4 | - | - | |

S5 | Chondropathy (maximum grade) | NMR, Arthroscopy | |

3 | NS1 | slight inflammation due to overweight | orthopedic medical examination |

NS2 | Chondropathy (third grade) | NMR |

Group | Subject | Right Knee | Left Knee | ∆R * (Ω) (R-L) | ∆X *(Ω) (R-L) | Rinr/Rinl* | ||||
---|---|---|---|---|---|---|---|---|---|---|

RE * (Ω) | X *(Ω) | Rext/Rin* | RE (Ω) | X (Ω) | Rext/Rin | |||||

1 | E1 | 69 | 32.6 | 1.74 | 65 | 31.6 | 1.47 | 4 | 1 | 0.87 |

E2 | 54 | 28 | 0.78 | 63 | 34.5 | 0.78 | −9 | −6.5 | 0.65 | |

2 | S1 | 70 | 31.6 | 0.53 | 62 | 29.6 | 0.53 | 8 | 2 | 1.14 |

S2 | 56.6 | 24.9 | 0.57 | 50.2 | 22.2 | 0.52 | 6.4 | 2.7 | 1.01 | |

S3 | 44.2 | 23.3 | 0.75 | 44.3 | 23.1 | 0.77 | 0.1 | 0.2 | 1.03 | |

S4 | 51.2 | 26.9 | 0.82 | 53.9 | 27.5 | 0.74 | −2.7 | −0.6 | 0.89 | |

S5 | 68.3 | 31.2 | 0.67 | 69.3 | 33.4 | 0.75 | −1 | −2.2 | 1.06 | |

3 | NS1 | 94 | 47.6 | 0.70 | 100 | 51.6 | 0.77 | −6 | −4 | 1.01 |

NS2 | 48.2 | 18.8 | 0.37 | 41.2 | 14.9 | 0.3 | 7 | 4 | 0.95 |

_{ext}/R

_{in}is the ratio between the extracellular and the intracellular resistances and R

_{inr}/R

_{inl}is the ratio between the intracellular resistances of the right and of the left knee.

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## Share and Cite

**MDPI and ACS Style**

Scandurra, G.; Cardillo, E.; Giusi, G.; Ciofi, C.; Alonso, E.; Giannetti, R.
Portable Knee Health Monitoring System by Impedance Spectroscopy Based on Audio-Board. *Electronics* **2021**, *10*, 460.
https://doi.org/10.3390/electronics10040460

**AMA Style**

Scandurra G, Cardillo E, Giusi G, Ciofi C, Alonso E, Giannetti R.
Portable Knee Health Monitoring System by Impedance Spectroscopy Based on Audio-Board. *Electronics*. 2021; 10(4):460.
https://doi.org/10.3390/electronics10040460

**Chicago/Turabian Style**

Scandurra, Graziella, Emanuele Cardillo, Gino Giusi, Carmine Ciofi, Eduardo Alonso, and Romano Giannetti.
2021. "Portable Knee Health Monitoring System by Impedance Spectroscopy Based on Audio-Board" *Electronics* 10, no. 4: 460.
https://doi.org/10.3390/electronics10040460