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International Journal of
eISSN: 2573-2838

Biosensors & Bioelectronics

Short Communication Volume 4 Issue 3

Nonlinear transfer function’s approach to non-invasive glucose measurement

Andres Garcia, Gustavo Monte

Universidad Tecnol

Correspondence: Andres Garcia, Grupo de Investigación en Mecanica Aplicada (GIMAP), Universidad Tecnologica Nacional. 11 de Abril 461, Bahia Blanca, Argentina, Tel +54-291-4448122

Received: April 19, 2018 | Published: May 25, 2018

Citation: García A, Monte G. Nonlinear transfer function’s approach to non-invasive glucose measurement. Int J Biosen Bioelectron. 2018;4(3):120122. DOI: 10.15406/ijbsbe.2018.04.00109

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Abstract

In this paper a non-invasive glucose sensor Fast Fourier Transform (FFT) base is suggested using the relatively new concept of nonlinear transfer function. From the conceptual idea to the electronic schematic circuit, showing some in-vivo measurements, this paper opens the discussion for a new idea improving the necessity of demanding for a reliably portable non-invasive glucose sensor, moreover being of low cost.

Keywords: non-invasive; glucose level; FFT, nonlinear transfer function

Introduction

Diabetes mellitus is a pathological condition that renders the blood glucose concentration level variable during the day (see for instance).1 It is well known that a poor regulation of blood glucose concentration leads severe complications such as cardiovascular diseases, damage of blood vessels; stroke, etc (see the survey and the references therein).2 For this reason a correct in-vivo measurement of glucose concentration is of vital importance being classified according to: invasive, minimally invasive, non-invasive. As it is clear, a portable non-invasive device is always desirable to alleviate the patient pain with several measurements a day. However, the development of a non-invasive device is a long story open problem (see for instance).3 Among the non-invasive techniques, the use of Near Infrared Spectroscopy (NIRS) appeared very promising (see).2 However, using NIR leads the great unsolved calibration for drawback different patients, even with the advantages of high reflective signals compared to mid-range and skin penetration of about 100 mm (see for instance)4 and the use of FFT. To overcome this drawback, this paper proposes replacing static FFT models using a novel technique: nonlinear transfer functions FFT based point of view (see for instance for a detail on nonlinear transfer functions).5

In field glucose measurement: in-vivo data capturing using arduino nano

The problem of model calibration along with the short periods of validity appears in all the modeling using static models and NIR (see).2 To overcome this issue to account for patient variability, a dynamical model: Pulses in an infrared diode-Glucose concentration is proposed. Assuming the glucose’s level as a dynamical system’s output, the block diagram depicted in Figure 1 can be described. The complete survey2 described that blood glucose concentration can be more effectively detected in the range of 1408nm to 2326 nm. However, lower wavelength can be used to detect glucose concentrations as well (see for instance).6 The clear advantage is the low cost of 980nm infrared diodes that can be used to implement NIR detection. Moreover, the available literature makes use of NIR through skin tissue (see for instance),7 this technique needs a complex and complicated hardware. To overcome this issue some papers describe the use of reflecting NIR (see for instance,8 in this paper, NIR is used taking measurements of the infrared rays returning after shocking the skin tissue (Figure 2). It turns out that the returning infrared ray must be used to extract glucose concentration. To this end, a cheap NIR commercial receptor is used and converted to digital (A/D) with a 10 bit low cost Arduino Nano platform.

Figure 1 Schematic block diagram.
Figure 2 Returning infrared’s energy and Arduino Nano.

Measurement’s format and matlab GUI

Once the data is captured by Arduino’s internal flash memory (a set of 500 points are taken), the data is sent to Matlab via RS232-USB.

This application allows saving data to hard disk, so as many patient samples as required can be taken and then analyzed off-line (Figure 3).

Figure 3 Matlab’s GUI collecting Arduino’s measurements.

Post-processing using FFT: non-linear transfer’s function approach

Besides the NIR diode’s returned energy, a salient property inspired by Bode’s linear system theorem (see for instance9 toward the implementation of a real non-invasive glucose sensor, FFT it is proposed to represent the data (500 points) with a further nonlinear transfer function identification (see for instance5 for further details on nonlinear transfer functions). Figure 4 depicts these ideas allowing two possibilities:

  1. Nonlinear transfer function identification.
  2. Minimal second order transfer function with minimum error.
Figure 4 Data-FFT conversion plus nonlinear transfer function.
Figure 5 Block diagram.

First possibility attempts to extract a truly optimal transfer function that represents the system: Pulse Width Modulated (PWM)-Glucose Concentration, whereas the second one aims to provide a simple, yet effective, representation with minimum amount of parameters inspired in the classical linear control literature and the low frequency effect observed in Figure 6:

G( j ω )=argmi n N,θ Σ i=1 M [ G( θ, ω i ) Y i ] 2 such that: θ N MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsafaqabe GabaaakeaajugibabaaaaaaaaapeGaam4raKqbaoaabmaak8aabaqc LbsapeGaamOAaiabgwSixlaacckacqaHjpWDaOGaayjkaiaawMcaaK qzGeGaeyypa0JaamyyaiaadkhacaWGNbGaamyBaiaadMgacaWGUbqc fa4damaaBaaaleaajugib8qacaWGobGaaiilaiabeI7aXbWcpaqaba GcpeGaeu4Odm1cdaqhaaqaaKqzadGaamyAaiabg2da9iaaigdaaSqa aKqzadGaamytaaaajuaGdaWadaGcpaqaaKqzGeWdbiaadEeajuaGda qadaGcpaqaaKqzGeWdbiabeI7aXjaacYcacqaHjpWDl8aadaWgaaqa aKqzadWdbiaadMgaaSWdaeqaaaGcpeGaayjkaiaawMcaaKqzGeGaey OeI0IaamywaSWdamaaBaaabaqcLbmapeGaamyAaaWcpaqabaaak8qa caGLBbGaayzxaaWcpaWaaWbaaeqabaqcLbmapeGaaGOmaaaaaOWdae aajugib8qacaWGZbGaamyDaiaadogacaWGObGaaiiOaiaadshacaWG ObGaamyyaiaadshacaGG6aGaaiiOaiabeI7aXjabgIGioprr1ngBPr wtHrhAYaqeguuDJXwAKbstHrhAGq1DVbacfaGae8xhHivcfa4damaa CaaaleqabaqcLbmapeGaamOtaaaaaaaaaa@859C@  Truly optimal transfer function (1)

G( jω )=argmi n { a 1 , a 2 , a 3 } Σ i=1 M [ a 1 ω i 2 +2 a 2 ω i + a 3 Y i ] 2   MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsaqaaaaa aaaaWdbiaadEeajuaGdaqadaGcpaqaaKqzGeWdbiaadQgacqGHflY1 cqaHjpWDaOGaayjkaiaawMcaaKqzGeGaeyypa0Jaamyyaiaadkhaca WGNbGaamyBaiaadMgacaWGUbWcpaWaaSbaaeaapeWaaiWaa8aabaqc LbmapeGaamyyaSWdamaaBaaameaajugWa8qacaaIXaaam8aabeaaju gWa8qacaGGSaGaamyyaSWdamaaBaaameaajugWa8qacaaIYaaam8aa beaajugWa8qacaGGSaGaamyyaSWdamaaBaaameaajugWa8qacaaIZa aam8aabeaaaSWdbiaawUhacaGL9baaa8aabeaak8qacqqHJoWulmaa DaaabaqcLbmacaWGPbGaeyypa0JaaGymaaWcbaqcLbmacaWGnbaaaK qbaoaadmaak8aabaqcfa4dbmaalaaak8aabaqcLbsapeGaamyyaSWd amaaBaaabaqcLbmapeGaaGymaaWcpaqabaaakeaajugib8qacqaHjp WDjuaGpaWaaSbaaSqaaKqzadWdbiaadMgaaSWdaeqaamaaCaaabeqa aKqzadWdbiaaikdaaaqcLbsacqGHRaWkcaaIYaGaeyyXICTaamyyaK qba+aadaWgaaWcbaqcLbmapeGaaGOmaaWcpaqabaqcLbsapeGaeyyX ICTaeqyYdC3cpaWaaSbaaeaajugWa8qacaWGPbaal8aabeaajugib8 qacqGHRaWkcaWGHbWcpaWaaSbaaeaajugWa8qacaaIZaaal8aabeaa aaqcLbsapeGaeyOeI0IaamywaSWdamaaBaaabaqcLbmapeGaamyAaa Wcpaqabaaak8qacaGLBbGaayzxaaWcpaWaaWbaaeqabaqcLbmapeGa aGOmaaaajugibiaacckaaaa@8BB4@ Second order (minimal parameter) estimation (2)

Figure 6 Data-FFT conversion plus nonlinear transfer function.

Where G(.) is a given universal form, Yi are power spectral density from FFT using the Arduino data (Figure 4), M is the number of points taken by Arduino, are the FFT frequencies estimated with the internal latency for the analog to digital (A/D) conversion considering the PWM frequency of 1KHz and  the set of N parameters to be identified. Mathematical models (1) and (2) are depicted in Figure 5: This is an ongoing project; however, to give a flavor’s overall idea, two real measurements are shown in Figure 6 taken from two different patients. These measurements suggest the glucose’s concentration could be related to the power spectral density of the FFT. The continuous decreasing behavior in Figure 6 inspires a further simplification in model (2):

G( jω )=argmi n { a 1 , a 2 , a 3 } Σ i=1 M [ a 1 ω i + a 2 Y i ] 2     MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsaqaaaaa aaaaWdbiaadEeajuaGdaqadaGcpaqaaKqzGeWdbiaadQgacqGHflY1 cqaHjpWDaOGaayjkaiaawMcaaKqzGeGaeyypa0Jaamyyaiaadkhaca WGNbGaamyBaiaadMgacaWGUbWcpaWaaSbaaeaapeWaaiWaa8aabaqc LbmapeGaamyyaSWdamaaBaaameaajugWa8qacaaIXaaam8aabeaaju gWa8qacaGGSaGaamyyaSWdamaaBaaameaajugWa8qacaaIYaaam8aa beaajugWa8qacaGGSaGaamyyaSWdamaaBaaameaajugWa8qacaaIZa aam8aabeaaaSWdbiaawUhacaGL9baaa8aabeaak8qadaWfWaqaaiab fo6atbWcbaGaamyAaiabg2da9iaaigdaaeaacaWGnbaaaKqbaoaadm aak8aabaqcfa4dbmaalaaak8aabaqcLbsapeGaamyyaSWdamaaBaaa baqcLbmapeGaaGymaaWcpaqabaaakeaajugib8qacqaHjpWDl8aada WgaaqaaKqzadWdbiaadMgaaSWdaeqaaKqzGeWdbiabgUcaRiaadgga l8aadaWgaaqaaKqzadWdbiaaikdaaSWdaeqaaaaajugib8qacqGHsi slcaWGzbWcpaWaaSbaaeaajugWa8qacaWGPbaal8aabeaaaOWdbiaa wUfacaGLDbaal8aadaahaaqabeaajugWa8qacaaIYaaaaKqzGeGaai iOaiaacckacaGGGcaaaa@79A3@

Clearly one of the best ways to identify parameters is the well-known Laguerre’s basis method (one simple pole with multiple data, see for instance.10

Micro-power solution using atmel attiny 85

Once the nonlinear transfer function is identified, the parameters of these transfer functions are programmed in a microcontroller to provide a real portable glucose instrument. The transfer’s function pole in previous section as long as an FFT algorithm is programmed on-board in a microcontroller Attiny85, so the DC level G(0) must be estimated to provide an indication of the glucose concentration in real time according to the conclusions in previous section (Figure 7). An estimation of the autonomy using a CR2032 battery can be envisioned:

Energy( CR2032 )=375mWhPWM( 1KHz )@2 secs( aprox ) with 0.25 Duty Energy( per measurement )=120mWsec 11125 samples MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsafaqabe GabaaakeaajugibabaaaaaaaaapeGaamyraiaad6gacaWGLbGaamOC aiaadEgacaWG5bqcfa4aaeWaaOWdaeaajugib8qacaWGdbGaamOuai aaikdacaaIWaGaaG4maiaaikdaaOGaayjkaiaawMcaaKqzGeGaeyyp a0JaaG4maiaaiEdacaaI1aGaamyBaiaadEfacaWGObGaeyO0H4Taam iuaiaadEfacaWGnbqcfa4aaeWaaOWdaeaajugib8qacaaIXaGaam4s aiaadIeacaWG6baakiaawIcacaGLPaaajugibiaacceacaaIYaGaai iOaiaadohacaWGLbGaam4yaiaadohajuaGdaqadaGcpaqaaKqzGeWd biaadggacaWGWbGaamOCaiaad+gacaWG4baakiaawIcacaGLPaaaju gibiaacckacaWG3bGaamyAaiaadshacaWGObGaaiiOaiaaicdacaGG UaGaaGOmaiaaiwdacaGGGcGaamiraiaadwhacaWG0bGaamyEaaGcpa qaaKqzGeWdbiaadweacaWGUbGaamyzaiaadkhacaWGNbGaamyEaKqb aoaabmaak8aabaqcLbsapeGaamiCaiaadwgacaWGYbGaaiiOaiaad2 gacaWGLbGaamyyaiaadohacaWG1bGaamOCaiaadwgacaWGTbGaamyz aiaad6gacaWG0baakiaawIcacaGLPaaajugibiabg2da9iaaigdaca aIYaGaaGimaiaad2gacaWGxbGaeyyXICTaam4CaiaadwgacaWGJbaa aiabgkDiElaaigdacaaIXaGaaGymaiaaikdacaaI1aGaaiiOaiaado hacaWGHbGaamyBaiaadchacaWGSbGaamyzaiaadohaaaa@A2B1@

With at least five measurements a day, this is more than two years’ autonomy with a single battery. Moreover, if any harvesting method is added: body heat, vibration walking, etc, the autonomy can be increased using optimal control as depicted for instance.11,12

Figure 7 3-D schematic with Attiny 85 and on-board battery CR2032.

Conclusion

The problem of a portable instrument with low cost able to provide a confident estimation of the blood glucose concentration was identified. After a short review of the available results, a new mathematical model based on nonlinear transfer functions and FFT was presented. This is an on-going project, so a flavor of the possible glucose-transfer function was depicted with the DC value G(0). A real prototype was presented using Atmel’s microcontroller Attiny85 with on-board FFT and real-time indication with three indications: normal, low and high glucose levels. As a future work, exhaust measurements will validate these ideas using the electronic prototype presented.

Acknowledgements

None.

Conflict of interest

Authors declare that there is no conflict of interest.

References

  1. Zimmet P, Alberti KG, Magliano DJ, et al. Diabetes mellitus statisctics on prevalence and mortality: facts and fallacies. Nat rev Endocrinol. 2016;12(10):616–622.
  2. Yadav J, Rani A, Singh V, et al. Prospects and limitations of non-invasive blood glucose monitoring using near infrared spectroscopy. Biomedical Signal Processing and Control. 2015;18:214–227.
  3. Kim J, Campbell A, Wang S. Wearable non-invasive epidermal glucose sensors: A review. Talanta. 2018;177:163–170.
  4. Khalil OS. Non-invasive glucose measurement technologies: an update from 1999 to the Dawn of the new millennium. Diabetes Technol Ther. 2005;1(7):174–197.
  5. Pavlov A, Van De Wouw N, Nijmeijer H. Frequency response functions and Bode plots for nonlinear convergent systems. Proceeding of the 45th IEEE Conference on Decision & Control; USA: 2006.
  6. Muller UA, Mertes B, Fischbacher C, et al. Non-invasive blood glucose monitoring by means of near infrared spectroscopy: methods for improving the reliability of the calibration models. Int J Artif Organs. 1997;5:285–290.
  7. Haxha S, Jhoja J. Optical Based Noninvasive Glucose Monitoring Sensor Prototype. IEEE Photonics Journal. 2016;8(6):1–11.
  8. Yadav J, Rani A, Singh V. Near-infrared LED based non-invasive blood glucose sensor. International Conference on Signal Processing and Integrated Networks (SPIN). 2014:591–594.
  9. Dorf R, Bishop R. Modern Control Systems. 12th ed. Pearson; 2010.
  10. Nelles O. Nonlinear System Identification: From Classical Approaches to Neural Networks and Fuzzy Models. Springer; 2001.
  11. García A, Pons L. Optimal Control for Energy Harvesting: Electrical Model and Measurements. International Journal of Circuits and Electronics. 2017;2:16–21.
  12. A García, Pons L, Perotti E. On the Internal Structure of Piezo-Electric Devices: Closed and Open Loop Optimal Strategies. WSEAS Transactions on Circuits and Systems. 2017;16(23):196–204.
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