Modelling of an open photoacoustic resonator for blood glucose measurements Computational Method

Abstract

Photoacoustic spectroscopy has been demonstrated as an effective technique for non-invasive measurement of blood glucose concentration [1-3]. The measurement is done by probing the glucose molecules in the interstitial fluid with an infrared laser source. The interstitial fluid lies a few micrometers under the skin surface and the glucose concentration in the interstitial fluid and in the blood is correlated [4-5]. If the acoustic resonator of the sensor was closed, skin transpiration during measurements would result in the build-up of humidity inside the resonator causing strong absorption of the infrared radiation. Leaving one end of the resonator open has been shown as possible solution that enables continuous non-invasive monitoring of the blood glucose concentration.
We demonstrate an accurate method for simulating the photoacoustic signal in an open resonator using finite element modelling. The resonator consists of three interconnected cylinders forming a T-like structure. This simulation method is based on the linearized Navier-Stokes equations in which viscous and thermal loss are the main sources of signal attenuation. The open end of the resonator is modelled by adding a hemisphere as an additional domain. The hemisphere represents the infinite free space. To avoid reflections of the radiated sound waves, it is terminated by perfectly matched layers.
The simulation results show good agreement with the experimental results as all the major acoustic resonances have been experimentally confirmed. The small frequency shifts of the resonances are mainly attributed to experimental inaccuracies.
The simulation method provides an accurate tool for modelling the performance of an open resonator. This is particularly useful when designing and optimizing the photoacoustic sensor for blood glucose measurements.

References
1. M.A. Pleitez, T. Lieblein, A. Bauer, O. Hertzberg, H.V. Lilienfeld-Toal, W. Mäntele1, Review of Scientific Instruments 84 (8), 084901 (2013) doi:10.10631/1.4816723
2. W.V. Gonzales, A.T. Mobashsher, A. Abbosh, Sensors 19 (4), 800 (2019) doi:10.3390/s19040800
3. J. Kottmann, J.M. Rey, M.W. Sigrist, Sensors 16 (10), 1663 (2016) doi:10.3390/s16101663
4. C. Laugel, N. Yagoubi, A. Baillet, Chemistry and Physics of Lipids 135 (1), 55 (2005) doi: https://doi.org/10.1016/j.chemphyslip.2005.02.001
5. P. Garidel, Physical Chemistry Chemical Physics 4 (22), 5671 (2002)

Full text

Modelling of an open photoacoustic resonator
for blood glucose measurements
Said El-Busaidy1,2, Bernd Baumann1, Marcus Wolff1, Lars Duggen2
1. Hamburg University of Applied Sciences, Heinrich Blasius Institute for Physical Technologies
2. University of Southern Denmark, Mads Clausen Institute
Computational Method
•Based on linearized Navier-Stokes
equation and continuity equations for
mass and energy.
•No slip and adiabatic boundary
condition on resonator walls.
•Opening is modelled using a
hemisphere to represent infinite free
space.
•The hemisphere is terminated using
perfectly matched layers (PML).
•PML prevents reflection of radiated
sound waves
Said El-Busaidy
T +49 40 42875 8655
saidalisaid.el-busaidyt@haw-hamburg.de
Hamburg University of Applied Sciences
Heinrich Blasius Institute
Berliner Tor 21
20099 Hamburg, Germany
References
1. M. A. Pleitez, T. Lieblein, A. Bauer, O. Hertzberg, H. von Lilienfeld-Toal, W. Mäntele. Windowless ultrasound photoacoustic cell for in vivo mid-
IR spectroscopy of human epidermis: Low interference by changes of air pressure, temperature, and humidity caused by skin contact opens
the possibility for a non-invasive monitoring of glucose in the interstitial fluid. Rev. Sci. Instrum. 84, 2013
2. J. M. Sim, C. Ahn, E. Jeong, B. K. Kim.In vivo microscopic photoacoustic spectroscopy for non-invasive glucose monitoring invulnerable to skin
secretion products. Sci. Rep. 8, 2018
3. B. Baumann, M. Wolff, B. Kost, H. Groninga. Finite element calculation of photoacoustic signals. Appl. Opt. 46, 2007
4. S. El-Busaidy, B. Baumann, M. Wolff, L. Duggen, H. Bruhns. Experimental and numerical investigation of a photoacoustic resonator for solid
samples: towards a non-invasive glucose sensor. Sensors 19,2019
Results
•Simulation results in good agreement
with the measurement.
•Resonances with small amplitude difficult
to clearly distinguish in measurement due
to noise.
•Peak frequency difference < 1.08 %.
Closed and open T-cell resonator respectively. Conventional
closed cells cause an accumulation of water droplets on the cell
walls.
a: Grey: The resonator and the hemisphere representing the open end. Blue: PML.
b: Boundary layers generated on the resonator to accurately map thermal and viscous losses while a swept mesh was used for the PML.
Conclusion
The method provides an accurate tool for
designing and optimizing open resonators
and hence enabling the enhancement of the
detection sensitivity of photoacoustic
sensors for non-invasive blood glucose
measurement.
Introduction
•Blood glucose measurements across skin samples are done using open photoacoustic
resonators [1-2].
•The open end reduces accumulation of humidity in the resonator during measurements
from skin transpiration.
•The opening deteriorates the photoacoustic (PA) signal and thus the detection sensitivity.
•Accurate modelling of PA signal enables optimization of the resonator‘s geometry for
maximum signal amplification.
•Resonant amplification strongly depends on the resonator‘s geometry [3-4].
•Finite element method of modelling the photoacoustic signal of an open resonator is
presented.
Frequency responce of the open cell
a
b
Pressure distribution plots of important modes.