The signal produced by the detector is proportional to the
square of the E-field of the light incident on it and is given by: Roger J.
McNichols, Brent D. Cameron, and Gerard L. Coté
Biomedical Engineering Program,
Texas A&M University,
College Station, TX 77843-3120
Diabetes mellitus is a disease in which cells fail to take up glucose either due to a lack of insulin (Type I) or an insensitivity to insulin (Type II) [1]. The associated elevation of blood glucose levels for prolonged periods of time has been linked to a number of problems including retinopathy, nephropathy, neuropathy, and heart disease [1]. A typical care regimen for Type I diabetics includes daily monitoring of blood glucose levels and injection of an appropriate dose of insulin. Glucose monitoring is presently accomplished via a “finger-stick” in which a lancet is used to prick the finger and withdraw a small amount of blood for testing in any number of home care diabetes monitoring kits all based on the electroenzymatic oxidation of glucose. Four years ago, the National Institute of Diabetes and Digestive and Kidney Diseases (NIDDK) of the National Institutes of Health (NIH) released the results of a study showing that tighter control of blood glucose led to a pronounced decrease in morbidity and mortality associated with diabetes [1]. Since the pain associated with the finger-stick method generally leads to low patient compliance as well as increasing the potential for infection by breaking the blood-skin barrier, a non-invasive method of blood glucose measurement would allow for a significant increase in the quality of life for the 14 million diabetics in the US and a reduction of the estimated $40 billion in annual associated health care costs [1]. In this article, we discuss some of the advances which we have made toward the development of a non-invasive polarimetric glucose sensor.
Polarimetric measurement of glucose concentration is based on optical rotatory dispersion (ORD) a phenomenon by which a solution containing a chiral molecule rotates the plane of polarization for linearly polarized light passing through it. The rotation is the result of a difference in refractive indices nL and nR for left and right circularly polarized light traveling through the electron cloud of a molecule. In a large ensemble of randomly oriented molecules, the net rotation by the sample averages to zero. However, in the case where the molecule is chiral and no mirror image orientation exists, the rotation is additive and can be observed with a fairly simple apparatus. The angle of this rotation depends linearly on the optical path-length, the concentration of the chiral species, and a constant for the species known as the specific rotation; it is expressed as f=alLC where al is the specific rotation in °dm-1(g/ml)-1 at wavelength l, L is the path length in dm, and C is the concentration in g/mL. Glucose in the body is dextrorotatory (rotates light in the right-handed direction) and has a specific rotation of +52.6° dm-1(g/ml)-1 at the sodium D-line of 589 nm [2]. Generally, al for glucose decreases with increasing wavelength across the visible spectrum and exhibits a rise in magnitude near optical absorption bands of a particular molecule (a phenomenon known as the Cotton-Mouton effect).
Advantages of polarimetric methods include the use of readily available visible sources, the concomitant ability to use substantial pathlengths in aqueous solutions, and the employment of optical components which can be miniaturized. Many body tissues such as skin exhibit significant scattering and hence depolarize the light passing through them providing low signal-to-noise ratio. However, the anterior chamber of the eye provides a unique window into the body with relatively low scattering properties. The clear space directly beneath the cornea is filled with a fluid called the aqueous humor. It has been shown that the glucose concentration in the aqueous humor closely mimics glucose levels in the blood, and in work by Pohjola aqueous humor glucose concentration was found to reflect an age-dependent steady-state value approximately 70% that of blood glucose levels [3]. A time lag on the order of minutes between blood and aqueous humor glucose concentrations has been reported by March et al. who performed in vivo measurements in a rabbit model [4, 5]. Finally, though the collagen structure of the cornea attributes to it some degree of birefringence, it may be possible to account for this with appropriate optics [4], or the use of multiple wavelengths. Alternatively, a polarization system designed to extract the full Jones or Mueller matrix for the system could be used in order to separate specific rotation from birefringence.
The simplest of polarimeters takes the form of a monochromatic optical source and a detector on either side of two crossed polarizers enclosing the sample under study. The intensity of light incident on the detector will be proportional to the square of the amplitude of the E-field of light passing through the second polarizer which is in turn proportional to the sine of the angle f by which the light was rotated in the sample. For small rotation angles, this becomes E2 µ sin2f = 1-cos2f »2f. More sophisticated polarimeters employ modulation techniques in order to increase stability of the measurement and to get away from 1/¦ noise associated with DC measurements. One particular topology first suggested by Gillham [6] is shown below.
The figure below illustrates schematically what happens to the polarization vector. Modulator M1 causes the polarization vector to vary by an angle q about the vertical. In the presence of an optically active sample which induces an additional DC rotation f, the polarization vector now varies asymmetrically about the vertical. An asymmetric signal is now seen at the detector.
The signal produced by the detector is proportional to the
square of the E-field of the light incident on it and is given by:
(1)
where the approximation has been made that sin(x)» x for small x. If a lock-in amplifier is used with reference the same as the modulation signal, then the 2qfsin(wt) signal which is proportional to the sample rotation f may be picked up.
In a system used by Goetz in which he was able to obtain in
vitro rotational measurements on the order of 3 microdegrees [7], M1 and M2 are
Faraday rotators which consist of a solenoidal coil wrapped on a rod of crown flint glass.
The Faraday rotator induces a rotation of the plane of linearly polarized light
proportional to the Verdęt constant of the glass, the length of the rod, and the magnetic
field produced by (and hence the current in) the coil. Cameron later adapted this system
to provide computer control of M2 and to sweep through a range of rotation angles
searching for the one which best nulled the rotations by the sample [8]. In another system
used by King et al., a single Pockel’s effect electro-optic modulator was used in
place of the two Faraday rotators to effect both modulation and feedback [9].
Glucose is not the only optically active component present in the aqueous humor. Ascorbate and albumin are also present in varying quantities and their rotations will serve to change the net rotation by the aqueous humor in an additive way [10, 11]. In order to account for the effects of these confounders, polarimetric measurements can be taken at multiple wavelengths and a calibration matrix formed to eliminate the effects of confounders. For example, in the case where two wavelengths are used, we have
(2)
where jl1 and jl2 are the
observed rotations at wavelengths l1 and l2, 
is the specific rotation of analyte i at
wavelength lj, C1 and C2 are the concentrations of the analytes, and L is the
pathlength which is a constant for both analytes and wavelengths. King et al. used a two
wavelength system with HeNe lasers at 594nm and 633nm in the Pockel’s cell based
system [9]. More recently, we have used diode lasers at 670nm and 830nm in our
computer-controlled Faraday rotator system [12].
While production of a viable non-invasive glucose sensing technique is likely to be several years away, the polarimetric optical approach is attractive because the visible spectrum and significant path lengths may be used. The anterior chamber of the eye holds potential as a non-invasive glucose sensing site that is particularly well-suited for polarimetric measurements since it provides a unique “window to the body” with minimal scattering and a glucose concentration well correlated to that of the blood.
References:
[1] National Institutes of Diabetes and Digestive and Kidney Diseases (1994). Diabetes Overview, NIH: 94-3235
[2] CA Browne and FW Zerban. Physical and Chemical Methods of Sugar Analysis, 3/ed. John Wiley and Sons. New York: 1941. pp 263-5
[3] S Pohjola. “The Glucose Content of the Aqueous Humor in Man” Acta Ophth. Munksgaard, Copenhagen, 1966, suppl. 88, pp 11-80.
[4] W March, R Engerman, and B Rabinovitch. “Optical Monitor of Glucose” Transactions of the American Society of Artificial Internal Organs. Vol. 25:28-31. 1979
[5] W March, B Rabinovitch, and L Adams. “Noninvasive Glucose Monitoring of the Aqueous Humor of the Eye: Part II. Animal Studies and the Scleral Lens” Diabetes Care. Vol. 5(3):259-65. 1982
[6] EJ Gillham. “A High-precision Photoelectric Polarimeter” Journal of Scientific Instruments. Vol. 34:435-9. 1957
[7] MJ Goetz. Microdegree polarimetry for Glucose Detection. M.S. Thesis, University of Connecticut, Storrs, CT. 1992
[8] BD Cameron and GL Coté. “Noninvasive Glucose Sensing Utilizing a Digital Closed-Loop Polarimetric Approach” IEEE Transactions on Biomedical Engineering. Vol. 44(12):1221-7. 1997
[9] TW King, GL Coté, RJ McNichols, and MJ Goetz. “Multispectral Polarimetric Glucose Detection Using a Single Pockels Cell” Optical Engineering. Vol. 33(8):2746-53. 1994
[10] RJ McNichols, GL Coté, MJ Goetz, and TW King. “Linear Superposition of Specific Rotation for the Detection of Glucose” Proceedings of the IEEE-EMBS. Vol. 14. 1992
[11] SP Kozaitis, FM Ham, GM Cohen, G Han. “Laser Polarimetry for Measurement of Drugs in the Aqueous Humor.” Proceedings of the IEEE-EMBS. Vol. 13: 1570-1. 1991
[12] GL Coté, H Gorde, J Janda, and BD Cameron. “Multispectral Polarimetric System for Glucose Monitoring” Presented at the SPIE-BiOS. San Jose, CA. January 1998.