2.1.

Instrument

We constructed an instrument to measure the temperature-dependence of tissue localized reflectance. It comprised two identical independently temperature-controlled probes mounted on a common fixture and brought in touch with the forearm. Figure 1 shows a schematic diagram of the optical system. Figure 2 shows the details of an optical probe. Each optical probe had a light source module, a human interface module, and a signal detection module that are interconnected through a branched fiber bundle.

Fig. 1

Schematic of the dual probe system.

Fig. 2

Detailed schematic of a single optical probe showing the illumination, detection, and body-interface elements and optical components.

The light source module had four light emitting diodes (LEDs) mounted into a circular disk (a), each LED plastic cap was machined to a flat end and was placed in touch with the end of one of four fibers (b), each was a $400\text{-}\mathrm{\mu }\mathrm{m}$ diameter silica fiber. Light from the end ferrule passed through a 7-mm aperture and was focused onto the input end of the illuminating fiber (g), using lens system (c), which is a combination of two achromats. Part of the light was diverted by a beamsplitter (d) and focused onto a reference silicon photodiode (e) and amplifier (f) to correct for LEDs intensity fluctuations. Four drive circuits modulated the LEDs.

Each probe had a common tip at the center of a 2-cm diameter aluminum disk (h) glued to a thermoelectric element (i) (Marlow Industries, Dallas, Texas). A T-type thermocouple (j) embedded in the disk provided feedback to the temperature controller (k) (Marlow Industries). The disk touched skin surface (l). Reemitted light was collected by four detection fibers (m), which ended in detection tip (n), and were imaged onto a photodiode (PD) (o). The signal from each PD was separately amplified by (p) and routed to the analog-to-digital boards in the personal computer chassis. The wavelengths and modulation frequency of each of the LEDs were $590\mathrm{nm}$ at $819\mathrm{Hz}$ , $660\mathrm{nm}$ at $1024\mathrm{Hz}$ , $890\mathrm{nm}$ at $455\mathrm{Hz}$ , and $935\mathrm{nm}$ at $585\mathrm{Hz}$ . The half-bandwidth of the LEDs was 25, 25, 50, and $50\mathrm{nm}$ , respectively. The illumination power for each fiber was 1.4 to $5.0\mathrm{\mu }\mathrm{W}$ . The wavelengths were in the hemoglobin absorption bands. The 660- and 935-nm LEDs approximate wavelengths used in measurements of blood oxygen saturation. None of these wavelengths corresponds to glucose absorption. The signals detected are predominantly due to light scattering by cutaneous structural components and light absorption by blood hemoglobin.

Distances between the source fiber and the light collecting fibers, source-detector (S-D) distances $\left(r\right)$ , were 0.44, 0.90, 1.21, and $1.84\mathrm{mm}$ , respectively. We selected the S-D distances to limit collected light to within a 2-mm sampling depth, where temperature can be easily varied and controlled independent of the body core temperature.^{16, 17, 18} The signal from each detector corresponded to one S-D distance $\left(r\right)$ , and the signal at each modulation frequency corresponded to one $\lambda$ . Signals were collected every $5\mathrm{s}$ . The optical probes shown in Fig. 3 touched the dorsal side of the forearm at a constant force of $\approx 45\mathrm{g}∕{\mathrm{cm}}^2$ . A ${\mathrm{LABVIEW}}^{™}$ program controlled instrument functions, thermal management, and data acquisition.

Fig. 3

A photo of the two temperature-controlled localized reflectance probes mounted in the body interface. The outer black ring is an insulating ${\mathrm{Delrin}}^{™}$ ring. The large metallic inner disk is a 2-cm diameter aluminum disk with the thermoelectric element glued to its back. At the center is a ferrule of the fiber optic bundle having the illumination fiber and the detection fibers.

2.2.

Subjects

The study was conducted at Abbott Clinical Pharmacology Research Unit, Victory Memorial Hospital (Waukegan, Illinois), using a protocol approved by the hospital institutional review board. Twenty diabetic volunteers on insulin treatment and within the age range of 18 to 65 years were recruited and signed informed consent forms. Fifteen of them had multiple comorbidities and diabetes complications. Volunteers had insulin injections, oral diabetes medications, and other prescribed medications during a three-day confinement and were served meals with known caloric-content depending on their weight. Those $<130$ pounds had $1800\mathrm{kcal}$ in the first day and $2000\mathrm{kcal}$ in the other days, and those $>130$ pounds had $2000\mathrm{kcal}$ in the first day and $2500\mathrm{kcal}$ in days 2 and 3. The caloric intake was varied over the course of the study to provide ranges of glucose concentration for the calibration set. The first day had the lowest caloric content to ensure that patient’s [BG] values did not substantially increase above their usual range. Ten reference [BG] values per day were determined using a home glucose meter (Bayer ${\mathrm{Elite}}^{\mathrm{R}}$ , Bayer Corporation, Elkhart, Indiana). Its accuracy was $<10\%$ .

The probes temperature was raised to $30°\mathrm{C}$ at the start of the experiment. We applied a thin layer of silicon oil to an area on the dorsal side of the left arm to enhance heat transfer. The subject sat in a chair and with the left arm in the body-interface cradle, retracted the spring-loaded dual probe with the right hand and started a countdown. At count zero, the subject released the probe toward the skin as the operator clicked the start-run icon. The probes were maintained at $30°\mathrm{C}$ for $30\mathrm{s}$ , temperature was then ramped at a rate of $-3.33$ or $+3.33°\mathrm{C}\bullet {\min }^{-1}$ for $180\mathrm{s}$ , leading to a $-10°\mathrm{C}$ change of the cooling probe and a $+10°\mathrm{C}$ change of the heating probe. The temperature of each probe was then returned to $30°\mathrm{C}$ and maintained at this final temperature for $30\mathrm{s}$ . Data collection time was $240\mathrm{s}$ . Probe temperatures and measurement duration times were selected based on a test for maximum comfort on a set of volunteers. The upper and lower temperature limits ensured that skin redness for fair-skinned volunteers disappeared in less than $5\min$ of end of the measurement.

3.1.

Signal Output

We identified data sets that had sudden changes in the optical signals caused by the movement of the forearm relative to the probes (motion artifacts) by running an exponential moving point average on the stream of data points. Data sets that showed changes in the signal magnitude higher than a set threshold were rejected.¹⁹

Figure 4 shows examples for the outputs of the cooling probe and the heating probe expressed as $2.303\log (R_t∕R_{30\mathrm{s}})$ for the first run on the first patient at the $0.44\mathrm{mm}$ S-D distance. Signals were normalized to the $30\text{-}\mathrm{s}$ time point, that is at a $30°\mathrm{C}$ temperature point. The signal changed at $\approx 210\mathrm{s}$ when both probes were brought back to $30°\mathrm{C}$ .

Fig. 4

Time series of the output of the cooling and heating localized reflectance probe at $0.44\text{-}\mathrm{mm}$ S-D distance and at the four wavelengths. Open symbols are for the cooling probe and solid symbols for the heating probe $◇$ $590\mathrm{nm}$ , $◻$ $660\mathrm{nm}$ , $\circ$ $890\mathrm{nm}$ , and $▵$ $935\mathrm{nm}$ .

3.2.

Data Analysis

Signals were collected at each $\lambda$ , $r$ , and probe temperature $T$ , as the localized reflectance, $\mathcal{R}({\lambda }_i,r_j,T)$ . The natural logarithm of the ratio of the signals at two temperatures was calculated for each probe as $\ln \left[\mathcal{R}\right({\lambda }_i,r_j,T_2)∕\mathcal{R}({\lambda }_i,r_j,T_1\left)\right]$ , $T_1$ and $T_2$ are the probe temperatures at the start and end of temperature ramping. Since the change in temperature induces a small change in $\mathcal{R}$ using the expansion $\ln (1+x)=x+x^2∕2!+x^3∕3!+\cdots \approx x$ , when $x\ll 1$ , leads to Eq. 1

There is a minus sign for $\mathrm{\Delta }{\mathrm{OD}}_T({\lambda }_i,r_j)$ because the reflected light intensity varies in the opposite direction to change in optical density, that is, opposite to the light absorbed. Figures 5a, 5b, 5c, 5d display examples of combined plots of $\mathrm{\Delta }{\mathrm{OD}}_{TC}({\lambda }_i,r_j)$ and $\mathrm{\Delta }{\mathrm{OD}}_{TH}({\lambda }_i,r_j)$ as expressed by Eqs. 3, 4 plotted as a function of temperature. $\mathrm{\Delta }{\mathrm{OD}}_{TC}$ response is depicted by traces in the $20°\mathrm{C}$ to $30°\mathrm{C}$ temperature range, and $\mathrm{\Delta }{\mathrm{OD}}_{TH}$ response is depicted by traces in the 30 to $40°\mathrm{C}$ temperature range of the plots of Figs. 5a, 5b, 5c, 5d. The traces in Fig. 5a show increase in reflected light intensity $(-\mathrm{\Delta }{\mathrm{OD}}_T)$ with increasing temperature, indicating the prevalence of scattering at the 0.44-mm S-D distance. The S-D distance increases, and the change in reflected light intensity with temperature decreases, that is, OD increases and reaches a maximum at 1.84-mm S-D distance for the heating probe due to increased blood perfusion, as shown in Fig. 5d. Light sampled at the longer S-D distance is reflected from deeper cutaneous layers. The cooling probe causes light penetration to deeper layers whereby the light beam samples the deeper vascular structures.¹⁶

Fig. 5

Plots of the change in $\mathrm{\Delta }{\mathrm{OD}}_T$ as a function of temperature for the two probes various S-D distances at wavelengths (a) $D=0.44\mathrm{mm}$ : $◇$ $590\mathrm{nm}$ , $∎$ $660\mathrm{nm}$ , $\mathsf{X}$ $890\mathrm{nm}$ , and $▴$ $935\mathrm{nm}$ ; (b) $D=0.90\mathrm{mm}$ : $◇$ $590\mathrm{nm}$ , $∎$ $660\mathrm{nm}$ , $\mathsf{X}$ $890\mathrm{nm}$ , and $▴$ $935\mathrm{nm}$ ; (c) $D=\mathrm{0.1.21}\mathrm{mm}$ : $◇$ $590\mathrm{nm}$ , $∎$ $660\mathrm{nm}$ , $\mathsf{X}$ $890\mathrm{nm}$ , and $▴$ $935\mathrm{nm}$ ; (d) $D=1.84\mathrm{mm}$ : $◇$ $590\mathrm{nm}$ , $∎$ $660\mathrm{nm}$ , $\mathsf{X}$ $890\mathrm{nm}$ , and $▴$ $935\mathrm{nm}$ .

We tested the correlation between [BG] and either or both of $\mathrm{\Delta }{\mathrm{OD}}_{TC}$ and $\mathrm{\Delta }{\mathrm{OD}}_{TH}$ using the four-term linear regression Eqs. 5, 6

We determined $\mathrm{\Delta }{\mathrm{OD}}_{TC}({\lambda }_i,r_j)$ and $\mathrm{\Delta }{\mathrm{OD}}_{TH}({\lambda }_i,r_j)$ from $({\mathcal{R}}_{20°\mathrm{C}}∕{\mathcal{R}}_{30°\mathrm{C}})$ and $({\mathcal{R}}_{40°\mathrm{C}}∕{\mathcal{R}}_{30°\mathrm{C}})$ and were fitted to [BG] values using Eqs. 5, 6. We calculated the set of coefficients $c_0$ , $d_0$ , $c_n$ , and $d_n$ for each possible combination of $\mathrm{\Delta }{\mathrm{OD}}_{TC}$ and $\mathrm{\Delta }{\mathrm{OD}}_{TH}$ to provide a least-squares fit to [BG]. We used 16 ${\lambda }_i∕r_j$ combinations in the regression analysis, leading to a total of 1820 possible four-variable combinations for a single probe, and 32 ${\lambda }_i∕r_j$ variables or $35960$ possible four-variable combinations using the output of both probes. We selected the regression model having the lowest standard error of predicting [BG] in day 3 (see Table 1 ). We designed a statistical test to rank the likelihood of a true correlation of $\mathrm{\Delta }{\mathrm{OD}}_T$ with [BG] rather than with random noise.

Table 1

Results of four-variable linear model prediction of third-day [BG] values. (*) designates the rank of R2 for the correlation with glucose concentration with respect to the R2 values obtained by fitting 499 permutations of randomized day 3 glucose data to the optical signals. Values in bold lettering ranked above the set noise thresholds.

We calculated the model’s correlation coefficient $\left(R^2\right)$ in day 3 and ranked its magnitude against the model’s $R^2$ values that were similarly calculated using randomized [BG] values and the experimentally determined $\mathrm{\Delta }{\mathrm{OD}}_T$ data in day 3. We performed the calculation separately for each volunteer and used the results to assess the contribution of random noise to the correlation between $\mathrm{\Delta }{\mathrm{OD}}_T$ and [BG].

We established a noise threshold above which we considered that a [BG] prediction is valid by generating 499 random sequences of reference [BG] values in day 3 for each volunteer and correlating these sets with $\mathrm{\Delta }{\mathrm{OD}}_T$ values. We assumed these random permutations to mimic the sum of body-interface noise and physiological noise. We applied the regression model to predict glucose values for each random permutation and to identify a new optimum set of $\mathrm{\Delta }{\mathrm{OD}}_T$ , which we used to recalculate the $R^2$ value for day 3. This process yielded 499 new $R^2$ values for each patient to compare with the $R^2$ value corresponding to the correct sequence of [BG] in day 3. We considered a volunteer to exhibit a valid correlation between [BG] and $\mathrm{\Delta }{\mathrm{OD}}_T$ if the $R^2$ value for true glucose correlation ranked higher in magnitude than arbitrary threshold of 70% of the 499 new $R^2$ values generated using randomized [BG] data (see Table 2 ). We considered a ranking less than the 70% threshold to indicate that biological and body-interface noise dominated $\mathrm{\Delta }{\mathrm{OD}}_T$ data and produced a correlation with [BG] that was comparable to results from pure random chance correlation.

Table 2

Volunteer characteristics and correlation parameters for ΔODTC versus [BG]. (*) designates the rank of R2 for the correlation with glucose concentration with respect to the R2 values obtained by fitting 499 permutations of randomized day 3 glucose data to the optical signals. Values in bold lettering ranked above the set noise thresholds.

3.3.

Linear Regression Results

Using the 16-variable $\mathrm{\Delta }{\mathrm{OD}}_{TC}$ resulted in 8 of 15 patients (53%) having an $R^2$ that ranked above the 70% threshold. There was a stronger correlation between [BG] and $\mathrm{\Delta }{\mathrm{OD}}_{TC}$ (53%) rather than between [BG] and $\mathrm{\Delta }{\mathrm{OD}}_{TH}$ (13%), or the combined $\mathrm{\Delta }{\mathrm{OD}}_{TC}$ and $\mathrm{\Delta }{\mathrm{OD}}_{TH}$ (27%). We calculated the dependence of $\mathrm{d}\left(\mathrm{\Delta }{\mathrm{OD}}_{TC}\right)∕\mathrm{d}T$ and $\mathrm{d}\left(\mathrm{\Delta }{\mathrm{OD}}_{TH}\right)∕\mathrm{d}T$ on the S-D distance, which represents in different cutaneous depths. Figures 6a and 6b show these plots. The cooling response curves showed systematic decrease in $\mathrm{d}\left(\mathrm{\Delta }{\mathrm{OD}}_{TC}\right)∕\mathrm{d}T$ with S-D distance. The response was nearly linear with S-D distance for the cooling probe. The slope $\mathrm{d}\left(\mathrm{\Delta }{\mathrm{OD}}_{TH}\right)∕\mathrm{d}T$ showed a linear steep decrease up to a distance of $1.21\mathrm{mm}$ , an inflection point at $1.21\mathrm{mm}$ , and then flattened between 1.21- and $1.84\text{-}\mathrm{mm}$ S-D distances. The temperature effect on the scattering coefficient is linear and reversible.¹⁶ This difference in $\mathrm{d}\left(\mathrm{\Delta }{\mathrm{OD}}_{TC}\right)∕\mathrm{d}T$ and $\mathrm{d}\left(\mathrm{\Delta }{\mathrm{OD}}_{TH}\right)∕\mathrm{d}T$ suggests that the vascular response to heating differs from that due to cooling. It is difficult to establish if this is one of the sources of loss of correlation between $\mathrm{\Delta }{\mathrm{OD}}_{TH}$ (heating) and [BG].

Fig. 6

Plot of the dependence of $\mathrm{d}\left(\mathrm{\Delta }\mathrm{OD}\right)∕\mathrm{d}T$ as a function of the S-D distance: (a) $\mathrm{d}\left(\mathrm{\Delta }{\mathrm{OD}}_{TC}\right)∕\mathrm{d}T$ $◇$ for $0.44\mathrm{mm}$ , $∎$ for $0.90\mathrm{mm}$ , $\mathsf{X}$ for $1.21\mathrm{mm}$ , and $▴$ for $1.84\mathrm{mm}$ ; (b) $\mathrm{d}\left(\mathrm{\Delta }{\mathrm{OD}}_{TC}\right)∕\mathrm{d}T$ $◇$ for $0.44\mathrm{mm}$ , $∎$ for $0.90\mathrm{mm}$ , $\mathsf{X}$ for $1.21\mathrm{mm}$ , and $▴$ for $1.84\mathrm{mm}$ .

We tested the dependence ability to correlate $\mathrm{\Delta }{\mathrm{OD}}_{TC}$ and [BG] above the noise threshold with the age of the volunteer, mean body mass index, %HbA1c, gender, and duration of diabetes as summarized in Table 3 . There was considerable overlap among patient data, except for the presence of two distinct groups, one with diabetes duration $<20$ years $(\mathrm{mean}=11.1\pm 4.2)$ and another with diabetes duration $>20$ years $(\mathrm{mean}=24.3\pm 7.3)$ . Six of the eight volunteers with $R^2$ above the noise threshold (75%) had diabetes duration $<20$ years. Five of these six patients (62%) were females. One female patient had diabetes duration $<20$ years, but $R^2$ for her data set was lower than that of the noise threshold.

Table 3

Summary of clinical data

The wavelengths used in this study (590 to $935\mathrm{nm}$ ) fall within the hemoglobin absorption spectrum. The observations are not due to light absorption by glucose molecules, but due to cutaneous light scattering and light absorption by hemoglobin molecules, that is, cutaneous structural and vascular response. Skin as an optical window changes its properties due to diabetes. These include skin thickness at the extremities and collagen structure. ^{10, 11, 12, 13} Skin thickness also varies with gender.¹⁴ Diabetes affects the response of the cutaneous vascular system to temperature and pressure changes^{15, 20, 21} and affects skin structural properties.^{22, 23} This, in turn, affects its optical parameters and heat transmission between the probe and the skin, and hence the effect of the transmitted heat on cutaneous structural and vascular properties. Females have thinner cutaneous layers and thicker subcutaneous fat layers than males.¹⁴ Variation in skin thickness by gender and diabetes duration may have caused this subpopulation result reported here. Extending these arguments (in Refs. 10, 11, 12, 13, 14, 15 and 20, 21, 22, 23) to the results of the present study, females with short diabetes duration have thinner cutaneous layers than males with longer diabetes duration, which may have led to a correlation between $\mathrm{\Delta }{\mathrm{OD}}_{TC}$ and [BG]. The heating temperature perturbation program may have introduced more noise into the measurement, probably due to sweating or to the erratic opening of capillary shunts as the skin temperature was raised.