3.1.

Instrument

The schematic diagram of the temperature-controlled optical system used in this study is shown in Fig. 1. The instrument consists of a light source module, a human interface module, and a signal detection module. These three modules were interconnected through a branched optical fiber bundle. The light source module had four light-emitting diodes (LEDs) mounted in a circular holder, A. Light from the LEDs was focused onto the source tip, F, end of an illuminating fiber, G, by an objective lens, B (28-mm focal length RKE precision eyepiece, Edmund Scientific, part No. 30787). The LEDs were modulated by drive circuits (not shown), with each LED modulated at a different frequency. A portion of the light was diverted by a beamsplitter, C, and focused onto a silicon photodiode reference detector, D, which was amplified by amplifier, E, to generate a reference signal, which was used to correct for fluctuations in the intensity of the LEDs. A previously described optical system used up to six wavelengths and six source-detector distances that were varied sequentially though the use of stepper motor-controlled wheels.^{22 24} This optical system uses a quadrant photodiode to allow simultaneous detection at four distances. Frequency modulating the LEDs and demodulating each detected signal allowed the simultaneous detection of four wavelengths.

Figure 1

Schematic diagram of the temperature-controlled optical system used in this study. A, circular holder for the LEDs; B, objective lens; C, beamsplitter; D, reference detector; E, amplifier for reference detector; F, source tip; G, source on illumination fiber; H, thermoelectric element; I, aluminum disk; J, thermocouple; K, temperature controller; L, skin surface; M, detection fibers; N, detection tip; O, quadrant photodiode; P, detection amplifiers. The dashed arrows depict an electronic signal and the solid arrows depict light beam directions.

The wavelengths and frequency at which each LED was modulated were 590 nm at 819 Hz, 660 nm at 1024 Hz, 890 nm at 455 Hz, and 935 nm at 585 Hz. The half-bandwidth of the first two LEDs was 25 nm and that of the last two was 50 nm. The power at the end of the illumination fiber was in the range of 1.4 to 5.0 μW for each LED, as measured by a power meter. The four photodiodes and the four LEDs were combined for the sixteen combinations of wavelengths and source–detector distances.

The output end of the illuminating fiber and the input ends of the light-collecting fibers were mounted in a common tip. All fibers were 400-μm diameter, low-OH silica. The distances between the source fiber and the light-collecting fibers were 0.44, 0.90, 1.21, and 1.84 mm, respectively. The common tip was situated at the center of a 2-cm diameter temperature-controlled disk, I, located in the human interface module. The disk temperature was controlled by a thermoelectric element, H. A thermocouple, J, embedded in the disk, provided feedback to the temperature controller, K (Marlow Industries, Dallas, Texas). The disk and common tip touched the skin surface, L. The light reemitted from the skin was collected by four detection fibers, M, and the output end of each fiber in the detection tip, N, was imaged onto one quadrant of a quad silicon photodiode detector, O (Hamamatsu S4349). The signal from each quadrant of the detector was separately amplified by transimpedance detection amplifiers, P, and measured by a Hewlett-Packard 3458A multimeter. The amplifiers and the frequency modulation drive boards were designed and built in house. The optical signals were collected every 3 s. Data were transferred to the computer every 30 s.

The signal from each quadrant of the detector represented light from one detector fiber, which corresponds to the signal at one source–detector distance. The signal at each modulation frequency corresponded to one wavelength.

The body interface module was mounted on a cradle (shown in Fig. 2), which was mounted on an arm of a standard clinical reclining chair (not shown). The subject sat in the chair with the forearm resting on the cradle. The optical probe located in the body interface module was pressed against the dorsal side of the subject’s forearm at a constant force of 160 g (approximately 45 g/cm²). A personal computer employed a LabView program (National Instruments, Austin, Texas) to manage data acquisition and set the temperature of the disk via the controller.

Figure 2

Schematic drawing of the body interface. The interface is mounted on the armrest of a clinical reclining chair or is placed on a table. A, aluminum disk; B, common tip; C, thermocouple; D, cross-section of the arm; E, lower part of the armrest; F, upper part of the armrest; G, thermoelectric element; H, carriage carrying the detector head; I, fiber optic bundle to the sources and the detectors.

3.2.

Experimental Protocols

We measured the localized reflectance signals at two sites on the dorsal side of the arms of the volunteers (Fig. 3). The two sites were not overlapping and were selected to be morphologically similar in such aspects as the absence of hair, closeness to bone, and appearance of veins. The company’s institutional review board approved the test protocol, and each volunteer read and signed an informed consent form.

Figure 3

Sketch of the two areas on the arm that are used as the optical measurement sites.

3.2.1.

Qualitative study

Three experiments were conducted. The first experiment involved three subjects. Two of them were diabetic and the third was nondiabetic. The subjects were of similar build (a body mass index less than 27) and age. Each subject was tested three times. Reflectance measurements were performed on each subject using the following temperature perturbation program: The probe temperature at the first area was maintained at 38 °C for 300 s, then was gradually lowered to 22 °C over the course of 60 s, and then maintained at 22 °C for 120 s. Thus, temperature perturbation of the optical probe at this area changed from heating at 38 °C to cooling to 22 °C. The nine plots are shown in Fig. 4(A) and Sec. 4.1.

Figure 4

(A) Thermo-optical differential response at 660 nm at one site of the skin plotted as the temperature-induced fractional change in localized reflectance {ln[(R _A1Tm/R _A1T30)]} versus probe–skin contact time. The source–detector distance is 0.90 mm. Temperature perturbation of the optical probe at this site was changed from 38 to 22 °C. The dashed lines are data from diabetic subjects. The solid lines are data from nondiabetic subjects. (B) A plot similar to that of Fig. 4(A) but the temperature perturbation of the optical probe at this site was changed from cooling at 22 °C to heating to 38 °C. The dashed lines are data from diabetic subjects. The solid lines are data from nondiabetic subjects. (C) Thermo-optical differential response at 660 nm plotted as differences in the temperature-induced fractional change in localized reflectance [ln(R _A1Tm /R _A1T30)−ln(R _A2Tm/R _A2T30)] versus probe–skin contact time. The graph is plotted from the data in Figs. 4(A) and 4(B). The dashed lines are data from diabetic subjects. The solid lines are data from nondiabetic subjects. Each subject was measured three times.

The test was immediately repeated on a second site on the skin. The probe temperature at this second site was maintained at 22 °C for 300 s, then was raised to 38 °C over the course of 60 s, and was maintained at 38 °C for 120 s. Data are plotted in Figs. 4(B) and 4(C) and discussed in Sec. 4.1.

A second experiment was also conducted on the same three subjects once, with the temperature perturbation program being the same at the two sites. Two of the three subjects were diabetic and the third was nondiabetic. The data are shown in Fig. 5.

Figure 5

Thermo-optical differential response at 660 nm plotted as [ln(R _A1Tm/R _A1T30)−ln(R _A2Tm/R _A2T30)] versus probe–skin contact time, for a source–detector distance of 0.90 mm. Both sites were heated and then cooled; therefore the temperatures of two probes are the same at any time point. The dashed lines are data from two diabetic subjects. The solid line is for a nondiabetic subject.

In a third experiment, three additional volunteers of different age, ethnicity, and build (a body mass index greater than 32) than those tested in experiment 1 were tested using the same test protocol and temperature programs as in experiment 1. Each subject was tested twice. One subject was diabetic and two were nondiabetic. The combined data of the first group and the second group are shown in Fig. 6 and discussed in Sec. 4.1.

Figure 6

Thermo-optical differential response at 660 nm plotted as [ln(R _A1Tm/R _A1T30)−ln(R _A2Tm/R _A2T30)] versus probe–skin contact time, for a source–detector distance of 0.90 mm. The data are normalized to the 30-s time point from initial probe–skin contact. The subjects include those whose data are plotted in Fig. 4(C) and additional ones with a different body mass index.

3.2.2.

Classification study with three sets of temperature programs

Localized reflectance was measured at two sites on the dorsal side of the arms of the test subjects as in Sec. 3.2.1. The time of the skin–probe contact was reduced by half, resulting in two sequential measurements, each lasting 240 s. The time the skin was kept at a constant temperature was 30 s and the transition time for a temperature change was 180 s. Three different temperature limits were attempted and will be described later.

Nondiabetic subjects and type 2 diabetic subjects with a diabetes duration of 2–15 years volunteered for the experiment. The subject’s disease status was determined as diabetic or nondiabetic by previous diagnoses. Two data sets were collected, a training set and a prediction set. The training set consisted of four diabetic and four nondiabetic subjects, each tested six times (for a total of 48 data points). Measurements for the training set were performed at the time slots given in Table 1. These time slots were selected to cover different times during the day to allow the inclusion of several blood glucose concentrations and physiological and circadian rhythm conditions in the training set. The independent prediction set consisted of six diabetic and six nondiabetic subjects, each tested twice (a total of twenty-four data points). Measurement times for the prediction set were randomly chosen within a week.

Table 1

Test times for the training and prediction sets.
Calibration Set	Test Set
8 subjects, each tested 6 times within 2 weeks	12 subjects each tested two times
1 Early morning, 8:00 to 10:00 a.m.	Two measurements taken at arbitrary time slots within a week.
2 Late morning, 10:00 to 11:00 a.m.
3 Before lunch, 11:00 to 12:00 a.m.
4 After lunch meal, 1:00 to 2:00 p.m.
5 Mid-afternoon, 2:00 to 4:00 p.m.
6 Late afternoon, after 4:00 p.m.

Each subject sat in a clinical chair with the left forearm resting on the cradle. Prior to each measurement, the subject retracted the spring-loaded optical probe with the right hand, started a countdown to zero, then released the probe to contact the skin. Simultaneously, the operator initiated the temperature perturbation and data collection program. After completion of the test, the subject removed his or her arm from the cradle. The steps were repeated for the second programmed temperature perturbation.

Three sets of temperature perturbation programs were used and are illustrated in Figs. 7(A), 7(B), and 7(C). In the first experiment, the probe at site 1 on the skin was maintained at 34 °C for 30 s and then lowered to 22 °C at a rate of 4 °C per minute, which required 180 s. The probe at site 2 was maintained at 34 °C for the 240 s of the measurement.

Figure 7

(A) Temperature perturbation program corresponding to data in Table 3a. (B) Temperature perturbation program corresponding to data in Table 3b. (C) Temperature perturbation program corresponding to data in Table 3c.

In the second experiment, site 1 on the skin was maintained at 38 °C for 30 s and then lowered to 22 °C at 5.33 °C per minute, which required 180 s. Site 2 was maintained at 22 °C for 30 s and then raised to 38 °C at 5.33 °C per minute.

In the third experiment, skin site 1 was maintained at 30 °C for 30 s and then cooled to 22 °C at a rate of 2.67 °C per minute over 180 s. Site 2 was treated in the opposite way; it was maintained at 30 °C for 30 s and then raised to 38 °C at 2.67 °C per minute.

4.1.

Qualitative Difference in Thermo-Optical Response of Diabetic Skin

The natural log of the reflectance at the same site, for each wavelength and source–detector distance, was determined at two different temperatures to give ln{R _A1(λ_i,r_j,T_l)/R _A1(λ_i,r_j,T_k)} and then at the other site to give ln{R _A2(λ_i,r_j,T_q)/R _A2(λ_i,r_j,T_p)}, representing the temperature-induced fractional change in reflectance at the first and second sites, respectively. These localized reflectance changes are simplified in the form ln[(R _A1Tm/R _A1T30)] and ln[(R _A2Tm/R _A2T30)]. The reflectance value R _A1Tm is the localized reflectance at site 1 after m seconds of probe–skin contact for a particular wavelength and distance. R _A1T30 is the localized reflectance at site 1 after 30 s of probe–skin contact. Similarly, R _A2Tm is the localized reflectance at site 2 after m seconds, and R _A2T30 is the localized reflectance at site 2 after 30 s of probe–skin contact.

Figure 4(A) shows the temperature-induced fractional change in localized reflectance plotted as ln[(R _A1Tm/R _A1T30)] versus probe–skin contact time at a single source–detector distance of 0.9 mm and at 660 nm. The plot represents the thermo-optical response at a site on the skin. The data are for two diabetic and one nondiabetic subject, each tested three times as described in the first experiment in Sec. 3.2.1. The temperature perturbation of the optical probe at the first area was changed from heating at 38 °C to cooling to 22 °C. There is an apparent separation of the temperature-induced localized reflectance signals generated by the diabetic subjects and those signals generated by the nondiabetic subject.

Figure 4(B) shows a similar plot for the measurement at the second site, where the temperature change during the measurement was opposite to that applied for the case presented in Fig. 4(A). The temperature perturbation of the optical probe at this site was changed from cooling at 22 °C to heating to 38 °C. The separation between the signals generated by the diabetic subjects and those generated by the nondiabetic subject was less apparent.

Figure 4(C) shows a difference plot of the thermo-optical response curves. These are the differences in the temperature-induced localized reflectance change at site 1 and site 2; [ln(R _A1Tm/R _A1T30)−ln(R _A2Tm/R _A2T30)] plotted against probe–skin contact time. The data for this graph were calculated from the combined data in Fig. 4(A) and Fig. 4(B). For the cases presented in Fig. 4(A), Fig. 4(B), and Fig. 4(C), probe temperatures were different at each of the two sites at any comparable time point. A qualitative separation of diabetic and nondiabetic skin responses after a temperature change at 360 s in probe–skin contact is quite noticeable. The subtraction product ΔR_T, as expressed in Eq. (1), is the difference in the temperature-induced fractional change in localized reflectance at two skin sites, each subjected to a different temperature perturbation.

Figure 5 shows the thermo-optical differential response plots for the second experiment when the programmed temperature perturbation was the same at both sites. The experiment was performed on three subjects; two were diabetic and one was nondiabetic. The separation between the signals of the diabetics and the nondiabetic at the temperature inflection point at 360 s from probe–skin contact, which was noticeable in Fig. 4(C), is not present in Fig. 5. The temperature response at the two sites is essentially the same, and a difference in temperature at the two sites is essential to the observed separation of the data between the diabetic and nondiabetic subjects.

The results for the third experiment, involving three additional volunteers of higher body mass (an index greater than 32), were also plotted. The qualitative separation between the plots of the temperature-induced fractional change in the localized reflectance [ln(R _A1Tm/R _A1T30)−ln(R _A2Tm/R _A2T30)] versus the skin–probe contact time of the diabetic subject was also observed (not shown). When the seven nondiabetic (one subject tested three times and two subjects tested twice) and eight diabetic response curves (two subjects tested three times and one subject tested twice) were plotted together, some overlap between the response curves of the diabetic and nondiabetic subjects was observed, as shown in Fig. 6.

The qualitative separation of the thermo-optical response curves (temperature-induced fractional change in the localized reflectance versus time) for each body mass index group was also noticeable at 890 nm and a 0.9-mm source–detector distance. The separation was not as noticeable under the same programmed temperature change at other source–detector distances. It is then apparent that the use of a thermo-optical response at a single wavelength and at a single source–detector distance is not sufficient to overcome person-to-person differences in skin properties.

4.2.

Assessing the Relationship between a Temperature-Induced Localized Reflectance Change and Diabetic Status

We used the two-site localized reflectance from multiple wavelengths and multiple source–detector distances in an attempt to separate the opto-thermal response of the skin of diabetic subjects from that of the nondiabetic subjects. The experimental protocol included the following improvements: (1) the number of subjects and the number of times they were tested was increased; and one portion of the data was used as a training set and another portion as a prediction set in a discriminant analysis approach; (2) all combinations of sixteen source–detector distances and wavelengths were incorporated; (3) different temperature limits were used; and (4) a nonlinear discriminant function was used as a classifier of the diabetic status instead of the visual inspection of graphs.

4.3.

Nonlinear Discriminant Functions for Data Analysis

The difference in the temperature-induced fractional change in localized reflectance (ΔR_T) is expressed as a function f:

The function(s) f(R _A1t1,R _A1t2,R _A2t1,R _A2t2), determined at each of the four source–detector distances and at four wavelengths, together with the known diabetic or nondiabetic state of each subject in the training set, is used to generate a discriminant function D. A subject is classified as diabetic if D>0, and nondiabetic if D<0. D is a quadratic expression containing multiple functions of the type expressed in Eq. (3), and has the form:³³

where

The true diabetic status of a subject was represented by S_i where S_i=+1 for a diabetic subject and S_i=−1 for a nondiabetic subject. D was calculated for each subject i as D_i. The subject is categorized as concordant if D_i and S_i had the same sign and was discordant if they had different signs. The coefficients of the quadratic function D of the calibration set were used to calculate the value of the function D_i for the prediction set. If D_i>0, the subject was classified as diabetic. On the other hand, if D_i<0, the subject was classified as nondiabetic.

The optical data points collected were divided into two classes, diabetic and nondiabetic subjects. A 2×2 prediction matrix [_χ β ^α γ] was established. Designating the number of true diabetics identified as “α,” the number of true nondiabetics identified as “γ,” the number of diabetic subjects identified as nondiabetic (false negative) as “χ,” and the number of nondiabetics identified as diabetic (false positive classification) as “β,” the sensitivity=α/(α+χ), specificity=γ/(γ+β), positive predictive value (PPV)=α/(α+β), and negative predictive value (NPV)=γ/(χ+γ) were calculated.

Classification was then attempted utilizing Eqs. (4), (5a), and (5b), and using optical signals at eight wavelength–distance combinations (i.e., K=8) at t₁=30 s and at any of these time points t₂: 120, 150, 180, and 210 s from the probe–skin contact. Prediction of the diabetic status using the three different temperature perturbation conditions and using the signal at 120 s from the onset of probe–skin contact is given in Table 2. The data in the table indicate that it was possible to achieve a separation between the diabetics and nondiabetics using the nonlinear discriminant function and eight distance–wavelength combinations, which was not consistently achievable at a single wavelength and a single source–detector distance.

Table 2

Differentiation between diabetic and nondiabetic subjects was not sensitive to the contact time between the skin and the probe beyond 120 s, as shown for the first temperature perturbation program in Table 3a. Similar data were obtained for the two other temperature perturbation programs as shown in Tables 3b and 3c. The data presented in the three tables indicate that prediction of diabetic status was achievable at 120 s of probe–skin contact. The quality of the data was not appreciably enhanced by increasing the probe–skin contact times. The total time for each sequential measurements was less than 5 min. Furthermore, the classification was not limited to one unique programmed temperature perturbation. Any of the three temperature programs resulted in a separation of the test population into diabetic and nondiabetic subjects.

Table 3a

Table 3b

Table 3c