2.1.

Instrument

A description of the basic components of our diffuse optical spectroscopic imaging (DOSI) instrument has been previously presented.^{14, 15} Briefly, DOSI consists of a combined frequency-domain photon migration (FDPM) component and a broadband steady-state (SS) component integrated together to produce broadband absorption and scattering spectra of tissues from 650 to 1000 nm. The FDPM component uses 6 laser diodes at the wavelengths 658, 682, 785, 810, 830, and 850 nm. The breast is illuminated sequentially by each laser diode, which is intensity modulated at 401 modulation frequencies swept from 50 to 400 MHz. The backscattered light is detected by an avalanche photodiode mounted inside a hand-held probe. The SS component uses a high-intensity tungsten-halogen source. The backscattered light is detected by a grating-based spectrometer that collects light from 650 to 1000 nm (1024 pixels). The FDPM and SS sources are coupled by optical fibers mounted into the hand-held probe. The source-detector separation was 28 mm for both FDPM and SS components.

FDPM and SS data are combined to provide broadband absorption (μ_a) and reduced scattering (μ _s ^′) spectra from 650 to 1000 nm. Briefly, we start with the FDPM measurement. The phase and amplitude as functions of modulation frequency are fit to a diffusive model of light transport (semi-infinite boundary conditions) to recover μ_a and μ _s ^′ at each of the six laser wavelengths. SS broadband spectra were converted into absolute absorption spectra using two simple steps. First, the spectral shape of the reduced scattering spectrum is assumed to follow a power law of the form μ _s ^′ = Aλ^−sp, where A is the scatter amplitude and sp is the scatter power, or the exponent of the scattering spectrum. The power-law fit to the FDPM discrete laser diode spectrum provides a scatter correction for the SS reflectance spectrum. We then fit the SS reflectance intensity at each of the laser diode wavelengths to the reflectance calculated from the FDPM-measured absolute absorption values. Thus, the SS reflectance spectrum intensity is scaled using the FDPM discrete laser diode measurements. The absolute absorption spectrum is then extracted by fitting the corrected reflectance spectrum to a diffusion reflectance model.

2.2.

Spectral Analysis

Spectral analysis is performed on the absorption data assuming that the absorption in normal breast is caused mainly by the following four chromophores: deoxy-hemoglobin (ctHHb), oxy-hemoglobin (ctO₂Hb), water (ctH₂O), and bulk lipid (ctlipid). We recover these chromophore concentrations by fitting a linear combination of their molecular extinction coefficient spectra to the scatter-corrected absorption spectrum.¹⁰ The STC is determined by taking the difference between sample and reference tissue absorption spectra and analyzing the residuals of the fit of this first differential to the four-component basis chromophores of breast tissue. Details of this SRDS method have been reported.¹²

In order to quantify the STC spectrum, an STC index was defined by the sum of all local residual variances L _k calculated over five specific spectral regions:¹²

2.3.

Patients and Measurement Procedure

Study protocols were approved by the Institutional Review Board of the University of California, Irvine, and written informed consent was obtained from all patients. A total of 11 female breast cancer patients were investigated. Patients were excluded in this study in the case of multiple unilateral lesions, big bilateral lesions, lesions smaller than 10 mm, or a noninvasive form of carcinoma. In addition, only datasets with available data from the contralateral breast, and performed as grid scan (and not line scan) were used in this study.

The patients’ information can be found in Table 1. The patients’ ages ranged from 31 to 64 years old, with an average age of 50, including 6 premenopausal (pre) and 5 postmenopausal (post) patients. Two patients had bi-lateral lesions; one patient had bi-lateral infiltrating ductal carcinoma (IDC), and the other patient had infiltrating lobular carcinoma (ILC) and sclerosing adenosis in the left and right breasts, respectively. In these two patients, only the lesion in the left breast was investigated. The lesion in the other breast (right breast) was small and was not in the measurement field of view. Therefore, the right breast was referred to as the contralateral normal side for these two patients. Two other patients were reported as having cystic breasts. For the remaining seven patients, the contralateral breasts were mass-free according to the diagnostic imaging reports. The current study included a total of 11 masses; 10 IDC, and 1 ILC. Out of the 11 patients, 3 had a breast density of BIRADS 4 (75% to 100% glandular tissue), 2 had BIRADS 3 (50% to 75% glandular tissue), 4 had BIRADS 2 (25% to 50% glandular tissue), and the remaining 2 patients had unknown breast densities.

Table 1

Patients’ characteristics.

DOSI maps from both breasts were collected for each patient. Patient-specific measurement grids to define DOSI measurement locations were chosen based on the lesion size, location, and on the breast size. DOSI measurements were performed over the region of the lesion and over surrounding normal tissue, and in the same location mirrored on the contralateral side. The measurement grids were drawn in 10 mm steps in both x and y directions. The dimension of the measurement grids ranged from 90 ×40 to 120 ×130 mm, resulting in up to 156 discrete measurement locations for each breast. The specific details of patient positioning have been recently described.¹⁶

In 1 out of the 11 patients, we were not able to visualize the lesion in the DOSI image. The lesion to background contrast was probably too low to be detected with our scanner. The dataset of this patient was therefore not included in the data analysis.

2.4.

Data Analysis

The areola was included, partly or entirely, in the field of view of the optical images in 7 out of 10 patients. For data analysis, the areolar regions were defined in the optical images based on a previously described contrast function, the tissue optical index (TOI = ctHHb ×ctH₂O/ctlipid) and on the size of the areola in the clinical report. The tumor location defined in the optical images was based on the TOI and ultrasound information of the clinical report. The “normal” reference tissue in the ipsilateral breast was defined by excluding the tumor region and an additional ∼1 cm wide zone around the tumor. Spectral analysis of tumors was performed on the tumor point showing the highest STC value.

2.5.

Statistical Analysis

The maps obtained using different referencing techniques were compared for similarity. To compare the equivalence between two methods, one must show that the difference between the data obtained using both methods is small enough to use the methods interchangeably. Statistically, one must reject the null hypothesis, which is the data obtained using both methods are not different, and a confidence interval of the subtracted data should lay within predefined equivalence limits. This range of equivalence is subjective and is defined a priori depending on the clinical/scientific context.^{17, 18} Here, we want to obtain similar features in the STC index maps such that the lesion is visible in the maps obtained using any referencing method. We estimated that the main features of the map would be preserved with a 20% maximum difference and hence, the clinical diagnosis would not be affected. Using this threshold, we statistically compared the STC index maps by computing the two one-sided test for equivalence (TOST) using R (version 2.13.1).¹⁹

3.1.

Impact of Amount of Reference Points

Random measurement points across the contralateral side have been selected and used as reference for the calculation of the STC. Fig. 1a presents the averaged STC spectra in the lesion of patient 6 calculated successively with 4, 9, 18, 27, 36, 45, 54, 63, and 72 reference locations in the contralateral side. The locations were randomly selected 10 times and the resulting 10 spectra were averaged on the graph. We observe that the spectra overlap closely; 4 reference points produce the same STC spectrum as 72 reference points, i.e., almost the whole contralateral side. This result suggests that only a few measurement points in the contralateral normal breast are required to obtain a reliable STC spectrum. Fig. 1b presents the 10 averaged STC spectra in the lesion of patient 9 calculated with successively 6, 9, 20, and 30 random reference points in the contralateral side. In this case, small fluctuations are seen between the spectra: they represent the biggest deviations that were visualized in the 10 patients. For a more quantitative analysis, we compared for all patients the averaged STC spectra calculated with P = 6, 9, 20, and 30 reference points, randomly selected 6 times, to the gold-standard STC spectra obtained using the whole contralateral breast. We observed that P = 6 reference points results in the largest variance compared to the gold standard with an average correlation coefficient of 0.99 ± 0.01 (range 0.97 to 1.00) for all the patients. For spectra calculated with P> = 9, the correlation coefficient r > = 0.99 ± 0.01 (range 0.97 to 1.00). These small variations in STC have a negligible impact upon the STC index, and subsequently the STC index maps which were found to be statistically equivalent in all patients using the TOST analysis (p-value ≪ 10⁻⁶).

Fig. 1

Averaged STC spectra calculated using N number of reference locations, where all locations are randomly selected 10 times. (a) Patient 6. N = 4, 9, 18, 27, 36, 45, 54, 63, and 72. (b) Patient 9: patient with the worst deviations among the results. N = 6, 9, 20, and 30.

3.2.

Impact of Referencing on the Ipsilateral Side

A key question is whether the information contained in the STC is preserved when the selected reference normal tissue shifts from the contralateral to the ipsilateral side. To address this issue, we performed comparisons of STC obtained from the 10 lesions calculated using reference locations on both sides, as shown in Fig. 2. In six patients there were minimal differences between STC spectra [i.e., similar to Fig. 2a]. We found an average correlation coefficient of 0.98 ± 0.03 (range 0.92 to 1.00) between the spectra referenced on the areola compared with the whole contralateral breast for these six patients. These spectra produced negligible differences in the STC index maps. We found an average mean value of the subtracted maps (i.e., STC with ipsilateral reference versus STC via contralateral reference) of 0.018 (ranging from 0.009 to 0.027) with an average standard deviation (SD) of 0.013 (ranging from 0.007 to 0.023). In the remaining four subjects (Nos. 2, 5, 8, and 9) more noticeable variations were observed between STC spectra [i.e., similar to Fig. 2b] calculated with the contralateral breast and the normal healthy tissue in the ipsilateral breast for the reference. The STC spectra showed different magnitudes or small peak shifts around the spectral region 850 to 950 nm. We found correlation coefficients of 0.75, 0.88, 0.79, and 0.92 between the spectra referenced on the areola compared with the whole contralateral breast for patients 2, 5, 8, and 9, respectively. Fig. 3 presents the normalized STC index maps of these patients calculated with the contralateral breast and the normal healthy tissue in the ipsilateral breast for the reference, and their subtracted maps. Even though the STC spectra of these patients calculated with both referencing showed different spectral content, we observe here that the STC index maps are still similar: the lesion position and the main features of the image are preserved, as shown in Fig. 3a, 3b, 3d, 3e, 3g, 3h, 3j, 3k. This result is confirmed by the subtracted normalized maps of the STC index maps in Fig. 3c, 3f, 3i, 3l. The mean values of the subtracted maps of patients 2, 5, 8, and 9 were 0.006±0.003 (ranging from 0.000 to 0.014), 0.021±0.015 (ranging from 0.000 to 0.056), 0.074±0.045 (ranging from 0.000 to 0.140), and 0.044±0.028 (ranging from 0.000 to 0.159) respectively. For all the patients, the maps were found to be statistically equivalent using the TOST analysis (p-value ≪ 10⁻⁶).

Fig. 2

Normalized STC spectra: the solid line is the STC referenced on the ipsilateral side; the dashed line is the STC calculated using the contralateral breast as reference. (a) Patient 10, close STC spectra using the 2 different referencing approaches. (b) Patient 8, different spectral content in part of the spectra.

Fig. 3

(a) and (b) STC index maps of patient 2. (c) Subtracted map of patient 2. (d) and (e) STC index maps of patient 5. (f) Subtracted map of patient 5. (g) and (h) STC index maps of patient 8. (i) Subtracted map of patient 8. (j) and (k) STC index maps of patient 9. (l) Subtracted map of patient 9. The STC index maps in (a), (d), (g), and (j) are obtained using the contralateral breast as reference. The STC index maps in (b), (e), (h), and (k) are obtained using the background tissue of the ipsilateral breast as reference.

3.3.

Impact of Referencing with Areola Tissue

STC spectra calculated with the contralateral areolar tissue as reference were obtained for the seven patients whose areolas were located in the field of view of the optical measurement. Similar STC spectra as the ones obtained using the contralateral breast as reference were obtained in four out of the seven patients, as shown in Fig. 4a for patient 4. We found an average correlation coefficient of 0.98 ± 0.01 (range 0.97 to 0.99) between the spectra referenced on the areola compared with the whole contralateral breast for these four patients. These spectra produced negligible differences in the STC index maps. The mean average (standard deviation, minimum–maximum) deviations of the subtracted maps was 0.033 (ranging from 0.007 to 0.059) with an average SD of 0.0210 (ranging from 0.005 to 0.039). In three patients (Nos. 2, 9, and 11), the STC spectra calculated with the different referencing (i.e., contralateral areola vs. entire contralateral side) showed different spectral features, as shown Fig. 4b for patient 9. We found the following correlation coefficients: 0.56, 0.69, and 0.80, between the spectra referenced on the areola compared with the whole contralateral breast for patients 2, 9, and 11, respectively. In these patients with different STC spectra, we observe visually similar STC index maps, as shown by the subtracted maps in Fig. 5a, 5b, 5d, 5e, 5g, 5h. The average deviations of the subtracted maps, in Fig. 5c, 5f, 5i were 0.035±0.023 (ranging from 0.000 to 0.101) and 0.034±0.020 (ranging from 0.000 to 0.111) and 0.020±0.014 (ranging from 0.000 to 0.068) for these three patients. For all the patients, the maps were found to be statistically equivalent using the TOST analysis (p-value ≪ 10⁻⁶).

Fig. 4

STC spectra in lesion calculated with reference normal tissue in the whole contralateral side, solid line, and in the areola of the contralateral side, dashed line. (a) Patient 4. (b) Patient 9.

Fig. 5

(a) and (b) Normalized STC index maps of patient 2. (c) Subtracted map of patient 2. (d) and (e) Normalized STC index maps of patient 9. (f) Subtracted map of patient 9. (g) and (h) Normalized STC index maps of patient 11. (i) Subtracted map of patient 11. The STC index maps in (a), (d), and (g) are obtained using the contralateral breast as reference. The STC index maps in (b), (e), and (h) are obtained using the areola regions of the contralateral breast as reference.