A novel nonlinear perturbation model was successfully applied to the in vivo characterization of breast lesions (cysts and tumors) after detection by multi-wavelength time-resolved optical mammography. The model relies on the method of Padé approximants and consists in a nonlinear approximation of time-resolved transmittance curves in the presence of an inclusion. Tissue constituents (blood volume, blood oxygen saturation, lipids and water content) were estimated for both the bulk and the lesion areas. Cysts were reported to have high water content while tumors showed increased blood content as compared to bulk tissue.
©2003 Optical Society of America
The use of near infrared optical radiation for early diagnosis of breast cancer has been pursued for many years ago as a possible tool to complement conventional breast imaging techniques (x-ray mammography, ultasonography). Preliminary trials were performed with diaphanography in the late 1980s [1–2], while in recent works continuous wave , frequency-domain [4–7] and time-resolved [8–10] techniques have been used. Despite the lower spatial resolution of optical mammography as compared to x-rays, the interest in this novel non-invasive tool has not diminished. Currently, the potential of optical mammography relies in fact in the ability to complement imaging data (lesion detection) with spectroscopic information (lesion characterisation). In the spectral range 600–1100 nm oxy-hemoglobin (O2Hb), deoxy-hemoglobin (HHb), lipid and water are the major tissue constituents contributing to light absorption. Significant changes in lipid and water content with age, body mass index (BMI), and menstrual cycle have been observed in normal breast [11–14]. Also preliminary data on breast lesions have reported increased water content in fibroadenoma [15–16] or increased blood content in tumors [8, 16–19] as compared to surrounding normal tissue. Conversely, tissue structures influence the reduced scattering coefficient, although in a less straightforward manner [12, 14, 16, 19]. Clearly these data need to be confirmed on a statistical basis, however they are encouraging and have fostered the development of new instruments with multi-wavelength capabilities.
Current instruments for optical mammography can be divided into two distinct categories, based on how they acquire the image: coaxial scanning systems and tomographic systems. The former build up the image by scanning the breast slightly compressed between parallel transparent plates, and derive average optical properties along the line of sight by fitting data to a theoretical model for photon migration; the latter rely on a multi-source, multi-detector configuration and on model-based iterative reconstruction schemes to estimate tissue optical properties in a distribution of voxels.
Whichever the type of instrument, the accuracy in the estimation of tissue optical properties is of primary importance. This is in fact a crucial point to the derivation of accurate tissue constituents and tissue structure parameters. The biomedical community is in fact reluctant to accept absorption and scattering coefficients as clinical indicators, while parameters like total hemoglobin concentration (tHb=HHb+O2Hb), blood oxygen saturation (SO2=O2Hb/tHb), water and lipid content should be more easily linked to pathophysiological conditions.
The interest is therefore towards rigorous analytical or semi-empirical models to better estimate tissue optical properties from optical mammography data.
The authors have developed a multi-wavelength time-resolved optical mammograph which is currently undergoing a multinational clinical trial in Europe. The instrument is based on the coaxial scanning approach. The standard procedure for coaxial scanning detection of inhomogeneities embedded in turbid media is based on the combined use of an early time-gate and of a late time-gate to derive respectively the scattering contrast and the absorption contrast . The information on tissue absorption is in fact better encoded in the late photons, which travel long distances in a turbid medium before being eventually detected or absorbed, while scattering contrast mainly affects the early photons. However, an early timegate is typically affected by absorption and scattering cross-talk, therefore a semi-empirical procedure based on a homogeneous diffusion model (sensitive to the scattering contrast) and a late time-gate (sensitive to the absorption contrast) was experimentally proved to be effective on tissue phantom  to detect lesions and to qualitatively discriminate absorption and scattering contribution. Unfortunately, quantitative lesion detection and characterization by this semi-empirical model is clearly not possible. A homogeneous model in fact yields average optical properties, without possibility to clearly discriminate between bulk tissue and lesion. To overcome this limitation, perturbative-like methods have been developed working in the framework of diffusion theory [22–23] or random walk model .
In this paper we present the preliminary results of in vivo breast lesion characterisation by the use of a novel non-linear analytical model (Padè approximants model, PA) of photon migration. To our knowledge this is the first time a perturbation model is applied to produce images of the optical parameters from in vivo data. Maps of tissue constituents and structures are derived by fully exploiting the spectral features of the optical parameters.
2. Materials and Methods
2.1 System set-up
Figure 1 shows the scheme of the mammograph. Four pulsed diode lasers (PDL Heads, PicoQuant, Germany) emitting at 683 and 785 nm (VIS), and at 912 and 975 nm (NIR), with average output power of ~1–4 mW, temporal width of ~180–400 ps (FWHM), and repetition rate of 40 MHz are used as light sources. A single driver (PDL-808 “Sepia”, PicoQuant, Germany) controls all the four laser heads, and their output pulses are properly delayed by means of graded index optical fibers, and combined into a single coupler. A lens produces a 3-mm diameter collimated beam that illuminates the breast. A 5.6-mm diameter, 1-m length bundle collects the output light on the opposite side of the compression unit. The distal end of the bundle is bifurcated, and the two legs guide photons respectively to a photomultiplier tube (PMT) for the detection of VIS wavelengths (sensitive up to 850 nm, R5900U-01-L16, Hamamatsu, Japan) and a PMT for NIR wavelengths (sensitive up to 1100 nm, H7422P-60, Hamamatsu, Japan). Variable neutral density circular filters, placed in front of each PMT, are used to optimize the illumination power for in vivo measurements and for the acquisition of the instrument response function. A PC board for time-correlated single photon counting (SPC134, Becker&Hickl, Germany) allows acquisition of time-resolved transmittance curves. The illumination fiber and collecting bundle are scanned in tandem and data are usually stored every millimeter of path, i.e. every 25 ms. A complete scan with a count rate of about 106 counts/s typically requires 5 min. The Plexiglas plates can be rotated by an angle up to 90° in both clock-wise and counter-clock-wise direction, so that images of both breasts can be recorded in the cranio-caudal (CC) as well as medio-lateral or oblique (OB) views.
2.2 In vivo measurements
Conventional x-ray mammography and optical mammography were performed on patients (#032, #041, #044, #047, #057 and #060) on both breasts in the craniocaudal (CC) and oblique (OB) projections. After reading of the x-ray mammograms, patients #032, #041, and #047 were reported to bring a tumor, while in patients #044, #057, and #060 a cyst was diagnosed. Table 1 summarizes the main data on patients and lesions.
2.3 Data analysis
a) Tissue optical properties
Images of the optical properties are constructed with a pixel-wise approach. For each projection and each wavelength a reference curve is obtained by averaging all the timeresolved curves corresponding to the maximum of the distribution of the mean time of flight. The reference curve is subsequently fitted with the homogeneous model to find the bulk absorption coefficient μa0 and diffusion coefficient D 0=(3μ′s0)-1. Then, for each pixel the nonlinear contrast function C NL is derived:
This expression can be obtained by approximating the time-resolved collinear transmittance with :
where T 0 (t;μa0,D 0) is the collinear transmittance for the homogeneous background.
The experimental contrast function C NL is fitted with the corresponding theoretical function given by Eq. (1), where we inserted the analytical expressions of the Jacobians Ja and JD reported in Carraresi et al. , in such a way to derive the perturbations δμa and δD of the optical parameters. Due to the simple dependence of C NL from δμa and δD, a linear fitting has been performed. In the Jacobians are included all the geometrical properties of the inclusion, such as location in the phantom and volume. It is clear that an overestimation of the inclusion volume determines an underestimation of the variation of the optical properties caused by the presence of the inclusion, and viceversa. Therefore, we use the a priori knowledge of the size of the inclusion, typically derived from conventional x-ray mammography and/or ultrasonography. Furthermore, in the fitting procedure we make the assumption that the inclusion is always located half-way between source and detector. Then we expect the optical properties obtained in different points of the measured array to correspond to those of the inclusion only when it is actually located on axis. For the other points the fitting provides the optical properties of an “effective” inclusion located on axis, with optical properties in between those of the inclusion and of the background.
A detailed description of the PA method and an extensive characterization on tissue phantoms is reported in Spinelli et al. .
b) Tissue components and sructures
A further level of interpretation of the experimental results then allows one to derive information on tissue composition from the absorption data and tissue structure from the scattering data. Briefly, the absorption coefficients measured at four wavelengths [μa(λi)] are interpreted as the linear combination of the extinction coefficients [εj(λi)] of the four main tissue constituents absorbing between 680 and 980 nm (i.e., HHb, O2Hb, water, and lipids) weighted by their average concentration (cj ) in tissue:
The four concentration values can thus be estimated. A plot of the extinction coefficients over the relevant range of wavelengths is shown in Fig. 2. The few data on in vivo breast tissue constituents reported in the literature have usually been obtained by making the assumption that water content in breast tissue is about 30% [14, 17–18]. Also the assumption that lipids play a negligible role in the red part of the spectrum is made. Working with four wavelengths it is in principle possible to estimate the concentration of four independent cromophores, without any a priori information. However, in some cases, due to the very low signal-to-noise ratio no reliable data are obtained for the optical coefficients at the NIR wavelengths. Therefore we fix water and lipid contents at the values 20% and 80% respectively. This assumption is derived from the ensemble average over 30 patients (data not shown).
For what concerns the scattering data, they are interpreted using Mie theory, under the simplifying hypothesis of spherical and independent scattering centers of radius r:
where the size parameter x(λi) is defined as x(λi)=2πrnm (with the refraction index of the medium nm chosen to be 1.35), and a and b are free parameters [27–28]. In particular, a is proportional to the density of the scattering centers, while the scatterer size can empirically be obtained from the b value.
Figure 3 shows the x-ray and the optical mammograms of the right breast in the oblique projection (R_OB) for patient #044. The color scale used to generate optical mammograms, maps low (high) value as black (white). The x-ray image reveals the presence of a more absorbing area in the upper quadrant, which is identified as a cyst. The presence of the cyst is easily noted in the optical mammograms as a less scattering region at all the wavelengths as compared to the surrounding tissue. Since detection of this kind of lesion is somehow straightforward, no comparison with the controlateral breast is necessary. In the lesion area no well-defined structures are observed in the absorption images, but in the 975 nm image, where an increased absorption is found. These findings are consistent with the fact that the cyst is filled with liquid, which typically shows increased water content. Other interesting features can be observed looking at the optical mammograms. In particular, a more absorbing region is found in the area close to the nipple at 685 nm, 785 and 975 nm, while an increased absorption is observed at 975 nm in the mammary gland region. A change in the scattering coefficient in the region close to the boundary of the breast is an artefact due to the uncompensated reduction of breast thickness between the plates. This effect has little influence on the absorption properties.
Spectral differences between bulk tissue and lesion, reflecting differences in composition, can be better appreciated by looking at tissue constituents. By iteratively applying tissue constituent analysis pixel by pixel, it was in fact possible to calculate the maps of blood oxygen saturation, blood volume, and relative lipid and water content as shown in Fig. 4. The breast is classified as adipose (pattern 2) following , and this is consistent with the high lipid content (83%) and a low water content (17%) estimated as an average in the bulk tissue. Water content is higher (25%) in the region of the cyst, and also in the wider area of the mammary gland, while lipid content is lower in both regions. Conversely, no significant changes in blood content and blood oxygen saturation can be found between lesion and bulk tissue. Looking at Fig. 3 and Fig. 4 it is definitely clear that referring to bulk tissue is an oversimplification. The breast is in fact optically heterogeneous, and this reflects the heterogeneous distribution of tissue constituents.
Figure 5 illustrates the maps of tissue structures parameters as derived from the interpretation of the multi-wavelength scattering images in terms of Mie theory. The cyst is easily identified as a low density area, as shown by low a values. The scatter power, providing information on the equivalent size of scatterers, shows no significant changes.
In a second case (patient #057, R_OB) we have overall similar findings. The cyst is again easily identified as a less scattering region at all wavelengths (see Fig. 6), and increased water content is found (see Fig. 7). Differently from patient #044, the breast is fibrous / glandular (pattern 5). Therefore, water content in the bulk tissue is relatively higher (41%) as reported in Table 2. The cyst seems to be filled with water and little deoxygenated blood. The estimate of blood oxygen saturation (~0%) in the lesion may be affected by the very high water content.
In Fig. 8, as already observed for the previous case, we note that low a values characterize the lesion. Conversely, also the scatter power b shows a clear perturbation with higher values than the surrounding tissue (i.e. small radius of the scatterer). Both findings are consistent with an increased water content in the lesion.
Figure 9 reports a third example (patient #060, L_CC), a cyst in an adipose breast (pattern 2, bulk tissue has 75% lipid content). Increased water content and decreased lipid are again found in the cyst. Also the scattering coefficient is lower than the background, but for 685 nm. This can be explained by the presence of high absorption at 685 nm in the lesion area, due to an increased blood content (197 µM) with a reduced oxygenation (37% as compared to 50% in the bulk) as reported in Fig. 10. The presence of the very high absorption (0.7 cm-1) at 685 nm seems to determine a cross-talk between the optical coefficients. This is somehow consistent with the fact that the perturbation model works better if the perturbation is small. Finally, structure parameters analysis shown in Fig. 11 yields low density (i.e. a values) and high scatter power values (i.e. b values) for the cyst.
A summary of bulk and cyst tissue constituents for all patients is reported in Table 2.
More interesting to the biomedical community is the possibility to detect tumor by optical mammography. Here we report the detection and characterization of three tumors. Unfortunately, the signal-to-noise ratio at 912 nm and 975 nm was very low for these patients, therefore only data at 685 nm and 785 nm are reported.
The first example (patient #041) is a tumor (ductal carcinoma) in the right breast. The xray mammograms show a very high contrast between tumor and surrounding tissue (see Fig. 12). The same happens in the optical mammograms. In particular, the absorption coefficient is higher than the surrounding tissue both at 685 nm and at 785 nm. Little variation is observed in the scattering coefficient. A small decrease in somehow masked by the changes due to the edge effect.
Tissue components analysis (Fig. 13) reports a significantly increased tHb (approximatively twice) and a slightly increased blood oxygen saturation. The map of tHb is very similar to the map of the absorption coefficient at 785 nm. This is expected since this wavelength is close to the isosbestic point for HHb and O2Hb. It is worth noting that the comparison between left and right breast gives us the possibility to classify as an unsuspicious lesion the high absorption area in the internal part of the breasts (bottom of figure) and the central low absorbing area. No significant results were found from the structure analysis, therefore no images are reported for a and b parameters. This holds true also for the other two cases discussed in the following.
In a second example (patient #047, invasive ductal carcinoma) we can observe the same optical features, that is increased absorption clearly seen at both 685 nm and 785 nm (see Fig. 14). We also note in both breasts the increased absorption in the region corresponding to chest muscles. Tissue components analysis shows correspondingly increased tHb and decreased SO2 (see Fig. 15). Again small variations in the scattering coefficient were detected.
A final example (patient #032, invasive lobular/ductal carcinoma) is a rather difficult case to be interpreted with the perturbation approach. The lesion is in fact diffuse in a large area of the left breast, therefore no defined size was clinically assigned. The perturbation approach was performed with an equivalent size of 3.0 cm. The results indicate an increased absorption in a wide area of the breast (see Fig. 16), consistent with an increased blood content (see Fig. 17). The absolute values in this case should be considered as indicative. Nonetheless there is again a clear discrimination between bulk and lesion.
A summary of bulk and tumor tissue constituents for all patients is reported in Table 3.
All lesions presented were detected in both the oblique and the craniocaudal projections with comparable contrast.
The presented cases are a subset of the 126 patients examined up to now. Average size of lesion (calculated over the first 101 cases) is 1.8±1.5 cm for tumors, and 1.8±0.7 cm for cysts. On the basis of our experience, we observe that detected lesions have on average larger size than missed lesions: for example, 2.6 cm and 0.9 cm for detected and missed tumor, respectively. However, detection of lesions is not only dependent on lesion size, but also breast thickness and contrast of optical properties, in fact, play a major role.
A comment is needed to discuss the edge effect. In the μ′s images, the region close to the boundary of both breasts is affected by a decreased scattering due to reduction of breast thickness. In the fitting procedure we use the approximation of the tissue as an infinite slab with constant thickness. Correction of the edge effect can be partially obtained when working with a homogeneous model by recovering the correct breast thickness through the time-of-flight method [8, 29]. Work is currently in progress to extend this method to the perturbation approach. However, in many of the cases we have investigated the lesion was in the central part of the breast and the correction was not necessary.
As already stated, the application of the PA method requires the a priori knowledge of lesion size and location. The information on size can usually be derived by conventional x-ray mammography and/or ultrasonography. In alternative, a perturbation approach developed within the Random Walk model was effectively used to estimate the size of an inhomogeneity embedded in a tissue phantom , and is currently being tested on in vivo data. As for the depth, a direct estimate of lesion depth is impossible to derive using coaxial scanning systems. Ultrasound inspection can in some cases give an estimation of the depth of the lesion. In the data analysis reported, we have assumed the lesion always located half way between source and detector. This is clearly an oversimplification, but we have tested on tissue phantoms  that the sensitivity of the PA method to the depth of the inhomogeneity is low. Even when the position of the inclusion is wrong, the PA method provides a better estimate of the optical properties than standard homogeneous methods.
The possibility to discriminate breast lesions by noninvasive optical methods is currently less hypothetical than was the case few years ago. Clearly, the problem is that instruments currently used in clinical trials on optical mammography are far from achieving a complete 3D mapping of absorption and scattering of the female breast. Lesion detection and characterization for diagnostic purposes should therefore rely on semi-empirical and/or analytical methods like the ones presented in this paper. The results obtained are a first step toward a possible discrimination of lesions on a quantitative basis.
The work was partially supported by the EU Project “Optimamm” (Contract n. QLG1-CT-2000-00690. The EU Network “Medphot” (Contract n. QLG1-2000-01464) is also acknowledged.
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