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Blind Source Separation methods (BSS) aim for the decomposition of a given signal in its main components or source signals. Those techniques have been widely used in the literature for the analysis of biomedical images, in order to extract the main components of an organ or tissue under study. The analysis of skin images for the extraction of melanin and hemoglobin is an example of the use of BSS. This paper presents a proof of concept of the use of source separation of ex-vivo aorta tissue multispectral Images. The images are acquired with an interference filter-based imaging system. The images are processed by means of two algorithms: Independent Components analysis and Non-negative Matrix Factorization. In both cases, it is possible to obtain maps that quantify the concentration of the main chromophores present in aortic tissue. Also, the algorithms allow for spectral absorbance of the main tissue components. Those spectral signatures were compared against the theoretical ones by using correlation coefficients. Those coefficients report values close to 0.9, which is a good estimator of the method’s performance. Also, correlation coefficients lead to the identification of the concentration maps according to the evaluated chromophore. The results suggest that Multi/hyper-spectral systems together with image processing techniques is a potential tool for the analysis of cardiovascular tissue.
© 2015 Optical Society of America
1. Introduction
Multispectral Imaging Systems (MIS) allow capture information outside the human perception range, which may include analysis in ultra violet, visible, infrared bands, X-ray or other bands of the electromagnetic spectrum [1, 2]. In medicine these images are an effective tool, mainly for cancer diagnosis [3, 4]. In this sense, there are studies focused on the application of this imaging technique in the cardiovascular field [5, 6]. In fact, World Health Organization foresees that in 2030 more than 23 million people will die from cardiovascular disease [7]. For diagnosis of these pathologies, noninvasive medical imaging techniques have allowed for more accurate medical concepts. Although these techniques allow for tissue structural and functional evaluation, they do not always cover all different diagnostic requirements, which lead to the need to develop additional imaging systems [8].
This paper presents a proof of concept of the use of multispectral images together with blind source separation techniques, for the analysis of ex-vivo aorta tissue. The multispectral tool used in this work corresponds to a system based on interference filters. Those filters allow selecting the wavelength in which the tissue under study is illuminated. The filters used in this work correspond to the wavelengths that enhance the principal chromophores present in aortic tissue: hemoglobin and beta-carotene. In multispectral imaging systems, once the tissue is illuminated an image is acquired. The set of these images forms a multispectral cube where each pixel corresponds to a sampled spectral signature of a ROI of the tissue under study. In this work, the obtained multispectral images were processed by means of two algorithms: independent Components analysis and Non-negative Matrix Factorization. In both cases, it is possible to obtain maps that quantify the concentration of the main chromophores present in aortic tissue. Also, the algorithms allow for spectral absorbance of the main tissue components. Those spectral signatures are compared with the theoretical ones by using correlation coefficients.
The results of this work show that multispectral imaging systems are a potential tool for the analysis of ex-vivo an in-vitro cardiovascular tissue. Specifically, this tool can be used in studies that search for how cardiovascular tissue’s extra-cellular matrix is affected by external factors caused by diseases such as fibrosis and atherosclerosis. This can lead to the development of new tools for diagnosis in cardiology that allow for a global knowledge about the state of a lesion and its surrounding tissue. In this way, the clinicians can do a better choice in both the right time for intervention and choice of treatment [9].
2. Materials and methods
2.1. Tissue preparation
Aorta segments from excised bovine heart were obtained within 48 h of the time of death. Those segments were longitudinally and transversally opened. Then, they were imaged from the lumen side and media layer respectively. The imaged field of view (FOV) had an area of 10mm × 10mm. This protocol has the approval from the the Universidad Pontificia Bolivariana ethics Board.
2.2. Materials: interference filter-based imaging system
The aorta segments were illuminated with a system based on interference filters. The system is presented in Fig. 1.
Fig. 1 Configuration of a system based on interference filters: a). white light source, b). bandpass interference filters, c).liquid guide-light, d). 10X microscope objective, e).CCD camera, and f). sample.
This image acquisition setup is composed of: a halogen white light source, a series of interference filters in the visible region, a liquid wave guide, and a microscope objective together with a CCD camera. The central wavelength of the filters and their corresponding FWHM (Full Width at Half Maximum) are: 436−10nm, 450−10nm, 500−10nm, 520−10nm, 546−40nm, 550−10nm, 578−10nm, 600−10nm, and 650−10nm. The filters were selected so that they can target the absorption maxima of the principal chromophores present in aortic tissue (see Fig. 2). The objective of the interference filters is to select the desired wavelengths in which the cardiovascular tissue is illuminated. Once the tissue is lighted, a set of images (one per filter) are acquired by the microscope objective and the camera. The system was calibrated using a white reflectance standard that reflects 99% of the light. In this way, images from this white standard were acquired for each wavelength. The aim is to compensate the tissue multispectral images according to Eq. 1 [10]:
where: Iref is the tissue multispectral image after white balance (representing tissue reflectance spectra), Iraw is the pixel intensity from the tissue multispectral image without compensation, Idark corresponds to the camera dark current, and Iwhite is the pixel intensity given by the white standard image.Fig. 2 Theoretical absorbance spectra of the major chromophores present in cardiovascular tissue [9, 14].
2.3. Light-tissue model representation
The phenomena of light scattering, absorption and diffuse reflectance are produced in biological tissue by the iteration of light with the tissue biochemical components [11, 12, 13].
In the case of cardiovascular tissue, it is composed of a series of chromophores which the most significant in the VIS-NIR (visible-near infrared) region are: hemoglobin (oxygenated and deoxygenated), lipids/carotenoids, connective tissues (collagen and elastin), calcifications and ceroid [9] (see Fig. 2). In a general way, the absorption spectrum of cardiovascular tissue can be represented as the weighted sum of the contributions given by each one of the chromophores that compose the tissue. This can be expressed by Eq. 2 [15]:
where the terms , εHb, and εβ−car correspond to the absorbance spectrum of oxyhemoglobin, deoxyhemoglobin, and betacarotene (some of them represented in Fig. 2). The terms α1, α2 and α3 correspond to constants that quantify the contributions of the previously mentioned chromophores. The terms εOthers(λ) and α4 correspond to other components related to light-scattering phenomenon, which is not considered in this work.Since the system used in this work acquires multispectral images as a representation of the tissue’s reflectance R(λ), absorbance spectrum A(λ) can be estimated from reflectance by Eq. 3 [16]:
In this way, the acquired multispectral image can be represented as a 2D matrix Y corresponding to absorbance optical maps. This matrix Y is equivalent to the multiplication of two matrices: W and H. Matrix H represents the spectral absorbance of the main sources that compose cardiovascular tissue (hemoglobin, betacarotene, etc). Matrix W represents the weights or the quantity of the given sources, for each one of the pixels constituting the multispectral image. The decomposition of a given mutispectral image in matrix W and H is done by Blind Source Separation (BSS) methods.
2.4. Blind source separation methods
Blind source separation methods are used for the decomposition of cardiovascular tissue multispectral images in their main chromophores. The implemented source separation algorithms are based on independent component analysis (ICA) and on multiplicative coefficient upload (Non-negative Matrix Factorization - NMF) techniques.
2.4.1. Independent component analysis -ICA
ICA is a method for finding and quantifying the fundamental elements in multivariate data. For ICA decomposition, those fundamental elements are assumed to be both statistically independent and non-gaussian. For this analysis, kurtosis can be used for non-gaussianity search as a measure of independence. The aim is to maximize this non-gaussianity by means of a iterative algorithm such as fast-Ica [17, 18]. This algorithm requires a previous step of data sphering or whitening.
- Data whitening: Data whitening is based on Principal Components Analysis method. PCA is a technique that decomposes a signal or image in its main components. PCA allows dimension reduction, as well as sphering or data whitening in ICA [19]. PCA is based on statistical analysis, where from a given data Y ∈ Rm, its covariance matrix C is calculated. From this covariance matrix, the eigenvectors E ∈ Rm×m and eigenvalues D ∈ Rm×m are calculated. Finally, the reduced subspace matrix X is calculated as indicated by Eq. 4: where matrix M is the whitening matrix and is calculated as indicated by Eq. 5:
One element of the matrix H (hi) can be calculated by:
After this step of data whitening, kurtosis maximization is used to quantify the components present in signal or image under evaluation.
- kurtosis: in order to estimate the independent components in multispectral images from cardiovascular tissue, kurtosis maximization is used as a measure of non-gaussianity [17, 18]. Kurtosis of a random variable y with zero mean can be defined as given by Eq. 7: where: E {y4} is the fourth moment and E {y2} is the second one.
In this case, the problem of kurtosis maximization turns into the search of a vector a that allows for the maximization of the cost expression given by Eq. 8:
where he expression E {(ATX)4} corresponds to the mean value.The fixed point algorithm used to optimize kurtosis is as indicated by Eq. 9:
The previous equation only applies for the optimization of functions with one variable ap. In the case of problems with multiple variables, Eq. 9 applies with the addition of the following term for decorrelation of the outputs a. This step is done according to the Gram-Schmidt-like decorrelation given by Eq. 10 [18, 19]:
2.4.2. Non-negative matrix factorization-NMF
NMF is a technique well suited for our problem since it relies in the non-negativity of the sources. This is a constrain well suited for our data which correspond to reflectance spectrum[20].
As described in section 2.3, BSS approximates a given n × m matrix Y, with Ynm ≥ 0, into the product of two non-negative matrices W ∈ Rn×r (matrix of weighted coefficients Wnr) and H ∈ Rr×m (matrix of main sources Hrm), i.e. Y ≈ WH [21, 22]. NMF finds the matrices W and H by minimizing the difference between Y and WH:
In a simple way, the minimum of the cost function f (W,H) can be found by updating the terms W and H with the following multiplicative update way [21]:
Matrix W is initialized with random numbers, while matrix H is initialized with the reference values given by the main components to be found. Then, the multiplicative update load is repeated until a certain number of iterations are reached. This iterative way guaranties that the cost function, given by Eq. 11, arrives to a value less than 1.5.
3. Results
The results obtained for the longitudinal and transversal opened tissues are presented as follow.
3.1. Lumen section analysis
Figure 3 presents one of the obtained images at 600nm, as well as the sampled spectrum obtained for two regions of interest (ROI): region A corresponding to a flat area, and region B corresponding to a folded one.
Fig. 3 (a) Image at 600nm from bovine aorta tissue obtained by interference filter-based system. The tissue was illuminated from the lumen side. (b) Sampled spectrum of the ROI denoted by arrows A and B in Fig. (a).
The obtained images are processed by means of ICA and NMF methods. Results for NMF and ICA are presented in Fig. 4 and Fig. 5 respectively.
Fig. 4 Normalized concentration maps obtained by applying NMF method on cardiovascular tissue multispectral images acquired by the interference filter-based system.
Fig. 5 Normalized concentration maps obtained by applying ICA method on cardiovascular tissue multispectral images acquired by the interference filter-based system.
With those methods it is possible to obtain both concentration maps and spectral absorbance of the main chromophores present in aorta tissue. In the case of NMF, the obtained components correspond to beta-carotene, deoxy-hemoglobin and oxy-hemoglobin (images 4). For ICA analysis, only two components are obtained: hemoglobin and beta-carotene (represented in Fig. 5). The fact that with NMF is possible to obtain more components than it is possible with ICA, can be explained by the source component matrix initialization (matrix H in Eq. 4 and Eq. 12). Different to NMF, this matrix is initialized with random numbers in ICA method.
The concentration maps obtained with those methods are presented in a scale from 0 to 1 where 0 means absence of chromophore and 1 high content of this component. In these results, the tissue under analysis present and average value of 0.3 in all components, which can be an indicator of a healthy tissue. However, there are some areas in the tissue (demarked with an arrow in Fig. 3) that present higher levels of Beta-carotene and lower levels of oxy-hemoglobin. This can be due to the folded structure that the tissue presents in that area. The corresponding spectral reflectance (ROI A and B in Fig. 3) show that fold structures reflect lower quantity of light than flat regions. According to Galeano et al [23] and Larsen et al [9], low reflectance spectrum is an indicator of low hemoglobin content as well as high level of beta-carotene. This fact justifies the previous mentioned result analysis. The latter can be useful as indicator of lipid presence, which can lead to the classification of atherosclerosis plaques[9].
3.2. Transverse section analysis
The ascending aorta is a vessel that for its proximity to the heart requires elastic composition. As presented in Fig. 6(a), the elastic membranes in aorta appear as separate fibers, sometimes with wavy appearance, which alternate with thin layers of smooth muscle cells [24].
In order to observe these fibers, multispectral images of the cross section of the ascending aorta were processed by ICA. The result of this processing is presented in Fig. 6(b).
In this image, a horizontal pattern that can represent the orientation of the elastic fibers is recognized. Such fibers consist primarily of elastin. By comparing the obtained result (6b) with the histology of aorta stained with a technique for elastin (6a), it is possible to observe that both images have horizontal structures, typical of these elastic tissue wavy lines.
3.3. ICA and NMF performance
The correspondence between the computed components and the theoretical ones are calculated by means of correlation. The results of this calculation are shown in table 1 where it is possible to see that most of values are higher than 0.9.
Table 1. Degree of correlation between: the calculated component’s absorbance and the theoretical one.
The correlation between the measured multispectral images and the calculated one (multiplication of matrix W with vector H) corresponds to 0.9 for both systems. These two results are good estimators of the method capabilities.
4. Conclusion
This work shows that multispectral imaging systems together with image processing techniques are a potential tool for the analysis of ex-vivo and/or in-vitro cardiovascular tissue. From one side, spectral images retrieve spectral reflectance maps of the tissue under study. Then, by using image processing algorithms, such as NMF and ICA, in is possible to retrieve maps of quantification of the principal biochemical components present in cardiovascular tissue. Also, it is possible to retrieve microstructures such as elastic fibers.
MI systems can be used in studies that search for how cardiovascular tissue’s extra-cellular matrix is affected by external factors caused by diseases such as cardiac fibrosis and atherosclerosis. This can lead to the development of new tools for diagnosis in cardiology, as well as to the construction of robust models to understand behaviors caused by the previous mentioned diseases.
Acknowledgments
The authors would like to acknowledge the financial support given by Instituto Tecnológico Metropolitano (Medellín-Colombia), and by Universidad Pontificia Bolivariana (Medellín-Colombia), under the project number P14129.
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