2.1.

Animal Model and Experimental Procedure

Eight male New Zealand white rabbits (10 to $15\mathrm{lbs}$ body weight) were included in this study. Each rabbit was fed a high cholesterol diet for at least eight weeks prior to study. The experimental procedure involved exposing the intimal luminal surface of the rabbit aorta, and obtaining TR-LIFS measurements from areas visually identified as either normal or atherosclerotic. After spectroscopic investigations, the interrogated arterial segments were removed for histological analysis. A detailed description of the animal model and experimental protocol has been described in detail elsewhere.^{24, 25}

2.2.

Time-Resolved Laser-Induced Fluorescence Spectroscopy Instrumentation

The experiments were conducted with a TR-LIFS prototype system, recently developed by our group and previously described.²⁶ Briefly, artery autofluorescence was induced with a pulsed nitrogen laser (wavelength $337\mathrm{nm}$ , pulse width $700\mathrm{ps}$ ). Laser excitation output measured at the tip of the probe was set at $2\mathrm{\mu }\mathrm{J}∕\mathrm{pulse}$ .²⁷ Excitation and collection were performed via a bifurcated fiber optic probe. The collected autofluorescence was dispersed by an imaging spectrometer/monochromator, and detected with a gated multichannel plate photomultiplier tube (rise time $180\mathrm{ps}$ ). The autofluorescence was temporally resolved using a digital oscilloscope (bandwidth $1\mathrm{GHz}$ , sampling rate $5\mathrm{Gsamples}∕\mathrm{s}$ ) coupled to a preamplifier (bandwidth $1.5\mathrm{GHz}$ ).

2.3.

Time-Resolved Laser-Induced Fluorescence Spectroscopy In-Vivo Measurements

TR-LIFS measurements were obtained with serial scanning of the monochromator across the spectral range of 360 to $600\mathrm{nm}$ , in increments of $5\mathrm{nm}$ . The total acquisition time across the scanned emission spectrum was about $37\mathrm{s}$ . After acquisition of each time-resolved fluorescence spectrum, the laser pulse temporal profile was measured at a wavelength slightly below the excitation laser line. This profile was used as the input signal (system response) in the deconvolution algorithm to estimate the intrinsic fluorescence decays.

2.4.

Histological Analysis

Following in-vivo TR-LIFS measurements, the aortic segments were removed, fixed, processed routinely, and evaluated microscopically by two cardiovascular pathologists. Each sample was characterized based on its overall histopathology (normal versus atherosclerotic lesion), intima thickness (thin versus thick), and biochemical composition (collagen-rich versus macrophage-rich). A lesion was defined as thin if the intima thickness was less than $50\mathrm{\mu }\mathrm{m}$ , or as thick otherwise. A collagen-rich lesion was defined as having collagen content greater than 50% and macrophage content less than 20%. A macrophage-rich lesion was defined as having macrophage content larger than 20% and collagen content smaller than 50%. Overall, the following five categories were identified: 1. normal artery (normal), 2. thin collagen-rich lesion (thin-collagen), 3. thin macrophage-rich lesion (thin-mac), 4. thick collagen-rich lesion (thick-collagen), and 5. thick macrophage-rich lesion (thick-mac).

2.5.

Time-Resolved Laser-Induced Spectroscopy Data Analysis

The arterial TR-LIFS measurements were processed using the Laguerre deconvolution technique (LDT). This nonparametric method expands the intrinsic fluorescence decay or impulse response function (FIRF) on the discrete time Laguerre basis.^{9, 28} The Laguerre functions (LF) form an orthonormal basis with a built-in exponential term that makes them suitable for modeling physical systems with asymptotically exponential relaxation dynamics.²⁹ Due to the LF’s orthogonality, LDT can reconstruct FIRFs of arbitrary form, providing a unique and complete expansion of the decay function.

In the context of time-domain TR-LIFS, the measured fluorescence intensity decay data $y\left(n\right)$ can be expressed as the (discrete) convolution of the FIRF $h\left(n\right)$ with the system response $x\left(n\right)$ ^{9, 30}:

Once the FIRF was estimated for each emission wavelength, the steady-state spectrum $\left(I_{\lambda }\right)$ was computed by integrating each $h\left(n\right)$ as a function of time. To characterize the temporal dynamics of each fluorescence decay, three sets of parameters were estimated: 1. the average lifetime $\left({\tau }_{f-\lambda }\right)$ , computed as the interpolated time at which the FIRF decays to $1∕\mathrm{e}$ of its maximum value; 2. the time constants ( ${\tau }_{1-\lambda }$ and ${\tau }_{2-\lambda }$ ) and the relative amplitude $\left(A_{1-\lambda }\right)$ from a biexponential model of the FIRF; and 3. the normalized value of the corresponding LECs $(c_{j-\lambda },j=0,\dots ,L-1)$ . Therefore, a complete characterization of the fluorescence TR spectrum for each investigated aortic segment was given by the variation of these spectroscopic parameters $\{I_{\lambda },{\tau }_{f-\lambda },{\tau }_{1-\lambda },{\tau }_{2-\lambda },A_{1-\lambda }$ , and $c_{j-\lambda }\}$ as a function of emission wavelength ${\lambda }_E$ .

2.6.

Statistical Analysis

A univariate statistical analysis (one-way analysis of variance, ANOVA) was used to compare the parameters $\{I_{\lambda },{\tau }_{f-\lambda },{\tau }_{1-\lambda },{\tau }_{2-\lambda },A_{1-\lambda }$ , and $c_{j-\lambda }\}$ at specific ${\lambda }_E$ ’s for each category of aortic segments as defined by histopathology. A post-hoc comparison test (Student-Newman-Keuls) was used to complement the results of the ANOVA test. A p-value of $<0.05$ was assumed to indicate statistical significance. Results of this statistical analysis provided a semiempirical evaluation of those spectroscopic parameters likely to provide discrimination among the different histopathological categories. All the results are presented as mean $\pm$ standard error (SE).

2.7.

Classification Methods

Three linear classification algorithms were investigated: linear discriminant analysis (LDA),^{10, 31} stepwise linear discriminant analysis (SLDA), and principal component analysis (PCA).^{10, 11, 32} A nonlinear classifier, the feed-forward neural network (FFNN), was also evaluated.^{12, 13, 31} Based on the statistical analysis described before, three different sets of TR-LIFS parameters were selected and defined as: 1. spectral (SP: ratios of $I_{\lambda })$ , 2. TR Laguerre (LAG: values/ratios of $c_{j-\lambda })$ , and 3. TR biexponential (BEXP: values of ${\tau }_{1-\lambda },{\tau }_{2-\lambda },A_{1-\lambda }$ ) features. Based on the histopathological categories defined in the previous sections, two classification criteria were applied. Classification 1 was designed to discriminate normal, thick-collagen, and thick-mac specimens. Classification 2 was designed to distinguish normal, thin-collagen, and thin-mac specimens. These two criteria were used to evaluate the performance of the different feature types and classification algorithms.

3.1.

Histology

A total of 73 sections of aorta (eight rabbits) were investigated in vivo. Out of these, 26 sections corresponded to normal aorta and 47 sections to atherosclerotic lesions. The lesions were divided as thin-collagen $(N=10)$ , thin-mac $(N=7)$ , thick-collagen $(N=16)$ , and thick-mac $(N=14)$ .

3.2.

Time-Resolved Fluorescence Spectra

Representative time-resolved fluorescence spectra are shown in Fig. 1 (left panels). All spectra presented a main peak at $\sim 385$ to $395\mathrm{nm}$ . A secondary peak was observed at $\sim 440$ to $450\mathrm{nm}$ . The peak intensity values of the latter were found as being tissue-type dependent, as they were the corresponding decay rate. The corresponding measured and estimated decays at $390\mathrm{nm}$ (right panels) and the normalized error (NErr) as retrieved by LDT are shown in Fig. 1 (right panels). NErr values were $<5\%$ of the peak fluorescence amplitude and randomly distributed around zero. The autocorrelation function of the residuals did not present low-frequency oscillations characteristic of nonrandom residuals, and was mostly contained within the 95% confidence interval for random independent time series (dotted lines). These observations indicate excellent fit between the measured and estimated fluorescence decays, showing that the fluorescence FIRFs were properly estimated using LDT.

Fig. 1

Representative time-resolved fluorescence spectra, measured and estimated decays (at $390\mathrm{nm}$ ), and the corresponding normalized error (NErr) and autocorrelation function (ACorr) for: (a) and (b) normal, (c) and (d) thin-mac, (e) and (f) thick-collagen, and (g) and (h) thick-mac.

3.3.

Spectroscopic Parameters

The group values (mean $\pm$ SE) of the spectroscopic parameters along the emission wavelengths are depicted in Fig. 2 .

Fig. 2

Group values (mean $\pm$ SE) of the spectroscopic parameters along the emission wavelengths: (a) normalized spectrum, (b) lifetimes, and Laguerre coefficients (c) LEC-0 and (d) LEC-1.

3.4.

Statistical Analysis

The results of the statistical analysis (mean $\pm$ SE) of the main spectroscopic parameters providing discriminant information among distinct types of tissues are depicted in Fig. 3 . The statistical analysis indicated that spectral parameters such as the ratios of intensities at a few emission wavelengths (360, 390, and $450\mathrm{nm}$ ) provided information for discriminating normal and thin-collagen lesions from thin-mac and thick lesions. For example, the ratios of emission intensities at $450\mathrm{nm}$ over $360\mathrm{nm}$ $(I_{450}∕I_{360})$ from the normal and thin-collagen groups were both significantly larger than those from the other groups. More interesting, the ratio $I_{450}∕I_{360}$ from the thick lesions was significantly smaller than those from the other tissue types [Fig. 3a]. The opposite was found for $I_{390}∕I_{450}$ [Fig. 3b].

Fig. 3

Results of the statistical analysis (mean $\pm$ SE) of the main spectral and time-resolved (Laguerre and bi-exponential) parameters.

The statistical analysis also indicates that time-resolved parameters such as the Laguerre expansion coefficients at a few emission wavelengths (390, 450, and $500\mathrm{nm}$ ) and their ratios provide information to discriminate the tissues in question. The LEC-1 at $450\mathrm{nm}$ $(LEC-1_{450})$ from the thick-mac group was significantly larger than those from the other groups [Fig. 3c]. More interesting, the ratio of $LEC-2_{500}∕LEC-2_{390}$ was significantly different for every group, except for the normal and thin-collagen samples [Fig. 3d]. The biexponential parameters at 390 and $450\mathrm{nm}$ were also different among tissue types. The ${\tau }_2$ at $450\mathrm{nm}$ $\left({\tau }_{2-450}\right)$ was significantly smaller for the thick-mac lesions, relative to the collagen lesions [Fig. 3e]. The relative amplitude $A_{1-450}$ was significantly smaller for the normal and thin-collagen group, and larger for the thick-mac group, with respect to the thin-mac and thick-collagen lesions [Fig. 3f]. Table 1 summarizes the values of the main spectral and time-resolved parameters used for classification.

Table 1

Representative set of spectroscopic parameters that allows for tissue subgroup discrimination.

3.5.

Classification

Classification 1 was designed to separate normal, thick-collagen, and thick-mac subgroups. The classification results are summarized in Table 2 . Based on the statistical analysis, a total of five SP, 14 LAG, and six BEXP features were selected for developing the classification algorithms. LDA and FFNN used the complete sets of features, while SLDA selected three SP, eight LAG, and six BEXP features. In the PCA classification, a total of five SP, six LAG, and six BEXP principal components were used. Classification with only SP parameters discriminated normal from thick lesions, but not thick-collagen from the thick-mac lesions. Classification with combined SP and time-resolved features (either LAG or BEXP parameters) discriminated the three groups from each other. There was no significant difference in using the LAG or the BEXP features in terms of classification performance (86.5 and 87.6%, respectively). The comparison among the different classification algorithms [Table 2 and Fig. 4a ] showed that for our data, SLDA and PCA approaches provided the best performance (86.7 and 86.3%, respectively), followed by LDA and FFNN (81.5 and 78.2%, respectively).

Fig. 4

First classification results (normal versus thick-collagen versus thick-mac): (a) classification performance for the different feature types (SP, SP-LAG, SP-BEXP) and algorithms (LDA, SLDA, PCA, FFNN); and sample maps in the discriminant function domain from the SLDA classification with (b) SP, (c) SP-LAG, and (d) SP-BEXP features.

Table 2

First classification results: normal/thin versus thick-collagen versus thick-mac.

The classification based on SLDA provided the best performance (92.9%). Figures 4b through 4d depict samples of the three representative groups and the corresponding means in the space spanned by the two discriminant functions. For the case of the SP-based classification [Fig. 4b], the normal samples were discriminated from the thick samples( $\mathrm{SE}>90\%$ , SP 100%); however, the thick-collagen and thick-mac samples were not classified correctly $(\mathrm{SE}<65\%)$ . For the case of the SP-LAG-based classification [Fig. 4c], the normal samples were also separated from the thick samples( $\mathrm{SE}>96\%$ , SP 100%). More important, the thick-collagen samples were also discriminated from the thick-mac samples( $\mathrm{SE}>93\%$ , $\mathrm{SP}>95\%$ ). Similar results were observed for the SP-BEXP-based classification [Fig. 4d].

Classification 2 targeted the discrimination of normal, thin-collagen, and thin—mac samples using the best-performed SLDA and PCA algorithms. The classification results are summarized in Table 3 . The classification based on only SP parameters did not allow discrimination of any of the groups. The classification using both SP and TR features (either LAG or BEXP parameters) facilitated discrimination of most of the thin-mac samples ( $\mathrm{SE}>85\%$ , $\mathrm{SP}>94\%$ ), but did not allow discrimination of normal and thin-collagen samples from each other. The classification performance based on LAG (67.5%) was similar with that based on BEXP features (66.3%).

Table 3

Second classification results: normal versus thin-collagen versus thin-mac.

As shown in Fig. 5a , the SLDA performed better than PCA (69 and 62%, respectively). The classification with the SLDA algorithm is shown in Figs. 5b, 5c, and 5d. In the case of SP-based classification [Fig. 5b] none of the groups were discriminated. While in the case of SP-LAG and SP-BEXP [Figs. 5c and 5d], the thin-mac samples were separated from normal and thin-collagen samples. It is important to note that only seven thin-mac samples were available for this analysis; thus these results need to be carefully interpreted.

Fig. 5

Second classification results (normal versus thin-collagen versus thin-mac): (a) classification performance for the different feature types (SP, SP-LAG, SP-BEXP) and algorithms (SLDA in black, PCA in gray); and sample maps in the discriminant function domain from the SLDA classification with (b) SP, (c) SP-LAG, and (d) SP-BEXP features.

4.1.

Laguerre Deconvolution Technique as a Method for Analysis of Time-Resolved Laser-Induced Spectroscopy Data from Tissue

Our results demonstrated that the Laguerre deconvolution technique represents an accurate and robust approach for the analysis of TR-LIFS data. The technique was able to estimate the FIRF of a variety of arterial samples presenting distinct biochemical compositions with good precision $(\mathrm{NErr}<5\%)$ . An important observation was that the estimation of the conventional biexponential parameters at wavelengths above $530\mathrm{nm}$ became less accurate as the signal-to-noise ratio decreased [error bars in Figs. 2e and 2f], while the estimation based on Laguerre expansion coefficients remained unaffected [error bars in Figs. 2e and 2f]. This suggests that the Laguerre deconvolution technique represents a more robust method for TR-LIFS data analysis than the conventional iterative multiexponential method.

The traditional multiexponential technique involves the estimation of intrinsic nonlinear parameters (the decay constants), which requires more complex and computationally expensive nonlinear least-square iterative approaches.³⁰ Although single exponential fitting can be linearized via logarithmic transformation, complex fluorescence systems containing more than one fluorophore cannot be accurately modeled with a single decay. An alternative for fitting complex decays is the stretched exponential method, which also allows for fast convergence. One drawback of this approach, however, is that curve fitting instead of actual deconvolution is usually applied. In the Laguerre deconvolution technique, the problem of deconvolving the system response and estimating the FIRF is reduced to finding the expansion coefficients of an overdetermined system of linear equations [Eq. (5)] via the linear least-square minimization approach.^{9, 29} Such a linearization of the convolution equation via an orthonormal expansion allows fast and robust TR-LIFS data deconvolution. These specific advantages of the Laguerre method become even more important in the context of TR-LIFS-based in-vivo tissue diagnosis, where the quality of the signal cannot always be warranted and the speed of data analysis is of crucial importance.

4.2.

Laguerre Expansion Coefficients as New Means for Characterizing the Time-Resolved Laser-Induced Spectroscopy Data

It was observed that the Laguerre expansion coefficients (LEC) were highly correlated with the intrinsic lifetime values (especially LEC-0), suggesting that the LECs describe the dynamics of the fluorescence intensity decay.⁹ This can be explained by the orthogonality of the Laguerre basis, which implies that the value of each LEC depends exclusively on the fluorescence decays to be fitted.^{18, 30} The fluorescence time-decay characteristics captured by the LECs also reflect the biochemical composition of the artery. The normal and thin-collagen groups presented constant lifetimes values $(\sim 1.9\mathrm{ns})$ along the emission spectra (370 to $450\mathrm{nm}$ ), suggesting that their fluorescence emission is dominated by elastin, characterized by a fairly constant lifetime value of $\sim 2\mathrm{ns}$ between $\sim 360$ and $500\mathrm{nm}$ .^{1, 8} The thick lesions presented slightly longer but decreasing lifetimes $(\sim 2\mathrm{ns})$ at increasing wavelengths, similar to the lifetime-wavelength dependency found in collagen.^{1, 8} The LEC-0 presented the same tissue dependency variation as the lifetime values, indicating that this coefficient captures the average fluorescence time-decay characteristics of the tissue.

Lipid components exhibit shorter-lived emission when compared to the structural proteins of elastin or collagen.^{1, 8} This was consistent with our results showing a significant decrease in lifetime in the lesion rich in macrophages relative to those rich in collagen. Also, a large normalized LEC-1 is characteristic of a faster FIRF decay.⁹ Thus, lipids should also present large LEC-1 values. This was reflected in the thick-mac samples, which were characterized by the largest LEC-1 and provided the best discrimination of the thick-mac group [Figs. 2f and 3c]. This particular result indicates that important characteristics of the fluorescence decay shape, not reflected on their conventional lifetime values, can be captured by the higher-order Laguerre expansion coefficients. All these results taken together demonstrate that Laguerre expansion coefficients offer a new domain for representing time-resolve information in a very compact, accurate, complete, and computationally efficient way.

4.3.

Feature Selection

The results of the statistical analysis showed that TR-LIFS information most relevant for discriminating atherosclerotic lesions was concentrated at a few number of emission wavelengths (360, 390, 450, and $500\mathrm{nm}$ ), confirming previous observations.^{10, 12} This indicates that it is no longer necessary to acquire the complete time-resolved fluorescence spectrum, but only the fluorescence at a reduced number of emission wavelengths. Consequently, the acquisition time could be reduced significantly, thus facilitating the real-time diagnostics of atherosclerotic plaque. We hypothesize that similar concentrations of discriminant information in a reduced number of emission wavelengths might be found in other biological tissue and biochemical systems, as it has been suggested elsewhere.^{2, 4, 6}

4.4.

Classification

Although in this study we used a small database, our results indicate that classification algorithms derived from the Laguerre expansion coefficients are robust enough to allow good detection of macrophage infiltration in arterial intima ( $\sim 70\%$ for thin-foam and $\sim 93\%$ for thick-foam lesions). Moreover, the classification accuracy could be further improved once the number of samples for each tissue type in the training set increases. It was also observed that features from the steady-state fluorescence spectrum can discriminate a normal artery from more advanced thick lesions. However, they cannot detect the presence of macrophages. On the other hand, by incorporating features related to the fluorescence time-decay characteristics of the artery (i.e., LECs or biexponential parameters), it is possible not only to improve the detection of advanced (thick) lesions, but also to discriminate lesions with macrophages infiltration. Thus, our results showed that time-resolved fluorescence information derived from the LECs can be used to develop TR-LIFS-based tissue diagnosis methods, and specifically to detect macrophage infiltration in atherosclerotic plaques, an important predictor of plaque rupture.

It was also observed that classifications with either LECs or biexponential parameters provided similar performance. One important advantage of LDT over the multiexponential approach, however, is that the former performs significantly faster. This would be of special importance in the context of real-time tissue diagnosis using fluorescence lifetime imaging (FLIM), where conventional methods of analysis are time consuming, making it almost impossible to allow real-time applications.³³ The LDT technique can be easily adapted for FLIM analysis³⁴ and, combined with proper classification algorithms, has the potential for imaging features of plaque vulnerability (such as the presence of macrophages) and other interesting tissue pathologies in real time.

The use of redundant features may generate a classifier that is specifically designed to discriminate the training set and may unduly weight less distinct features.^{10, 12, 31} This could result in a discriminant function with decreased ability to classify new samples. Such outcome was observed in the LDA and FFNN algorithms, which use all the features available. In contrast, SLDA and PCA, which use a reduced but more selected group of features, provided the best classification performance. One possible additional explanation of the poor performance of the FFNN approach is that the number of parameters to be estimated is much larger, thus demanding a larger number of training samples. These results also support the empiric observation that the differences in the fluorescence emission of the various types of atherosclerotic lesions are manifested in a reduced number of spectral and TR features.^{10, 12}

Another interesting observation was that all four algorithms correctly classified most of the normal samples $(\sim 96\%)$ , while the classification accuracy of atherosclerotic samples was lower $(\sim 90\%)$ . This is explained by the greater heterogeneity of atherosclerotic lesions relative to normal aorta. In the present study, lesions were characterized based on their intima plaque thickness and their relative collagen/macrophage contents. Because atherosclerosis is a progressive disease, the lesions are quite heterogeneous and present a large variability in their morphology and biochemical composition.¹⁷ Thus, a histopathological categorization of the lesions (the gold standard for the development of our TR-LIFS classifiers) can by itself be difficult to define. This might explain the difficulty on classifying different types of atherosclerotic lesions, as compared to normal arterial walls. Thus, a more comprehensive classification of the plaques based on their histopathological, morphological, and biochemical characteristics should help to improve the diagnosis capability of TR-LIFS.