Parameter estimation of atherosclerotic tissue optical properties from three-dimensional intravascular optical coherence tomography

Abstract. We developed robust, three-dimensional methods, as opposed to traditional A-line analysis, for estimating the optical properties of calcified, fibrotic, and lipid atherosclerotic plaques from in vivo coronary artery intravascular optical coherence tomography clinical pullbacks. We estimated attenuation μt and backscattered intensity I0 from small volumes of interest annotated by experts in 35 pullbacks. Some results were as follows: noise reduction filtering was desirable, parallel line (PL) methods outperformed individual line methods, root mean square error was the best goodness-of-fit, and α-trimmed PL (α-T-PL) was the best overall method. Estimates of μt were calcified (3.84±0.95  mm−1), fibrotic (2.15±1.08  mm−1), and lipid (9.99±2.37  mm−1), similar to those in the literature, and tissue classification from optical properties alone was promising.

Trained cardiologists and image analysts can identify tissue types (calcified, lipid, and fibrous tissues) with some accuracy and repeatability, as shown in preclinical and clinical studies. 4,6,[12][13][14] Many use rules established by Yabushita et al. 13 to manually classify tissues. However, modern OCT systems can create over 500 image frames in a single 2.5-s pullback scan, making manual image analysis for research very labor intensive, typically precluding measurements from every image frame. During a demanding clinical procedure, it would be even more difficult to manually analyze hundreds of image frames in clinical decision making. Although IVOCT image quality is outstanding, its limited depth penetration can sometimes confound plaque characterization, 6,[25][26][27] posing challenges for manual analysis, especially in the case of lipid or calcified plaques underlying a fibrous cap. Image quality is affected by any residual blood, but this is not a major concern with current IVOCT blood clearing strategies. Additionally, catheter eccentricity during IVOCT image acquisition may alter the appearance of various plaque features and confuse IVOCT image analysts. 28 To be successful, an automatic computer classification algorithm will need to use all image information available to the human such as intensity, intensity changes, texture, border sharpness, three-dimensional (3-D) shape characteristics, and, perhaps most importantly, physical optical properties.
Several groups have measured tissue optical properties from OCT images in vascular and other tissues using a variety of experimental and theoretical methods. Most use a single-scattering model. We will review reports that measured attenuation and backscattering coefficients in vascular tissues first. [29][30][31][32][33] Xu et al. 29 used a noncatheter-based approach by imaging transverse, fixed tissue sections of coronary arteries; averaged 400 Alines over time; applied a single-scattering light model; and performed least squares fitting of log transformed, average A-lines to a linear equation. It was concluded that the calcified and fibrotic plaques had a much lower optical attenuation coefficient, μ t , than lipid plaques, and that lipid and fibrotic plaques had a much higher backscattering coefficient, μ b , than calcified plaques (lipid: μ b ¼ 28.1 AE 8.9 mm −1 , μ t ¼ 13.7 AE 4.5 mm −1 , calcified: μ b ¼ 4.9 AE 1.5 mm −1 , μ t ¼ 5.7 AE 1.4 mm −1 , and fibrotic: μ b ¼ 18.4 AE 6.4 mm −1 , μ t ¼ 6.4 AE 1.2 mm −1 ). Using a catheter-based system and a stationary acquisition without pullback, van Soest et al. 30 measured μ t in both in vivo and ex vivo specimens. They corrected for the nonideal imaging system; averaged 15 to 20 A-lines in time; fitted a linear model to log transformed data; and applied an elegant algorithm to determine regions in one dimension corresponding to a single, homogenous tissue type. van Soest et al. argued that μ b cannot be estimated accurately along with μ t using a single magnitude OCT value alone at each point and reported only μ t for calcified (2 to 5 mm −1 ), fibrotic (2 to 5 mm −1 ), and lipid (>10 mm −1 ), yielding trends similar to values reported by Xu et al. 29 Levitz et al. 31 applied a multiple scattering model to OCT images of phantoms and ex vivo aortas and estimated scattering coefficients and anisotropy factors. In other studies, OCT data from both phantoms and ex vivo arterial samples were fit to single and multiple scattering models. 32,33 Since temporal averaging of frames from a stationary acquisition is undesirable in the clinical setting, frequency domain multiplexing with improvement as compared with simple linear filtering has been proposed to reduce speckle in single A-lines for optical property measurement. 34 As reviewed in Sec. 5, there is variability in reported μ t values between research groups due to methodological differences including parameter estimation approaches.
Optical properties have also been estimated in other tissues using OCT. Yang et al. 35 determined the optical scattering coefficient, μ s , from unfixed normal and malignant, ex vivo ovarian tissues. They found that the absorption coefficient, μ a , for ovarian tissue is small (∼0.006 mm −1 ) and that μ t was a good approximation to μ s . Knu et al. 26 determined the optical parameters from OCT images of pig and human skin using a multiple scattering model. Lee et al. 36 have studied the performance of single and multiple scattering models using in vitro rat livers and in vivo human skin. The methodologies were similar to those used in blood vessels with 100 to 200 A-lines averaged prior to fitting. In general, it is evident from the literature that a single-scattering model is reasonable and is probably the only statistically appropriate solution for noisy clinical IVOCT images.
A goal is to fully automate tissue characterization in 3-D IVOCT clinical pullbacks. Some recent reports use machine learning for plaque classification from both preclinical and clinical IVOCT data. 37,38 Ughi et al. 38 used μ t estimates from a layer model applied to single A-lines and two-dimensional (2-D) texture and geometric measures as features for classification. Athanasiou et al. 37 used 2-D texture and intensity features alone and assumed "islands" of calcified tissue surrounded by other tissue types, which is not necessarily true in many image frames. These reports are encouraging and show that improved 3-D estimation of optical properties could improve the classification.
The rationale for our research plan is as follows. Although it is clear that the optical properties of plaques, such as the attenuation coefficients, will be useful discriminatory features for automated tissue classification, extracting optical properties from clinical IVOCT data remains a challenge. Stationary acquisitions 29,30 are untenable, as they will require an additional blood clearing operation to sample a single location. Estimation from single, noisy A-lines gives large estimation variance. Hence, our solution is to estimate optical properties from small 3-D volumes of pullback image data and to use advanced parameter estimation approaches which are robust against noise outliers. In addition, we use in vivo clinical data rather than image data from ex vivo samples as is typically used. This avoids typical limitations of ex vivo imaging including potential tissue degradation, no mean and/or pulsating pressure, no cardiac motion, unrealistic temperatures, no blood artifacts, and a straight path pullback rather than actual 3-D coronary geometry. Moreover, in the event of spatially inaccurate, sparse histological sampling, one can make inappropriate "ground truth" determinations using ex vivo data. Instead we use ground truth volumes of interest (VOIs) identified by trained analysts using well-established criteria. Although independent histological verification is desirable, there is no way to obtain it on in vivo clinical data. Moreover, our approach is quite appropriate for optimizing the 3-D parameter estimation methods in this report. Methods should be equally applicable to 3-D cancer imaging.
In this report, we correct the nonideal characteristic of OCT imaging systems, use noise reduction filtering, estimate optical parameters from small VOIs rather than single A-lines, reject outliers, identify goodness-of-fit measures suitable for determining the quality of optical property estimates, and determine how well optical properties alone can be used to classify plaque types. Our basic paradigm is to compare estimation results across 311 manually annotated VOIs.

Experimental Methods and Catheter Correction
Images used in this study were selected from the database available at the Cardiovascular Imaging Core Laboratory of the University Hospitals Case Medical Center (Cleveland, Ohio), called the Core Lab. These images were collected on the C7-XR swept-source OCT system (St. Jude Medical Inc., Westford, Massachusetts). It has a swept laser source with a 1310-nm center wavelength, 110-nm wavelength range, 50-kHz sweep rate, 20-mW output power, and ∼12-mm coherence length. The pullback speed was 20 mm∕s and the pullback length was 54 mm. A typical pullback consisted of 271 image frames spaced ∼200 μm apart. The test dataset consisted of 35 IVOCT pullbacks of the left anterior descending and the left circumflex coronary arteries and was chosen to be representative of typical OCT scans obtained from patients prior to stent implantation. To more accurately estimate μ t , we need to account for certain characteristics of the IVOCT imaging system. We used methods similar to those of van Soest et al. 30 The imaging system response in the presence of tissue attenuation μ t is given below: 30 with where r is the depth, I is the detected intensity, I 0 is the initial intensity, I off is the detected intensity at a depth of r ¼ 0, μ t is the attenuation coefficient, TðrÞ is the confocal function with z 0 , the position of the beam waist and with z R , the Rayleigh length, and SðrÞ accounts for the spectral coherence of the source in Fourier-domain OCT with parameters z W (representing the half-width of the intensity roll off) and z C (representing the center of the scan).
Intact catheters without a guide wire were inserted into a bottle containing water or low concentration intralipid solution. The catheter was firmly held in place using a vice-grip on the catheter outside the bottle. The water image was used to estimate background intensity. A low concentration 1∶128 intralipid (Sigma Aldrich, 20%, emulsion) diluted in water provided an image of scatterers without significant attenuation. Stationary image sequences of 121 image frames and pullback sequences of 271 image frames were obtained. About 100 IVOCT magnitude images were averaged. From the average frame, we averaged 500 A-lines to obtain a very low noise A-line.
In intralipid images, we assumed μ t to be low, eliminating the tissue attenuation term [expð−μ t rÞ]. I off was estimated from the water images. z C and z W were obtained from the interferometer setting and the specifications of the light source, respectively. With these parameters fixed, I 0 , z 0 , and z R were estimated by fitting Eq. (1) to average A-line data using nonlinear least squares with the Nelder-Mead simplex optimization. A-line data were truncated to exclude bright reflection from the catheter sheath. Model fits were compared over pullbacks, catheters, and acquisition modes (stationary versus pullback). Similar fits were obtained in each case with less than 3% variation in parameters. Clinical images were corrected using Eq. (1). We subtracted I off , the baseline intensity, and divided A-line intensities by the term I 0 · TðrÞ · SðrÞ.
3 Image Analysis

Volumes of Interest
We developed specialized software in MATLAB for obtaining user-defined VOIs and for evaluating their optical properties. In the software, pullbacks were loaded and image frames were presented to the expert, an IVOCT image analyst, in both ðx; yÞ and ðr; θÞ views. Image data came from a manually analyzed Core Lab study aimed at classifying plaque types and plaque burden prior to stent implantation. The study classified quadrants of IVOCT images as either fibrous, lipid, calcium, or normal. Core Lab analysts were well trained in interpreting OCT image data. For our study, the analyst determined start and stop image frames for a homogeneous VOI. Then, in the ðr; θÞ view, the analyst segmented the VOI using freehand brush strokes and applied a plaque-type label (fibrous, lipid, or calcified). All segmentations and labels for VOIs were saved in a convenient data structure for easy retrieval and analysis. Standard criteria were used by analysts to identify the various plaque types in pullback image frames. 13 Fibrous plaques were characterized by homogeneous, signal-rich regions; calcified regions by signal-poor regions with sharp borders; and lipid plaques by signal-poor regions with diffuse borders. In this study, we used 311 VOIs from 35 pullbacks. The VOIs were of various sizes and shapes. Most consisted of 2 to 5 image frames, 50 to 200 A-lines, and 20 to 50 sample points in each A-line.

Parameter Estimation of Tissue Optical Properties
Each VOI was processed as follows. We applied 2-D noise reduction filtering to linear data using a variety of filters [average filter (AF), median filter (MF), and Lee speckle reduction filter (LF) 39 ] with parameters listed later. To avoid any "edge effects" during filtering, we applied 2-D filtering to entire image frames and subsequently used the stored spatial coordinates of each VOI to extract a "filtered" VOI. Any A-line with fewer than five samples (points) was removed from consideration. Rearranging and taking the natural logarithm of Eq. (1), we get the equation below: In the event that the left-side term within square brackets was ≤0, we set its value to þ1. Equation (4) reduces to fitting a straight line to the data. Parameter estimation methods included individual line (IL) fits and parallel line (PL) fits to A-lines. In IL fitting, a slope and intercept are fit to each A-line in a collection of adjacent A-lines. In PL fitting, we fit one slope and multiple intercepts to the collection as is rationalized next. Assuming locally homogeneous tissue within a VOI, there should be a single characteristic μ t value and a single slope. Intercepts depend upon distance from the catheter, the angle of incidence with the lumen, depth in tissue, and so on, which are observations consistent with the PL approach. Moreover, a PLs' model has many fewer parameters making it less sensitive to noise. In addition, we have also employed methods that perform statistical analysis to reject data outliers for which we use the term "robust." The methods were:

IL, individual A-lines: Each corrected A-line was fit to
Eq. (4) yielding a set of μ t and I 0 values. Extreme outliers, i.e., lines with negative μ t , were removed. Means of μ t and I 0 were reported. Standard errors (SEs) were computed from SE ¼ SD∕ p n, where SD is the standard deviation and n is the number of A-lines processed. α-T-IL, individual A-lines with α trimming: In this robust parameter estimation approach, we determined μ t and I 0 for each A-line, removed extreme outliers, and rank ordered results. A predetermined percentage, α, of μ t 's (and corresponding I 0 's) from the top and bottom of the distribution was removed, and new mean μ t and I 0 values were obtained. SEs were computed using the same strategy as above. IT-IL, individual A-lines with iterative trimming: In this robust parameter estimation approach, we determined μ t and I 0 for each A-line, removed extreme outliers, and computed a new mean μ t and I 0 . We then iteratively removed A-lines with μ t 's outside mean AE 2 ðSDÞ, with empirically determined n ¼ 3 iterations. Finally, a mean μ t and I 0 were computed from the remaining A-lines and reported. SEs were computed as above. PL, Parallel line fit to A-lines: We determined a μ t and I 0 for each A-line using IL fits and removed extreme outliers. On the remaining A-lines, a PL model with a single slope and multiple intercepts was estimated, giving a single μ t and multiple I 0 's. SEs were computed from the MATLAB toolbox function aoctool. α-T-PL, Parallel lines with α trimming: In this robust approach, we determined a μ t and I 0 for each Aline using IL fits, removed extreme outliers, and rank ordered results. A predetermined percentage, α, of μ t 's (and corresponding I 0 's) from the top and bottom of the distribution was removed. A PL model was applied to the remaining A-lines. Parameter uncertainty errors were computed as above. IT-PL, Parallel lines with iterative trimming: In this robust approach, we determined a μ t and I 0 for each A-line using IL fits, removed extreme outliers, and computed a new mean μ t and I 0 . We then iteratively removed A-lines with μ t 's outside the mean AE 2ðSDÞ with an empirically determined n ¼ 3 iterations. A PL model was applied to the remaining A-lines. Parameter uncertainty errors were computed as above. NIL-PL-TM, Individual lines followed by parallel lines followed by noniterative trimming: In this robust approach, we determined a μ t and I 0 for each A-line using IL fits, removed extreme outliers, and applied a PL fit to obtain a single-slope μ PL and a standard deviation SD PL . Next, we kept only those A-lines with individual μ t 's within μ PL AE 2ðSD PL Þ. We then computed mean μ t and I 0 and reported values. SEs were computed using the strategy for IL. IL-PL-TM, Individual lines followed by parallel lines followed by iterative trimming: In this robust approach, we determined μ t and I 0 for each A-line and removed extreme outliers. We applied a PL model to obtain a single slope, μ PL , and a standard deviation, SD PL . Next, we kept only those A-lines with individual μ t 's within μ PL AE 2ðSD PL Þ. We iterated this process (PL fit and removal of A-line outliers) two more times. We computed a mean μ t and I 0 from the IL fits. SEs were computed using the strategy for IL.

Data Analysis
For each VOI, we obtained μ t and I 0 estimates for each combination of filtering (three methods) and parameter estimation (eight methods). Goodness-of-fit measures included coefficient of variation (CV) given by the ratio of the parameter uncertainty to the point estimate, the root mean square error (RMSE), and adjusted R 2 , calculated as described in Ref. 40. For good filtering and estimation methods, we want: (1) small parameter uncertainty intervals, (2) small spread of point estimates across many VOIs of a particular tissue type, (3) superior goodness-offit values (high adjusted R 2 , low RMSE, and low CV), and (4) high sensitivity/specificity from parameter estimates using a supervised classifier.

Processing Parameters
We optimized the processing parameters in preliminary experiments. The size of the filter window (7 × 7) and other parameters was tuned by examining their role on image appearance as well as μ t estimates. It should be noted that a filter kernel of length 7 is approximately the same size as the 35 μm axial point spread function of our system. We used a 7 × 7 window for the LF, AF, and MF. Since VOIs were of irregular shape, we obtained some short A-line segments which were omitted if they contained fewer than five samples. To avoid fitting the baseline noise floor, we ended consideration of A-line samples along r when there was a run of nine samples below the baseline value of six in the original linear data. This occurred in less than 1% of A-lines as experts did not mark VOIs at large depths in the tissue. For robust estimation with α trimming, we experimentally determined an optimal value of α ¼ 10%. For iterative estimation methods, we experimentally determined that three iterations and two SDs gave good results. More details about optimization experiments are in Sec. 4.
In an exploratory classification experiment, we used three features (μ t , hIi, I 0 ), and a support vector machine (SVM) classifier with a linear kernel, fivefold cross validation, and feature normalization. We used one-against-all to identify three tissue types. Parameter settings of the classifier were determined from preliminary optimization experiments with a subset of VOIs. We weighted samples in inverse proportion to their prevalence. 41 Performance results were averaged across the five folds.

Results
Example IVOCT images in Figs. 1(a)-1(d) show calcified, fibrotic, lipid, and normal (media) regions in the ðx; yÞ view. Figures 1(e) and 1(f) show a sample IVOCT image frame from a clinical pullback in both ðx; yÞ (anatomical) and ðr; θÞ (polar) views, with a calcified region identified in red. The VOIs were marked on ðr; θÞ view because all subsequent processings were done on ðr; θÞ image data. The VOIs were mapped to ðx; yÞ for presentation (Fig. 2). We have observed that, in general, the tissue types in a region of interest do not change much across successive frames, i.e., they have a high correlation, justifying the use of volumetric analysis in our study (Fig. 2).
We obtained images of intralipid and water and fitted the data to the system model. Average A-lines from a stationary acquisition are shown in Fig. 3. We ignored the very small upward trend in water and used an average value for I off . Water images were similar across the three tested catheters, and I off values were close to baseline values at large r in clinical images. Using the average A-line from dilute intralipid images, Eq. (1) was fit to data over the "imaging range" from 1 to 2.5 mm. As described previously, values for I 0 , z 0 , and z R were estimated using a least squares fit [ Fig. 3(b)] and other parameters were obtained from system specifications. Parameters for the typical catheter in Fig. 3 were: I 0 ¼ 155, z 0 ¼ 1.06 mm, z R ¼ 0.59 mm, I off ¼ 6.39, z C ¼ 0 mm, and z W ¼ 12 mm.
We determined the sensitivity of μ t estimates to the correction model parameter estimates. Table 1 shows the result for representative VOIs using PLs to estimate μ t . Values of μ t changed by only 3% to 7% with and without catheter correction. To study the potential effect of variation between catheters, we perturbed catheter parameters over a AE5% range (a variation much larger than observed) and determined the effect on μ t . In general, different catheter correction parameters had a relatively minor effect (typically <3%) on μ t , smaller than the uncertainty due to noise (see Sec. 4). Varying z 0 had a bigger effect than varying z R .
Preprocessing methods were systematically tuned. Individual A-lines with speckle were quite noisy and were visually evident only after filtering trends. Using IL parameter estimation, noise reduction filters substantially reduced SE uncertainties of μ t estimates [ Fig. 4(a)]. SE was reduced from 0.8442 [no filtering (NF)] to 0.5371 using AF, 0.446 using MF, and 0.1923 using LF. Therefore, LF was deemed the best filtering approach. Small variations in point estimates were obtained, but effects were Fig. 2 Marking of VOIs in images across frames. Columns contain three successive image frames for (1a-1c) calcium, (2a-2c) lipid, and (3a-3c) fibrous, corresponding to a single VOI. Because tissue types are preserved across a few image frames with 200 μm spacing, we can process A-lines within VOIs. In practice, such multiple VOIs would be obtained from a single homogenous region (not shown). inconsistent across VOIs, reducing the concern of potential bias. Effects of noise reduction were less dramatic when using other parameter estimation approaches, but trends were similar. Since we want estimates to help distinguish one tissue type from another, we analyzed the effect of filtering on the spread of estimates for a single tissue type across many VOIs. For calcium, LF reduced the spread of estimates by about 13% [Fig. 4(b)]. Similar results were obtained across other tissue types.
To optimize α in noniterative trimming, we varied α from 0% to 40% in steps of 5%, and at each step, we computed μ t and the resulting RMSE for each VOI in a set of 84 VOIs drawn from all three plaque types. Figure 5 shows the average RMSE across VOIs plotted against α. The optimum RMSE was α ¼ 10%, and this was used in subsequent experiments. Similarly, we optimized k in iterative trimming, which preserved A-lines with μ t s in the range (mean AE k · std). We estimated μ t and RMSE with k ¼ 1, 2, or 3 and obtained an average RMSE versus k curve. The optimal k ¼ 2 was used in subsequent experiments (not shown). Fig. 3 Determination of imaging system model parameters. The average A-line in water is shown in (a) with intensity on a linear scale. In (b), we plot the average A-line in intralipid (1∶128 dilution). We fit data within the "imaging range," as shown in red. z 0 ¼ 1.057 mm and z R ¼ 0.590 mm were estimated from these data. z C ¼ 0 mm and z W ¼ 12 mm were otherwise obtained. Image data were acquired in stationary mode and about 100 A-lines across time and θ were averaged. Fig. 5 Determination of optimal α for trimming. Using 84 VOIs drawn from all three plaque types, we obtained RMSE versus α for each VOI. The average RMSE curve plotted gave a minimum at α ¼ 10%. Table 1 Effect of catheter correction on μ t estimates obtained with the parallel lines' (PLs') method for a single-representative VOI from each tissue type. The first two columns show μ t estimates within the VOI with and without catheter correction. Fibrotic shows the least variation (3.8%), while calcium (7.8%) and lipid (7.6%) show a larger variation in μ t . We also applied a AE5% perturbation to z 0 (around a nominal value) keeping z R fixed, and repeated the experiment with a AE5% perturbation to z R (around a nominal value) keeping z 0 fixed. Perturbation had a minor effect (<3% in most cases) on μ t estimates.

Tissue type
No correction Correction w / Cath 5  We next compared the parameter estimation approaches. Figure 6 illustrates IL and PL. In this calcified VOI, PL gave a reduced parameter uncertainty (which results in a more robust and accurate estimate) as compared with IL (see legend). Using processing parameters from the above paragraph and LF, we examined the effects from the eight parameter estimation approaches. For a typical calcium VOI, α-T-PL and PL gave smaller parameter uncertainty and SEs than other techniques (Fig. 7). There were small changes in point estimates, but across VOIs, there were no obvious trends. Over 111 fibrotic VOIs, the distribution of μ t as a function of estimation methods is shown in Fig. 8(a) without censoring and Fig. 8(b) with censoring. Censoring was done to remove VOIs having bad fits, i.e., RMSE > 6. With censoring on RMSE, the number of outliers   in μ t was greatly reduced. Since censoring tended to remove VOIs having very large μ t estimates, means were reduced with censoring. Also, the error bars were smaller after censoring as compared with before censoring, which meant that the μ t estimates were more robust after censoring.
Since we are ultimately interested in automated processing, we analyzed the role of the size of the region of support on μ t estimates. Figure 9 shows a scatter plot of numbers of A-lines in VOIs versus SE of μ t . In general, lower SEs were obtained for VOIs containing more A-lines. A large percentage (>80%) of VOIs had 50 or more A-lines in them. This suggests that the experts identified many homogeneous regions with >50 Alines and average length of 35 samples. The VOIs having at least 50 A-lines resulted in an SE of typically <5% of the μ t estimate.
We are especially interested in goodness-of-fit measures because they could become features in an automated machine learning approach to classify plaque types. Adjusted R 2 (Ref. 40) is a good method for comparing fits of models with different numbers of parameters [ Fig. 10(a)]. Methods α-T-PL, PL, and IT-PL had higher adjusted R 2 than other methods, indicating the appropriateness of PLs, a general observation across VOIs. We observed improvements with PLs because the number of free parameters was reduced from 2M to M þ 1, where M was the number of A-lines. Although the adjusted R 2 is a good method to compare model order, its dependence on slope does not allow comparisons across VOIs. For fibrous VOIs, RMSE and CV histograms were plotted [ Figs. 10(b) and 10(c)].
More than 90% of VOIs had RMSE < 12. The RMSE was deemed the most appropriate goodness-of-fit for censoring VOIs. When VOIs with large RMSEs were omitted, the variability of μ t estimates was reduced (Fig. 8) and classification ( Table 3) improved.
To evaluate the usefulness of optical properties as features in an automatic classifier for atherosclerotic plaque tissue types, we used three features (μ t , hIi, I 0 ), where hIi was the mean intensity in the VOI. Intensity features are related to the backscattering characteristics of the tissue within the VOI as well as any attenuation prior to the VOI, features which should aid prediction of class membership. We used supervised classification, SVM, 41 fivefold cross validation, and one against all for each of the three classes (Table 3). Data were processed without and with RMSE-based censoring, where VOIs with RMSE > 12 were excluded. Classification improved with censoring [compare Tables 3(a) and 3(b)]. (The RMSE threshold is different from that used in Fig. 8 because we wanted to be uniform across all three tissue classes.) Figure 11(a) shows a clear separation of classes in 3-D feature space following VOI censoring. Features (μ t , hIi), the two best features, also demonstrated good separation in Fig. 11(b).
With all analyses considered, we determined that the PLs and α trimming were both useful, with PL and α-T-PL producing numerically close μ t estimates. In general, we recommend α-T-PL, LF, and possible censoring on RMSE value as best choices. Using these choices, we obtained the following values of μ t : calcified (3.84 AE 0.95 mm −1 ), fibrotic (2.15 AE 1.08 mm −1 ), and lipid (9.99 AE 2.37 mm −1 ). Computational estimation of μ t allowed us to distinguish between lipid plaques and calcium  plaques with a diffuse edge (Fig. 12). Typically, this is resolved by experts only after analyzing adjacent frames.

Discussion
The characterization of tissue optical properties from 3-D IVOCT clinical pullbacks will be an important step in reliable tissue classification. Previous methods for estimating optical properties have typically used time-averaged data in a stationary acquisition 29 or single A-lines from a pullback. 30 Since stationary acquisitions are clinically impractical and single A-lines are extremely noisy, we created a 3-D approach whereby groups of A-lines close to each other are analyzed together. Innovations in this report include: use of A-lines from within a 3-D VOI to improve stability of estimates; advanced, robust parameter estimation approaches including goodness-of-fit estimates; and a rigorous methodology for comparing estimation methods applied to clinical pullback data. Results suggest that filtering is desirable, that estimates vary some with the method used, that PL and its variants generally outperformed IL and its variants, and that RMSE is the favored goodness-of-fit measure which can be used effectively to "censor" VOIs with bad fits. As detailed later, we deemed α-T-PL as best. In general, we can conclude that the PL model, which fits one slope and multiple intercepts to a collection of spatially adjacent A-lines, is appropriate since there should be a single characteristic μ t value and a single slope for locally homogeneous tissue. LF 39 was the best filtering method among those tested. Filtering visually reduced the noise in A-lines. Comparing filters on a single VOI, the uncertainty of μ t was minimized with the LF [ Fig. 4(a)]. Also, LF reduced the spread of μ t across many VOIs for a given tissue [ Fig. 4(b)], presumably enabling better separation of tissues. We did not observe any consistent bias due to filtering on μ t estimates. It is satisfying that a filter designed for speckle noise gave the best results for parameter estimation because speckle is the dominant noise in OCT images.
Comparing parameter estimation methods via multiple assessments, we determined that PLs and α trimming were useful and that the best overall method was α-T-PL. Comparing results on a typical VOI, the uncertainty of μ t was least for α-T-PL (Fig. 7). Since we are ultimately interested in separating tissue types, reducing the spread of μ t estimates across many VOIs is desirable. α-T-PL and PL gave a reduced spread of μ t across many VOIs as compared with other methods (Fig. 8,  legend). Since results were variable across filters, VOIs, tissue types, and estimation methods, we developed a voting scheme for comparing parameter estimation methods. For each VOI, we picked a winning technique based on two different criteria: (1) the smallest uncertainty SE of μ t estimate, and (2) the smallest RMSE goodness-of-fit for a VOI. We then counted across all VOIs the number of times each technique was a winner and sorted results. Based on criterion (1), we obtained the following ranking of the four best techniques: α-T-PL > PL > IT-PL > NIL-PL-TM. Based on (2), we obtained the following ranking: IL-PL-TM > α-T-PL > NIL-PL-TM > α-T-IL. Since α-T-PL was in the top two for both criteria, we deemed it best. Although IL-PL-TM had the lowest RMSE, it had a large SE uncertainty [it was not in the top four based on criterion (1)]. It is worth noting that having a smaller SE uncertainty is more significant. This is because sometimes a good numerical fit could be obtained with a high SE. Similarly, α-T-PL was voted best when we rank-ordered standard deviations across many VOIs of each tissue type. The computational complexity of α-T-PL can be greatly reduced by saving intermediate calculations.

Fig. 12
Our robust estimation methods have helped us distinguish between a lipid plaque (a) and a calcified plaque with a diffuse edge (b), both shown by blue arcs. This is often a source of confusion at first glance during manual analysis. When we employed parameter estimation of μ t , we could see a significant numerical difference between the two cases (lipid: 8.62 AE 0.66 mm −1 , calcium with diffuse edge: 2.06 AE 0.23 mm −1 ), which we believe would aid in proper classification.
two previously reported studies that have estimated optical properties of clinically obtained atherosclerotic plaques using the same imaging system but different estimation procedures on stationary IVOCT acquisitions 29,30 ( [42][43][44] Because it is desirable to include the quality of assessment with parameter estimates, we investigated goodness-of-fit measures. Adjusted R 2 is a good way to compare models of different orders. The PL methods (α-T-PL, PL, and IT-PL) gave higher adjusted R 2 than other methods (Fig. 10), but R 2 depends on slope and is inappropriate for assessing the fit in a particular VOI. The CV was considered, but it was determined that the CV simply favored VOIs with more A-lines. We prefer RMSE because it is simple to compute and interpret. A histogram of RMSE across many VOIs [ Fig. 10(b)] shows that 90% of VOIs have "good fits" with RMSE<12. Classification results were improved when VOIs with RMSE > 12 were censored, indicating that the RMSE could be a useful feature for automated processing going forward. For example, one could estimate μ t from regions, but additionally use the computed RMSE value as a confidence in the μ t estimate and weight the feature accordingly during classification.
The exploratory classification study yielded surprisingly good results based solely on optical property parameters ( Table 3, Fig. 11). The choice of classifier and other parameter settings was determined from preliminary optimization experiments in which a small subset of VOIs of all three plaque types was employed. We used SVM, three tissue types, one-against-all training, three features (μ t , hIi, I 0 ), and fivefold cross validation to assess results. Censoring VOI data with poor fits (RMSE > 12) improved sensitivity and specificity as compared with uncensored data for calcium and lipid VOIs, and only slightly lowered specificity (while keeping the same sensitivity) for fibrotic VOIs [Tables 3(a) versus 3(b)]. It was encouraging that the optical parameter estimates allowed us to distinguish between lipid plaques and calcium plaques with a diffuse edge, often a problem during manual analysis (Fig. 12). In manual analysis, analysts typically analyze adjacent 2-D frames to make a determination using standard definitions provided by Yabushita et al. 13 It is promising that the computational methods can determine this from optical properties alone.
The aim of our study was to compare advanced parameter estimation methods applicable to clinical 3-D IVOCT pullbacks. This avoids the use of ex vivo data with its potential limitations including potential tissue degradation, no mean or pulsating pressure, no cardiac motion, unrealistic temperatures, no blood artifacts, and a straight path pullback rather than actual 3-D coronary geometry. Moreover, in the event of spatially inaccurate, sparse histological sampling, one can make inappropriate "ground truth" determinations using ex vivo data. Instead we used as ground truth VOIs identified by well-trained analysts using well-established criteria. Our VOI classification results overestimate that which would be obtained in automatic processing of pullback data. That is, analysts choose homogeneous, easily identified VOIs, giving rise to relatively unambiguous computer classification. In addition, analysts purposely did not choose regions of macrophages and thrombi because we were focusing on optical attenuation estimation rather than other features. Our approach should be quite appropriate for optimizing the 3-D parameter estimation methods in this report.
In summary, we believe that the robust processing methods make it possible to assess tissue optical properties from noisy, IVOCT clinical pullback data. In addition, optical parameters thus obtained will be important image features for an automated analysis of plaques. We believe that the 3-D methods reported here for assessing optical properties will also be applicable in volumetric OCT cancer imaging.