2.1.

Elastic Scattering Spectroscopy

The ESS system has been described in a number of previous publications.^{13, 14} In brief, the optical probe used in this study consists of one $365\text{-}\mu \mathrm{m}$ and one $200\text{-}\mu \mathrm{m}$ fiber bound closely together in a parallel geometry, resulting in a $315\text{-}\mu \mathrm{m}$ center-to-center separation, allowing for the fiber cladding. These fibers are brought into perpendicular contact with the tissue to be interrogated. A xenon short arc lamp (Perkin Elmer LS 1130/FX1100, California) delivers short pulses of white light ( $10\mu \mathrm{s}$ , $5\times {10}^{-7}\mathrm{J}$ ) via the $365\text{-}\mu \mathrm{m}$ fiber; the light is collected from the $200\text{-}\mu \mathrm{m}$ fiber and analyzed using a spectrometer (Ocean Optics S2000). All components are controlled by a laptop computer, which also performs the statistical analysis. The system takes a dark spectrum of the same duration just before the lamp is flashed to compensate for background light. A software-based “autoranging” algorithm is employed to examine the amount of light collected and adjusts the pulse number and integration time to ensure that the CCD does not saturate and that the signal is sufficiently high to give optimal signal-to-noise.

Before the collection of clinical data, a spectrum is collected with the fibers held at a short distance $(\sim 10\mathrm{mm})$ from a piece of spectrally flat material (Spectralon, Labsphere, UK). All subsequent spectra are divided by this spectrum to correct for the overall system response. This yields a system-independent measurement reflecting the intrinsic tissue optical properties.

2.2.

ESS Scanning

Random point measurements cannot be expected to give an accurate overall picture of lymph nodes—we would expect that a random, noncomprehensive sampling technique would inevitably miss small deposits of tumor in an otherwise healthy node. The smaller the deposit, the less likely random sampling is to coincide with it; and smaller deposits are less likely to be clinically apparent and hence more difficult to deliberately target with the ESS probe. A more comprehensive sampling method was called for and realized in the form of an ESS raster-scanning device.

The exposed surface of a typical bivalved node will be uneven, and so a method is required to provide smooth movement of the fiber probe across the sample and simultaneously give good optical coupling between the probe and tissue. We tackled this problem by using a fiber-optic plate (FOP; Hamamatsu Photonics, Japan), illustrated schematically in Fig. 1 . This plate measures $15\mathrm{mm}$ by $20\mathrm{mm}$ and is $3\mathrm{mm}$ thick. It is composed of contiguous $4\text{-}\mu \mathrm{m}$ optical fibers, running along the short axis. The tissue is pressed firmly but gently against the underside of the plate using a drop of sterile water or saline to ensure good optical coupling where necessary. The point of the optical fiber is coupled to the top surface of the FOP with microscope immersion oil. In this configuration, the image of the tissue is transmitted directly to the fiber via the plate. The numerical aperture of the plate channels is the same as the optical fiber, which means that the ESS geometry is almost perfectly preserved, notwithstanding the small attenuation due to the packing efficiency of the fibers within the plate.

Fig. 1

Schematic of ESS scanning device (not to scale). The bivalved node is mounted on a mobile scanning stage. It is coupled to a fiber-optic plate above it using a drop of saline or sterile water and gentle but firm pressure. The fiber-optic plate is coupled to a fixed fiber-optic probe with microscope immersion oil. Stepper motors move the scanning stage in an $x\text{-}y$ raster pattern to create a $20\times 20$ grid of spectra at $0.5\text{-}\mathrm{mm}$ intervals.

The UV transmission of the FOP is weaker, so to remove any spectral bias introduced by the plate, we performed our system-response calibration with Spectralon through a fiber-optic plate of the same geometry and construction.

This flat geometry enabled the smooth and efficient scanning of a $1\text{-}{\mathrm{cm}}^2$ area. The node and fiber-optic plate are mounted on an $x\text{-}y$ stage driven by stepper motors, and the node and FOP moved together in a raster-scanning pattern relative to the fixed fiber. A $0.5\text{-}\mathrm{mm}$ step size was used to generate a $20\times 20$ grid of spectral measurements. Applying the statistical discrimination algorithms allowed the construction of a false color map based on the canonical score for the spectrum from each pixel.

2.3.

Study Design

Our standard methodology is based on the statistical discrimination tools described here and requires a data set to train the machine learning algorithms to discriminate between normal and metastatic tissue. Therefore, the study was conducted in two phases: a training phase followed by a validation/test phase. Ethics committee approval was obtained.

2.4.

Training Data

Excised nodes from patients with a preoperative diagnosis of breast cancer undergoing sentinel node biopsy or ALND were included. Each node was bivalved along its long axis and a set of point ESS spectra collected by placing the optical probe manually on up to 16 random sites on the cut surface. The nodes were then fixed in 10% formalin and sent for routine histopathological analysis with hematoxylin and eosin (H&E) staining. Only nodes that subsequent histology showed to be either completely normal or completely replaced by cancer were used in the training set, avoiding misregistration of the fiber with respect to any metastases in the node.

2.5.

Scanned Nodes (Test Set)

Patients with a preoperative diagnosis of breast cancer who did not have known cancer in their axillary lymph nodes underwent sentinel lymph node biopsy (SLNB) using the combined technique of blue dye and radiocolloid for node localization.¹⁵ In brief, the approximate location of the sentinel node was established by external gamma camera after injection of the colloid into the breast adjacent to the tumor. An incision was then made over this area, and the node was identified by using a handheld gamma detection probe and uptake of blue dye, injected into the breast $10\text{to}15\min$ prior to surgery.

Excised nodes were immediately bivalved, ESS scans were taken from the cut surface as described earlier, and the node subsequently fixed in 10% formalin and sent for routine histology. Nodes found to contain cancer on histology were subclassified as macrometastases (cancer deposit $>2\mathrm{mm}$ ) or micrometastases (cancer deposit $0.2\text{to}2\mathrm{mm}$ ). It is possible to detect smaller cancer deposits using conventional histology or immunohistochemistry. However, the American Society of Surgical Oncology current guidelines do not recommend axillary clearance for metastases $<0.2\mathrm{mm}$ , so for the purpose of this study, these nodes have been regarded as nonmetastatic.¹⁵

2.6.

Algorithm Generation

The literature on physical correlation of ESS spectra suggests that the spectral components important in ESS are slowly varying, with features on the scale of tens of nanometers.¹² Therefore, applying moderate smoothing to ESS data should give improved signal-to-noise without obscuring important features within the spectrum. We applied a $3\text{-pixel}$ halfwidth $(\sim 1.5\mathrm{nm})$ cubic Savitzky-Golay algorithm. We cropped from $400\mathrm{nm}\text{to}800\mathrm{nm}$ , the region in which the signal-to-noise was highest, and reduced the data set by taking every seventh point. This reduced the size of each spectrum from 1000 to 87 points, ameliorating the computational complexity of the statistical analyses to follow.

Analysis of the training data set was undertaken by extracting spectral features using principal component analysis (PCA)¹⁶ and discriminating between classes by linear discriminant analysis (LDA).¹⁷ By projecting the spectral vector onto the axis of maximum discrimination, we derive a canonical score, which is our predictive measure of cancer risk. The resulting discrimination algorithms could then be applied to unseen spectra in the second phase of the study. The per-spectrum accuracy of the algorithm was assessed by leave-one-out cross-validation. These analyses were carried out in the statistical programming language R,¹⁸ and a number of algorithms developed for 5, 10, 15, 20, and 30 principal components (PCs). The optimum is chosen with reference to the scanned nodes, as described later. It should be noted that these PCs will contain the majority $(>99.9\mathrm{\%})$ of the variation within the data set.

2.7.

Image Analysis

In the previous section, the statistical procedure for analyzing individual spectra was described; we then developed tools to analyze the map of canonical scores and produce a binary decision of whether the node contained cancer, and hence whether an axillary clearance was called for.

It is desirable in the operating theater that interpretation of these images by the surgeon or a pathologist is not required, and that an automated and operator-independent result is generated by the system. The training data provides a rule (or more precisely, a number of rules, depending on the number of principal components selected and the cut-off applied to the canonical score) for classifying a pixel, but this needs to be extended to a rule for classifying an image. Making a diagnosis of a whole node based on isolated spectra is not reliable enough, with a considerable overlap between the canonical scores of spectra from normal and metastatic areas giving rise to individual false-positive pixels. In a tumor area, however, we are more likely to see a “clump” of positive pixels, so we considered that the simplest approach would be a “clump-counting” method. A clump was defined as a series of positive pixels contiguous via their vertical or horizontal but not diagonal edges. Diagonal contiguity was not considered because the distance between pixel centers linked diagonally is $0.7\mathrm{mm}$ , compared to the $0.5\mathrm{mm}$ for the horizontal/vertical separations. The volume of tissue interrogated at each position of the fiber probe is addressed in the following discussion. We examined all of the clumps within a node and counted the number of pixels within each clump. The size of the largest clump within the node was used for the classification of the whole node.

This was implemented by an iterative counting method; each metastatic pixel was identified in turn. Any metastatic neighboring pixels were noted; in the next cycle, any metastatic neighbors of these pixels were noted; and so on, iteratively, until no more contiguous neighbors were found. This gave rise to a clump size associated with every metastatic pixel; in general, these will not be unique—e.g., if all of the metastatic pixels in a hypothetical node are found in one clump of size 10, this analysis will generate 10 clump sizes, each of them having numerical value 10. Because we use only the largest clump size, this redundancy does not compromise our results.

The most robust test of discrimination accuracy would be achieved by using a test set independent of the data sets used to train the PCA/LDA algorithm and tune the additional discrimination parameters. For this study, there was a limited data set available, and so it was necessary to choose a statistical method that offered as robust an approach as possible, while acknowledging that a completely prospective test is not sensible. In order to both tune the classification rule and get a realistic assessment of its likely performance, the following leave-one-out procedure was adopted, with two variants: leave-one-node-out (LONO) and leave-one-patient-out (LOPO). The second approach should remove any overfitting due to the patients with multiple nodes: 40% of the patients had two or more sentinel nodes scanned, and 10% had three or more nodes scanned. Leaving out one node, or one patient, the classification rule was tuned on the remaining data. Three parameters were varied: the number of principal components used for the algorithm (5, 10, 15, 20, 30); the canonical score cut-off (0.5, 1.0, 1.5, 2.0, 2.5); and the clump size (1–20: In theory, we could allow this to vary from 0 to 400, but we want to ensure that the smaller metastases are not excluded. $20\text{pixels}$ corresponds to metastases $\sim 2.5\mathrm{mm}$ in diameter).

The tuning criterion was to find the highest sensitivity for a specificity of 95% or greater. The resulting tuned rule, and only this rule, was then used to classify the omitted node or nodes. This was repeated, leaving out each node, or patient, in turn. The result of this exercise is a classification for each node in which the tuning has been done without using the node being classified. One implication of the procedure is that the tuned rule may be different every time, and thus any assessment of performance using the resulting classifications does genuinely incorporate the uncertainty in the tuning process. Comparing the leave-one-out predictions with the known histology for the nodes, we generated four headline figures: sensitivity, specificity, (population) positive predictive value (PPV), and (population) negative predictive value (NPV). These are referred to as the leave-one-out results. The rules generated for each left-out node/patient were compared to investigate the stability of the tuning process, and the modal rule was identified and applied to all the nodes to generate a further set of predictions. We refer to the latter as the modal result.

3.1.

Training Set

The training set used in the first phase to develop the diagnostic algorithm consisted of 2989 spectra (2722 normal and 267 metastatic) collected from 361 nodes (330 completely normal and 31 completely metastatic) excised from 205 patients (184 with completely normal nodes and 21 with at least one completely metastatic node).

The leave-one-out analysis of our initial training set yielded a canonical score for each spectrum. Figure 2 shows the distribution of canonical scores for the 20-PC algorithm; the normal nodes have an asymmetric peak with a mean of $-0.2$ and a standard deviation of 0.8. In contrast, the metastatic scores are widely distributed between $-2$ and $+6$ (mean 2.4, standard deviation 2.4), with no clear structure within that range. It seems that the algorithm has the ability to classify the normal tissue consistently while giving a range of scores for the metastatic tissue. This is typical for the algorithms generated using other numbers of PCs (not shown).

Fig. 2

Distribution of canonical scores generated from the point-measurement training set. We show the scores generated using an LDA from 20 PCs.

By varying the cut-off, a receiver operator characteristic (ROC) curve for per-spectrum discrimination was generated for the point-measurement training set (Fig. 3 ). These gave similar results irrespective of the number of PCs used, with an area under curve (AUC) of 0.83 to 0.85 and sensitivities of 0.68 to 0.70 for a specificity of 0.90. It should be remembered that these results were generated on “totally normal” and “totally metastatic” nodes only; in these polarized cases, we might expect the gross changes to be detectable, no matter the number of PCs considered. However, the scanned nodes contained subtler cases—potentially, tumors as small as $0.2\mathrm{mm}$ —and there is no guarantee that each algorithm would be as sensitive in detecting these smaller deposits of cancer. We therefore selected a range of PCs (5, 10, 15, 20, and 30) and generated algorithms for each, to be validated in the next stage.

Fig. 3

ROC curve from leave-one-out cross-validation point measurement from the point-measurement ESS training set. These results are on a per-spectrum basis.

3.2.

Scanned Nodes

The scanned set comprised 129 nodes from 81 patients, including 72 normal, 3 with submicrometastases (regarded as nonmetastatic for this study), 4 containing micrometastases, and 50 with macrometastases. This constitutes 1 node each from 49 patients, 2 nodes each from 24 patients, 3 nodes each from 4 patients, 4 nodes from 1 patient, 5 nodes each from 2 patients, and 6 nodes from 1 patient.

Figures 4 and 5 show examples of scanned nodes with corresponding photographs. Applying the discrimination rules in a leave-one-out fashion gave us an estimate of the best combination of parameters and their accuracies. In optimizing specificity, the optimal parameters for both leave-one-node-out (LONO) and leave-one-patient-out (LOPO) analyses were 20 PCs, a canonical score cut-off of 2.0, and a clump size of $9\text{pixels}$ . This choice of parameters was identical for all runs in the LOPO and LONO analyses. The LONO and LOPO analyses both gave a leave-one-out specificity of 96% and a sensitivity of 69%, which was (trivially) identical to the modal result. Assuming a population prevalence of 30% and the same sensitivities and specificities, this choice of parameters would give us a positive predictive value (PPV) of 88% and a negative predictive value (NPV) of 88%. When considering macrometastases only, the sensitivity rises to 71%.

Fig. 4

A sample scanned node containing metastatic deposits. (a) The false-color map was constructed using point-wise analyses of spectra by a 20-PC LDA algorithm. Red shows regions of metastases; blue normal tissue. (b) Binary map on a cutoff of 2.0—pink identifies cancer; black normal tissue. (c) Photograph of cut surface of node. The two regions show (1) normal tissue and (2) a central region of normal tissue surrounded by a halo of metastases.

Fig. 5

Sample scanned node showing a $(\sim 2\mathrm{mm})$ metastatic deposit (confirmed on histology). (a) Scanned false-color image using 20 PCs. (b) Binary map based on a cutoff of 2.0—pink identifies regions of cancer; black denotes normal tissue or background. (c) Photograph of cut surface of node. This deposit was not detected with touch imprint cytology—possibly because the metastatis was below the cut surface of the node. However, this is an isolated case, and one should not draw too many conclusions from it.

Each pixel is separated by $0.5\mathrm{mm}$ , so a tumor with circular cross section that is detected in only $9\text{pixels}$ gives a diameter of at least $1.5\mathrm{mm}$ ; we do not want to introduce criteria that make us any less sensitive, indeed we would like greater sensitivity (see Sec. 4). We examined different parameter sets with an eye to improving PPV and found that it was very difficult to obtain a PPV above 90% in the leave-one-out analysis, possibly due to the small numbers involved in this data set—and therefore chose to focus on the sensitivity and specificity.