2.1.

Sample Preparation

This study was approved by the Institutional Review Board of the Cancer Hospital of Fudan University. Written informed consent was obtained from each patient. A total of ten patients with sporadic colorectal adenocarcinomas were involved, including seven males and three females, all Asians, at ages from 33 to 79 with an average of 57.1. Tissue specimens were obtained by surgical resection from the patients. From each patient, the adenocarcinoma and a small amount of normal mucosa adjacent to the tumor site (with $>6\mathrm{cm}$ separations) were removed. Histological assessments reported no tumor cell infiltration in all the normal mucosa sections. Upon removal, single-cell suspensions were prepared from small portions of the tissue specimens following primary culture protocols.³ Details of the processing procedure were described previously.¹ Two suspensions were produced for each patient, one from the tumor and the other from the normal.

Histopathology analyses were conducted on the tissue specimens by two pathologists working independently. Only the cases in which consensus was reached are included in the following study. The pathology conclusions serve as the golden standard for the training and testing of ANN. The training set comprises seven moderately-differentiated cases and one poorly-differentiated case, and the test set comprises two well-differentiated cases.

2.2.

LTRS Data Collection on Single Living Cells

Data were acquired by using an LTRS system described previously.^{1, 17} Briefly, the excitation beam of a diode laser (wavelength $782.5\mathrm{nm}$ ) was delivered into the back pupil of the objective ( $100\times \mathrm{oil}$ immersion) of a Nikon TE2000U differential interference contrast microscope. A laser trap was formed at the focal point. The excitation power was $11.5\mathrm{mW}$ , measured near the focal point.

Single-cell suspensions were analyzed in the sample chamber mounted on the microscope stage. Single living epithelial cells were selected, captured, transferred to clear regions, and measured. The measurement of a cell comprised a 60-s signal integration and a 60-s background integration with the cell captured and released, respectively. Their difference was recorded as the raw data signal $R\left(\overline{\nu }\right)$ , with $\overline{\nu }$ the Raman shift.

A total of 20 cancer cells and 20 normal cells were measured for each patient. The ten patients were divided into two groups according to the time sequence of their medical operations: data from the first eight were used to train the ANN, while data from the last two were used for testing. This generated a training set of 160 cancer and 160 normal cells and a test set of 40 cancer and 40 normal ones. Figure 1 presents the average spectra [cancer (curve $a$ ); normal (curve $b$ )] of the training set and their differences (curve $c$ ).

Fig. 1

Average spectra of the cancerous (a) and normal (b) cells in the training set and their difference spectrum $(c=a-b)$ . The inset is a photo of a captured epithelial cell.

2.3.

Diagnostic Modeling by Neural Network Approach

2.3.2.

Neural network architecture

The ANN we employed is a two-layer feedforward network with backpropagation training. The network architecture is depicted in Fig. 2 and belongs to the perceptron category. The open circles labeled with $h$ or $y$ represent the neurons, while the solid circles labeled with $x$ represent the inputs to the network. The two circles labeled with “1” are plotted in order to treat the biases in the same fashion as the weights. The network architecture is uniquely defined by the arrangement of the neurons and their interconnections. Each neuron can have multiple inputs but only one output. Each arrow into a neuron represents an input, and the arrow out represents the output. Each interconnection between two nodes is associated with a factor $w$ , called weight. For example, the arrow linking $x_I$ to $h_1$ carries a weighting factor $w_{1I}$ , which means that the contribution of $x_I$ to the input of neuron $h_1$ is $w_{1I}{x}_I$ [Eq. 6, shown later]. The $x$ nodes stacked on the left serve as the inputs to the network, and their values are substituted with the scores from Eq. 3. The $h$ neurons stacked in the middle form the hidden layer, and the $y$ neuron on the right denotes the output layer. The numerical outputs of the $h$ neurons and $y$ neuron are given by Eqs. 6, 7 later, respectively. Here, the output layer is set to one single node, since a cell is classified as either normal or cancerous. So our network is essentially a binary neural classifier (with modifications described later). The number of nodes in the input column $I$ and the hidden layer $H$ were determined in the training session by trial and test. Best results were achieved at $I=5$ and $H=8$ .

Fig. 2

Structure of the binary feedforward neural network.

The extreme flexibility of multilayer perceptron networks to approximate arbitrary complex posterior probability functions calls for special procedures to avoid overfitting and detect outliers. Outliers are data points that have been assigned to a wrong category of patterns in the original data set. They are defects of the experimental data. For example, if a cell in the training set is truly normal, but instead determined as cancerous by pathology, then it is an outlier, or vice versa. The existence of outliers is an outcome of the imperfectness of data collection. In our experimental data, the pattern of a cell was set to the pathological classification of the tissue from which the cell was harvested: if the tissue was normal, the cell was normal, or vice versa. However, there was a small possibility that a cell inside a malignant tumor was actually normal, but erroneously labeled as cancerous based on the histopathology grading on the tumor tissue, resulting in an outlier.

Outliers in the training set can significantly shift the decision plane of the network if uncorrected and consequently affect the accuracy of network predictions. An outlier probability $ϵ=[0,1]$ was introduced in Ref. 16 to correct the classification flipping due to the existence of outliers. In our binary case, this means that

Eq. 4

$$\{\begin{array}{c}P(1\mid \mathbf{x})\equiv P_0(1\mid \mathbf{x})(1-ϵ)+ϵP_0(0\mid \mathbf{x}),\hfill \\ P(0\mid \mathbf{x})\equiv P_0(0\mid \mathbf{x})(1-ϵ)+ϵP_0(1\mid \mathbf{x}),\hfill \\ P_0(0\mid \mathbf{x})=1-P_0(1\mid \mathbf{x}),\hfill \end{array}$$

where $P_0(1\mid \mathbf{x})$ and $P_0(0\mid \mathbf{x})$ are the posterior probability for cancer (class 1) and normal (class 0) at the absence of outliers, respectively and $P(1\mid \mathbf{x})$ and $P(0\mid \mathbf{x})$ are the actual posterior probability for cancer and normal, respectively. Here the term “posterior” means post-experiment, and the posterior probability is the conditional probability of the cell’s classification under the requirement that it has the characteristics to produce Raman spectrum $\mathbf{x}$ . Both $P(1\mid \mathbf{x})$ and $P(0\mid \mathbf{x})$ contain two terms, indicating that the cell data $\mathbf{x}$ carry $1-ϵ$ probability of not being an outlier and $ϵ$ probability of being an outlier. After straightforward calculations, Eq. 4 can be simplified to

Eq. 5

$$\{\begin{array}{c}P(1\mid \mathbf{x})=P_0(1\mid \mathbf{x})(1-2\beta )+\beta ,\hfill \\ P(0\mid \mathbf{x})=1-P(1\mid \mathbf{x}),\hfill \end{array}$$

where $\beta \equiv ϵ$ . The connection of Eq. 5 to the ANN output (Fig. 2) is through $P_0(1\mid \mathbf{x})$ .

In ANN, the response (the output) of a neuron to the stimuli (the inputs) is calculated through its activation function. In Fig. 2, the activation functions are hyperbolic tangent for the hidden layer, i.e.,

Eq. 6

$$h_j\left(\mathbf{x}\right)=\tanh (\sum _{i=1}^I{w}_{ji}{x}_i+w_{j0}),$$

and linear for the output layer, i.e.,

Eq. 7

$$y\left(\mathbf{x}\right)=\sum _{j=1}^H{\tilde{w}}_j{h}_j\left(\mathbf{x}\right)+{\tilde{w}}_0,$$

where $w_{ji}$ and $w_{j0}$ are the input-to-hidden weight and bias, and ${\tilde{w}}_j$ and ${\tilde{w}}_0$ are the hidden-to-output weight and bias. The ANN estimate to the posterior probability without outlier corrections $P_0(1\mid \mathbf{x})$ is predicted as

Eq. 8

$${\widehat{P}}_0(1\mid \mathbf{x})=\frac{1}{1+\exp [-y\left(\mathbf{x}\right)]}.$$

Consequently, the ANN estimates to Eq. 5 become

Eq. 9

$$\{\begin{array}{c}\widehat{P}(1\mid \mathbf{x})=\frac{1-2\beta }{1+\exp [-y\left(\mathbf{x}\right)]}+\beta ,\hfill \\ \widehat{P}(0\mid \mathbf{x})=1-\beta -\frac{1-2\beta }{1+\exp [-y\left(\mathbf{x}\right)]}.\hfill \end{array}$$

3.1.

Classification

The network was trained on the training set described in Sec. 2.2, comprising Raman spectra of 160 cancerous and 160 normal cells from eight patients. The network weights and biases were initialized with random numbers of Gaussian distribution at zero mean and ${\sigma }^2=1∕I$ . Best training results were accomplished at $I=5$ and $H=8$ by trial and test on various combinations of $(I,H)$ ; the network performance started to deteriorate when $I\ge 6$ .

We therefore restrict the following discussions to the case of $I=5$ and $H=8$ . The cost function $S\left(\mathbf{w}\right)$ had 47% chance of hitting the global minimum after runs on different initializations. Results at local minima were also close but were discarded anyway. There were no observable differences among the network predictions once the global minimum was reached, although the settled network weights varied from run to run. The final values of the hyperparameters were $\alpha =0.7126$ and $\beta \equiv ϵ=0.0374$ . The average outlier probability,¹⁶ defined as the average percentage of the second term inside the two-term summation on the right side of Eq. 4, was found to be 0.0252.

After the values for the network weights and hyperparameters were settled, the estimated posterior $\widehat{P}(1\mid \mathbf{x})$ was calculated for each cell and compared with a threshold value $p_{th}$ to predict its class; it was cancerous if $\widehat{P}(1\mid \mathbf{x})>p_{th}$ , or normal otherwise. A reasonable value $p_{th}=0.5$ was chosen. In the final classifications of the training set, 138 out of 160 cancerous cells and 138 out of 160 normal cells were correctly identified, reaching a sensitivity of 86.3% and specificity of 86.3%. These were considerably better than the results given by logistic regressions¹ (Table 1 ).

Table 1

Predictions of this model versus the logistic regression model.1 Major improvements are observed in the training set

A receiver operating characteristic (ROC) curve is commonly used by medical doctors to assess the performance of a diagnostic model. It displays the dynamic trend of the model’s predictions. In fact, it is possible to sacrifice specificity for higher sensitivity by reducing $p_{th}$ , or vice versa. For example, if we set $p_{th}=0$ , all the cells will be identified as cancerous, corresponding to 100% sensitivity but 0% specificity. By sweeping $p_{th}$ from 0 to 1, one can map out the ROC curve. In a perfect model, the curve is a step function along the upper-left corner (Fig. 3 , the OAB line). On the other hand, a random-guess model possesses no predictive power and thus produces an ROC curve along the diagonal. The closer an ROC curve to the upper-left corner, the better the model’s performance. In Fig. 3, the ROC of the current model shows much improvement over that of the logistic regression model.¹

Fig. 3

ROC curves for this model (solid line), logistic regression model¹ (dashed line), and a random-guess model (dotted line). The OAB line along the upper-left corner represents a perfect model, while the random-guess model flips a coin to assign a cell’s class.

In a double-blinded test of the ANN, we fed the data from two new patients to evaluate its capability of predicting new results, the so-called generalization. The test set, described earlier in Sec. 2.2, comprised the Raman spectra of 40 cancerous and 40 normal cells. The network predicted correctly 17 of 20 cancer cells and 17 of 20 normal cells for the first patient and 17 of 20 cancer cells and 20 of 20 normal cells for the second patient. The overall sensitivity and specificity were 85% and 92.5% respectively, compared with the corresponding 82.5% and 92.5% of logistic regression. The limited improvement in the test may be due to the samples. In fact, the tissue specimens of the test set were graded as well-differentiated by pathology, and a higher degree of differentiation in pathology points to a smaller difference between the normal and abnormal. In pathological terms, well-differentiated tissues show a regular order similar to that of normal tissues, where there are clear structures. Also cells from well-differentiated tissues exhibit morphology similar to those in normal tissues, such as the cell shapes, nuclear sizes, and uniformity of cells inside the tissues. On the other hand, in poorly differentiated tissues, the cells are aligned in a chaotic way, indicating a higher degree of invasiveness. Here, our test results may provide evidence that morphological similarities and biochemical similarities between the well-differentiated cells and the normal cells are correlated.

Nevertheless, the generalization of our ANN is excellent. A common problem in ANN algorithms is that a well-trained network predicts very poorly on new data. This is absent in our model.

3.2.

Sensitivity Analysis

The sensitivity map is presented in Fig. 4 . The split-half resampling technique was applied to investigate the reproducibility of sensitivity maps.¹⁶ The $Z$ scores of 100 split-half resamplings (corresponding to 100 pairs of independent networks trained separately on split-half data) were found to be above 2.3657, corresponding to a minimum 99.1% confidence interval. Therefore, Fig. 4 is reproducible at above 99.1% confidence level.

Fig. 4

Sensitivity map of the network and the training data. Major features are identified here and listed in Table 2. Do not confuse the sensitivity here with that in Fig. 3.

Table 2

Tentative assignments of the Raman bands identified in Fig. 4, mean intensity changes (increase + /decrease − ) of cancer relative to normal, and p-values of Student’s t-tests on band intensities. The spectral resolution of our system is 8cm−1 .

Prominent Raman bands are easily identifiable on Fig. 4. Tentative assignments²³ are listed in Table 2 . Intensities at these peaks were read out from the data and subjected to Student’s t-test. We observed mean intensity increases from normal to cancer at 940.988, 1004, 1096.433, 1209.015, 1265.006, 1304.081, 1341.605, 1437.853, 1520.245, 1655.304, and $1672.795{\mathrm{cm}}^{-1}$ and decreases at the remaining peaks. The increases occur mostly at the proteins and nucleic acids bands, indicating that cancer cells have higher DNA/RNA and protein activities. It is a surprise that glucose (decreasing, p- $\mathrm{value}=0.001$ ) and cholesterol (increasing, p- $\mathrm{value}=0.001$ ) appear on the list. However, signal alterations at 759.803, 940.988, 1004, 1096.433, 1209.015, 1341.605, and $1746.711{\mathrm{cm}}^{-1}$ cannot be ruled out as statistical fluctuations (p- $\mathrm{value}>0.05$ ). Furthermore, the cancer cells systematically (p- $\mathrm{value}<0.05$ ) have lower signals than the normal ones in the spectral region below $720{\mathrm{cm}}^{-1}$ (see Fig. 1, for example), which may require further investigation. This phenomenon is also reflected in Fig. 4 as increased sensitivity levels at the same region, and confirmed by the colon tissue spectra in Fig. 5B of Ref. 23. Finally, even though mean intensity changes with p-values less than 0.05 are considered as statistically significant by medical doctors, a p-value greater than 0.05 does not necessarily reject the correlation of a band to the disease transformation.

3.3.

Conclusions and Discussions

In this paper, we compared the technical characteristics of DNA FCM and LTRS, including working principles, sample preparations, hardware aspects, data collection schemes, operational procedures, and sample amount requirements, for single-cell investigation of cancers. LTRS can share the single-cell processing procedures already existing in hospitals for FCM, but removes the requirement of fluorescent dye staining. Unlike DNA FCM, which replies on the accumulative histogram of tens of thousands of cells, LTRS can decide on each individual cell, which makes LTRS very advantageous for diagnosing small tumors. In the meantime, by detecting the biochemical activities of cancers at the single-cell level, LTRS can provide deeper insight into the dynamics of carcinogenesis than tissue Raman spectroscopy, because cell functions are more fundamental than tissue functions.

Potentially, single-cell LTRS can achieve higher accuracy than tissue Raman spectroscopy, because the course of carcinogenesis starts within the epithelial cells, and the epithelial cells are the primary source of diagnostic information for early cancer detection. In literature, some tissue components like collagen are reported to show correlations to cancer developments. However, because genetical alterations are the foundation of structural changes, variations in these components are by-products of carcinogenic activities in the epithelial cells and thus serve only as the secondary source of diagnostic information. Furthermore, many other tissue components do not possess diagnostic information at all. Tissue Raman spectroscopy suffers from two sources of interference: one is the Raman signal from the irrelevant tissue components; the other is the strong fluorescence and its associated noise from the tissue bulk. Even at 785-nm excitation, tissue fluorescence is still considerably higher than tissue Raman signal, and mathematical preprocessing such as fifth-order polynomial fitting is typically required to subtract the slow-varying fluorescence background from the data. Unfortunately, the noises associated with the fluorescence are left in the processed data. Therefore, in Raman studies, it is desirable to avoid as many fluorescence sources as possible.

In a clinical study of colorectal adenocarcinoma, we measured the Raman spectra of 400 living epithelial cells from ten patients using LTRS. An ANN algorithm incorporating outlier probability corrections was developed to overcome the limitations existing in a previous study employing logistic regression.¹ Remarkable improvements were achieved in the sensitivity and specificity of the predictions. Unavailable to logistic regression, the sensitivity map of ANN was evaluated to objectively quantify the contribution of each Raman frequency in the course of carcinogenesis. Important Raman bands were identified from the map, and Student’s t-tests were performed on their intensities. Unlike the subjective visual inspections commonly used in spectral analysis, the sensitivity map technique provides an objective, quantitative, and automatic way to discover important Raman peaks.

In our experiments, only living epithelial cells were measured. The following discussions are restricted to living cells only. We cannot rule out the possibility of potential damage to some membrane proteins on the cell surface during the process of cell isolation from the tissue, but the primary culture procedure we employed is well-established and should reduce such damage to a minimum. In the meantime, the intracellular substances should be intact. Over the past decades, there have been intense studies on cancer cell culture techniques to prevent damage to the cells. Today, these techniques are already mature and widely applied in various fields. One example is the cell lines on the market, which came from the primary cultures originally harvested from patients. The demand for membrane protein protection might originally come from conventional FCM, which requires the binding of fluorescence markers to specific targets on the cell surface. After years of development, different protocols for different tissue types are already available in standard textbooks. LTRS on single cells can directly enjoy the fruits of other fields to keep possible cell damage under control. Furthermore, the major signal of LTRS originates from the volume inside the cell, so we do not expect a detectable alteration of the cell’s Raman spectrum due to the isolation processing.

The average Raman spectra of single epithelial cells [Figs. 1a and 1b] share many common features with those of tissues (Fig. 5B in Ref. 23). They exhibit a general resemblance in the overall spectral shapes. However, differences in spectral details are obvious due to the extra components in tissue other than the epithelial cells. The difference spectra between the abnormal and the normal [Fig. 1c in this paper and Fig. 6B in Ref. 23] also show similarity in general trends, but differ in details.

To establish our diagnostic model, we employed the tissue histopathology assessments as the golden standard and involved only those cases with consensus reached between two independent pathologists. A cell’s classification was set to the pathology classification of the tissue where it originated. There was a small possibility that a cell from a malignant tumor might be actually normal, resulting in an outlier. Unfortunately, it is impractical to obtain a cell’s classification from a direct single-cell histochemical analysis. To the best of our knowledge, immuno-histochemical analysis on cells/tissues is not for diagnostic purpose and cannot determine the normal/malignant nature of samples. It is rather used to supply assistive information for histopathology assessments. Besides, immuno-histochemical information alone is not reliable for diagnosis because the targeted proteins are also expressed in normal cells/tissues. Our way to assign a cell’s classification should provide the best accuracy for model training. In both the training set and the test set, around 14% of all cancer cells were misidentified by our model. But in our opinion, the outliers are only a minor source for this error, since it is highly unlikely that our cancer tissue samples contained such a high percentage of normal cells. As a matter of fact, our diagnostic model was built purely on experimental data with no prior knowledge and could be affected by the noises in the signals as well as the statistical nature of the individual variations of the cells.

Unlike the training stage of our model, the application stage does not require prior histopathology assessment on a sample. LTRS diagnosis can be run independent of or without histopathology. In a clinical application, cells from suspected tumor sites can be retrieved through fine needle aspiration or exfoliative cytology methods like brushing and washing and then examined by LTRS to determine the nature of the cells. Frequently, doctors do not know the definitive characteristics of a suspected site without resorting to sophisticated diagnostic techniques. This is where histopathology, LTRS, DNA FCM, etc. come into play.

In many situations, doctors need to know only whether a suspected cancer transform has occurred in the first place, before further investigation can be triggered to find its exact location. Exfoliative cells in pleural fluid, ascites, and urine can be collected and analyzed by LTRS to help doctors make decisions.

The extension of our work to other epithelial cancers is straightforward. The single-cell diagnosis technique presented here can be directly applied to clinical tests. Thanks to FCM, preparation of single-cell suspensions is already routine in hospitals today. Further, exfoliative cytology can also provide samples to our technique. The low requirement for sample amounts makes our technique very attractive to cancer screening.

The current work deals only with the question “Normal or cancer?” Future studies will focus on the subclassification of different tumor stages.