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The prognosis of hepatocellular carcinoma (HCC) varies following surgical resection and the large variation remains largely unexplained. Studies have revealed the ability of clinicopathologic parameters and gene expression to predict HCC prognosis. However, there has been little systematic effort to compare the performance of these two types of predictors or combine them in a comprehensive model.
Tumor and adjacent non-tumor liver tissues were collected from 272 ethnic Chinese HCC patients who received curative surgery. We combined clinicopathologic parameters and gene expression data (from both tissue types) in predicting HCC prognosis. Cross-validation and independent studies were employed to assess prediction.
HCC prognosis was significantly associated with six clinicopathologic parameters, which can partition the patients into good- and poor-prognosis groups. Within each group, gene expression data further divide patients into distinct prognostic subgroups. Our predictive genes significantly overlap with previously published gene sets predictive of prognosis. Moreover, the predictive genes were enriched for genes that underwent normal-to-tumor gene network transformation. Previously documented liver eSNPs underlying the HCC predictive gene signatures were enriched for SNPs that associated with HCC prognosis, providing support that these genes are involved in key processes of tumorigenesis.
When applied individually, clinicopathologic parameters and gene expression offered similar predictive power for HCC prognosis. In contrast, a combination of the two types of data dramatically improved the power to predict HCC prognosis. Our results also provided a framework for understanding the impact of gene expression on the processes of tumorigenesis and clinical outcome.
Hepatocellular carcinoma (HCC) is the fifth most common cancer in the world, accounting for approximately one million deaths, with an increasing trend of new incidences annually [1-3]. Surgical resection is regarded as the standard curative treatment of HCC [3]. However, prognosis following surgery varies substantially. This variation becomes a hurdle in searching for effective and efficacious therapies and cancer management strategies. There is an ongoing search for predictive biomarkers of cancer prognosis, where pathological parameters, protein biomarkers, mRNA expression levels, and genomic DNA abnormalities have been surveyed [4-9].
On two independent Hong Kong HCC cohorts that we previously described [10], the HCC prognosis was significantly associated with clinicopathologic parameters including tumor size, number of tumor nodules (NOTN), tumor stage (new AJCC and pTNM), venous infiltration status, serum albumin level (ALBU), and serum α-fetoprotein level (AFP). These parameters were further summarized into a linear score that was demonstrated to partially predict disease-free survival ([DFS] time to tumor recurrence) and overall survival (time to death) [10]. A natural path to further enhance this prediction model would be to incorporate molecular level biomarkers, for example, gene expression profiles in the tumor or adjacent normal tissues. Currently, such efforts have been limited due to the availability of fresh frozen tissues [4] forcing some studies to use paraffin-embedded samples [9,11]. Most importantly, the search for gene signatures should be conducted by conditioning on the clinicopathologic parameters, and focus on the identification of novel variance components that improve the prognosis prediction beyond that achieved by the clinicopathologic features alone.
Herein we carried out a carefully designed search for gene expression signatures underlying prognosis of HCC using tumor and adjacent normal tissue expression profiles. We identify a gene expression signature that significantly enhances our ability to predict HCC prognosis. Additionally, we demonstrate that this HCC prognosis signature is related to widespread changes we previously identified in the liver tissue network that are associated with HCC, providing additional mechanistic insights into tumorigenesis.
Study Subjects
A total of 272 HCC patients were included in the initial training dataset. Resected tumor and adjacent non-tumor liver tissues were collected from patients who had undergone hepatectomy for curative treatment of HCC at Queen Mary Hospital, Pokfulam, Hong Kong between 1993 and 2007 [10]. Informed consents were obtained from patients regarding to the use of the liver specimens for research. Additional File 1, Table S1 summarized the demographic and clinicopathologic features of these patients. All samples came from individuals who provided written informed consent to make their samples available for scientific research. In addition, all of the samples and patient data were approved for use in this study by IRBs specific to each of the participating organizations. Experimental research reported in this paper was also approved by IRBs of each participating organizations. Research reported in this paper was in compliance with the Helsinki Declaration.
Additional file 1. Supplementary. Supplementary Table 1
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Pathology Parameter Measurements
The clinicopathologic features of the patients analyzed were sex, age, tumor size, number of tumor nodules, cellular differentiation according to the Edmondson classification, venous infiltration without differentiation into portal or hepatic venules, tumor node metastasis stage (pTNM and AJCC), serum hepatitis B surface antigen (HBsAg) status, and background liver disease in non-tumorous liver tissue [12].
Sample processing to isolate RNA
Fresh frozen tissue was placed in a chilled milling tube along with a stainless steel bead, dipped in a liquid nitrogen bath and loaded onto the QIAGEN TissueLyser for milling (30 Hz in 30 second intervals). Multiple cycles of milling were sometimes required to achieve complete pulverization of the tissue to a fine powder. Isolation of RNA was achieved using the following procedures. The milled tissue samples were homogenized in cryopreservation tubes using a Polytron with disposable rotostator probes. The tissue was homogenized in 750 to 1000 uL of 100% TRIzol. 100% Chloroform was added to the TRIzol/GITC lysate (1:5 ratio) to facilitate separation of the organic and aqueous components using the phaselock (Eppendorf) system. The aqueous supernatant was further purified using the Promega SV-96 total RNA kit, incorporating a DNase treatment during the procedure. Isolated total RNA samples were then assayed for quality (Agilent Bioanalyzer) and yield (Ribogreen) metrics prior to amplification.
RNA amplification and hybridization
Samples were amplified and labeled using a custom automated version of the RT/IVT protocol and reagents provided by Affymetrix. Hybridization, labeling and scanning were completed following the manufacturer's recommendations (Affymetrix). Sample amplification, labeling, and microarray processing were performed by the Rosetta Inpharmatics Gene Expression Laboratory in Seattle, WA. The expression data has been deposited in GEO (GSE25097, http://www.ncbi.nlm.nih.gov/geo/ webcite).
Independent Validation Data Sets
Four recent studies were employed as independent validation. The first study consisted of 23 HCC tumor tissues collected in Singapore and assayed on the Affymetrix GeneChip HU133, resulting in the identification of a 57-gene signature associated with tumor recurrence [4]. The second study employed formalin-fixed paraffin-embedded non-tumor (i.e., adjacent normal) liver tissues from 82 Japanese HCC patients. A 186-gene signature was derived from this study using an Illumina array containing 6000 human genes [9]. The third study involved an HCC metastases cohort from Asia (N = 115 normal tissues) in which an Incyte 9, 180-reporter two channel array was used to profile the normal liver tissues [13]. Finally, a China-Belgium study (sample size N = 90) of mostly tumor tissues was profiled on a Qiagen 70-mer two channel array [14].
Statistical Analysis
Classification of patients into good and poor prognosis groups
Prediction of cancer prognosis was performed by using the clinicopathologic phenotypes recorded at the time of surgery. There are a number of statistical learning techniques able to serve as classifiers. However, many of these methods do not directly accommodate two-dimensional outcome (e.g. survival and DFS). Herein, application of a univariate parameter selection and multivariate Cox model classifier was employed [6,7]. Univariate Cox regression models were applied to search for clinicopathologic parameters associated with outcomes. All significant clinicopathologic parameters were included in a multivariate Cox model. The use of the model yields the relative hazard for each patient, which serves as the linear predictor for survival endpoints and further division of the patients into good and poor prognosis groups based on the linear predictor. This approach and its prediction power were assessed using a leave-one-out (LOO) procedure and an independent testing sample set also collected in Hong Kong [10].
Expression trait processing
The intensity of all gene array experiments were normalized together using RMA methods [15]. Afterwards, the intensity was adjusted for gender and age of the patients. To avoid the influence of outliers, we fit the robust linear model (rlm, M-estimation with Tukey's bisquare weights), and used the residuals as the gene expression trait in all following analysis.
Further Classification of good and poor prognosis groups using gene expression
We examined whether the clinicopathologic phenotypes that were recorded at the time of surgery might predict cancer prognosis. Again, we applied the univariate Cox model for feature selection and multivariate Cox model for classification/prediction. Importantly, the classifier should use both the clinicopathologic parameters and expression biomarkers. As discussed above, feature selection on the entire dataset firstly identified genes that associate with cancer stage, which are of significant scientific value. However, these genes may not improve the prediction performance since they carry information that is redundant with the clinicopathologic data. Further, in the good and poor prognosis groups defined by the clinicopathologic parameters, the gene signatures were likely to be different. Therefore, we conducted the feature selection in the two prognosis groups separately.
In brief, the univariate Cox regression models was applied to search for gene expression traits associated with outcomes. The top 100 genes were included in a multivariate Cox model as the prediction model. Given there are only slightly more than 110 patients in either the good or poor prognosis groups, a linear model with 100 regressors would be unstable. Therefore, we conducted a further reduction in dimensionality using principle component analysis (PCA), a common approach to handle gene expression data in prognosis predictions [7]. The primary motivation for this approach was the fact that the top 100 genes are correlated; therefore, the top principle components (PCs) are able to extract most of the information and only cost a few degrees of freedom in the linear model. The top 6 PCs were used to build the Cox model for prediction, since they on average explained 80% of the variation in the 100 genes. We also explored additional models varying the number of genes (e.g. 50 and 200) and number of PCs (e.g., 5), and the results were consistent. From the model, we derived the relative hazard for each patient, which serves as the linear predictor for survival endpoints [10]. Further, we divided the patients into two sub-groups using the linear predictor, and the performance of the prediction was assessed by a leave-one-out (LOO) procedure. In each LOO iteration, we reserved one patient for testing and used the remaining patients (say N-1 patients) for training. On these N-1 training patients, we ran the univariate Cox model on each gene and derived the pvalue for association between prognosis (e.g. survival) and the gene's expression value. We then picked 100 genes with the smallest pvalues. With the 100 genes over N-1 patients, we constructed the 6 PCs, which then served as independent variables in a multivariate Cox model. This model and its coefficients captured the association between HCC prognosis and the PCs. Next, we projected the gene expression values of the reserved patient on the PC space (defined on the training patients) to obtain the coordinates of the first 6 PCs. We plugged these 6 coordinates into the multivariate Cox model and calculated the relative hazard for the reserved testing patient. After N LOO iterations, we derived the relative hazard for every patient, which was actually the linear predictor. Lastly, we used the log-rank test and Kaplan-Meier plot to examine and visualize the performance of the linear predictor. This scheme is similar to a previous report using clinicopathologic parameters to predict HCC outcome [10], except for the extra step of PCA dimensionality reduction.
Clinicopathologic parameters predict HCC prognosis
Tumor and adjacent non-tumor liver tissues were collected from 272 Chinese HCC patients who received curative surgery (referred to here as the HCC cohort). Additional File 1 Table S1 summarizes the characteristics of this cohort. Nearly 2/3 of the patients were right-censored (67.8%) and the other 1/3 (32.2%) of the patients were deceased (failure) upon data analysis. Half of the patients (51.1%) suffered from tumor recurrence during the follow-up period. The primary endpoints (overall survival and DFS) were found to be significantly associated with tumor size, AFP, ALBU, venous infiltration, pTNM and new AJCC stage, and NOTN. Previous analysis has shown that these clinicopathologic parameters can classify patients in the HCC cohort into two groups (denoted as good and poor prognosis groups) that give rise to distinct clinical outcomes [10]. For the survival endpoint, the good and poor survival groups contained roughly equal numbers of patients and were significantly different with respect to clinical outcome (log-rank test p-value of 6.0E-6; Figure 1 left panels). The linear predictor (h) shown in Figure 1 was derived using a leave-one-out (LOO) cross validation procedure to reduce biases that result from over fitting. Similarly, we classified the patients into good-DFS and poor-DFS groups (log-rank test p-value = 5.6E-9, Figure 1 right panel) [10]. Within each survival or DFS group, the clinicopathologic parameters could not further partition patients into subgroups of significantly different prognosis. In other words, the variation of prognosis within each group was not explained by clinicopathologic parameters.
Figure 1. Clinicopathologic Parameters Predict Survival and DFS on Patients with Available Normal Tissue Gene Expression Data. In the left panels, the clinicopathologic parameters can classify the Hong Kong HCC patients into the good prognosis and poor prognosis groups that have distinct survival outcome. Similarly, in the right panels, we also classify the patients into two groups of distinct disease-free survival (DFS).
Combination of clinicopathologic and gene expressional biomarkers enhances prediction
To advance our understanding of the molecular processes and to extend the predictive power of the clinicopathologic variables, we explored the relationship of gene expression to outcome. Tumor and adjacent normal tissues were profiled using the Affymetrix whole genome expression array. The experiment surveyed 37, 585 unique transcripts, among which 23, 788 were mapped to well-annotated genes. Using the gene expression traits to predict group membership, we observed similar predictive power as was achieved using the clinicopathologic parameters alone.
In order to identify biomarkers that further enhance prognosis prediction based on the clinicopathologic parameters, a stratified analysis using univariate gene expression feature screening was carried out within each prognosis group (Figure 1&2). Under the null hypothesis the pvalues generated by this screening should follow a uniform distribution, substantial enrichment of low pvalues indicated a large number of prognosis-associated genes that might offer predictive power, shown Additional File 2 Figure S1. However, many of the prognosis-associated genes captured the same information as the clinical parameters, and contributed no extra prediction power. In the stratified analysis, we were able to identify genes associated with survival or DFS in each prognosis group. For example, many genes in the tumor tissue were associated with survival in the good-survival group but not in the poor-survival group (Additional File 3 Figure S2), suggesting that tumor gene expression may further enhance prognosis prediction in the good-survival group but not the poor-survival group. Interestingly, there were many normal tissue gene expression traits associated with DFS in the good DFS group, while many tumor tissue gene expression traits associated with DFS in the poor DFS groups (Additional File 3 Figure S2), again suggesting that the gene expression data may help stratify patients according to DFS beyond what could be achieved by the clinicopathologic parameters alone.
Figure 2. Clinicopathologic Parameters Predict Survival and DFS on Patients with Available Tumor Tissue Gene Expression Data. In the left panels, the clinicopathologic parameters can classify the Hong Kong HCC patients into the good prognosis and poor prognosis groups that have distinct survival outcome. Similarly, in the right panels, we also classify the patients into two groups of distinct disease-free survival (DFS).
Additional file 2. Figure S1. Crude Pvalues of Association between HCC Prognosis and Gene Expression Profiles. Histogram of p-values of the univariate search for genes associated with survival outcome. The substantial enrichment for small p-values indicated potential predictive power of the gene expression data.
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Additional file 3. Figure S2. Association between HCC Prognosis and Gene Expression Profiles in Strata Defined by Clinicopathologic Parameters. Histogram of p-values of the univariate search for genes associated with HCC outcome, conducted within good and poor prognosis strata.
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Motivated by these results, we combined the gene expression data with the clinicopathologic parameters to construct models to predict HCC prognosis and compare to those models constructed from the clinicopathologic data alone. We again employed a LOO cross validation strategy in each subset of patients to minimize over-fitting. For example, in the good-survival group, the LOO procedure was performed on the 113 patients with available normal tissue gene expression data (Figure 3, left panel).
Figure 3. Normal Tissue Expression Predicts Survival. Within the good prognosis and the poor prognosis groups, clinicopathologic parameters could no longer separate patients into partitions of different survival outcome. Meanwhile, adjacent normal tissue gene expression provided extra information to further refine the prognosis prediction. Using a LOO framework with the dimension reduction and multivariate Cox model, we assigned predicted hazard for each patient. The hazard was able to further separate the good prognosis group, but not the poor prognosis group.
The normal tissue expression data improved the prediction for the good-survival group (p-value = 0.011, Figure 3 left panel). The blue line in Figure 3 represented an excellent survival function (over 90%) for a group of patients carrying both favorable clinicopathologic and gene expression profiles. The same procedure was conducted on the 117 patients in the poor-survival group with available normal tissue gene expression data. As expected, the expression data could not further improve the predictive power of the model (Figure 3, right panel). Prediction in the good-DFS (p-value = 0.0027), but not the poor-DFS group was also further improved by incorporating normal tissue expression data into the model (Figure 4).
Figure 4. Normal Tissue Expression Predicts DFS. Using adjacent normal tissue gene expression data, we derived the predicted hazard within the good and poor DFS groups. The predictor (predicted hazard) further separated the patients in the good prognosis group, but not in the poor prognosis group.
We carried out the same analysis just described using the tumor tissue expression data. It was noted that the sample sizes of the tumor tissue analysis was different from that of normal tissue (Figure 1&2). Figure 5 shows that the prediction in the good-survival (p value = 9.0E-4) and poor-survival (p-value = 0.0023) groups were further improved by the incorporation of the tumor expression data. Curiously, the pattern was opposite for DFS compared to what we observed in the normal tissues. For the poor-DFS group, tumor expression significantly further partitioned patients into good and poor DFS subgroups (p-value = 5.5E-8; Figure 6, right panel). No prediction improvement for the good-DFS group was observed. Since both normal and tumor tissues had predictive power in the good-survival group (Figure 3 and 5), we were motivated to explore predictive models incorporating expression traits from both tissue types. The number of patients with both tissues available was N = 110. The combined data resulted in a further improvement of the prediction performance (Additional File 4 Figure S3).
Figure 5. Tumor Tissue Expression Predicts Survival. Using tumor tissue gene expression profile, we obtained the predicted hazard within the good survival and poor survival groups. The predictor further separated the patients in both the good survival and the poor survival groups.
Figure 6. Tumor Tissue Expression Predicts DFS. Using tumor tissue gene expression profile, we obtained the predicted hazard within the good DFS and poor DFS groups. The predictor further separated the patients in poor DFS group, but not in the good DFS groups.
Additional file 4. Figure S3. Improving prediction in the good-survival stratum using normal tissue and tumor tissue gene expression profiles together. Shown in Figure 2 and 4, both normal tissue and tumor tissue had prediction value in the good-survival group. Restricted in the patients with both normal and tumor tissues available (N = 110), we followed LOO procedure and derived h incorporating expression data of both tissue. The prediction performance was further improved. Presented in the blue curve (lower right panel), we identified 55 patients with excellent clinicopathologic and gene expressional profiles (both normal and tumor tissues). Their 100 months survival was above 95%.
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Independent validation using published HCC prognosis gene signatures
The identification of prognosis-associated gene signatures in HCC is an active field of research, with previous reports indicating that different gene signatures may be harvested from tumor and adjacent non-tumor tissues [4,9,13,14,16]. To capture information from the expression data that was not yet covered by the clinicopathology, the clinicopathologic parameters should be conditioned on during the search for expression signatures, as we have done. Unfortunately, many of the reported studies did not follow such a strategy. Ideally, our gene signatures would be tested in independent HCC cohorts. However, raw clinical outcome data was not available for any of the published studies [4,9,13,14]. Therefore, we compared our gene signature, which showed predictive value towards HCC prognosis, with published signatures. We would not expect perfect concordance among the signatures given the different patient recruitment criteria, experimental conditions, array platforms, and statistical methods across the studies. For example, five different array platforms were used in studies listed in Table 1 and 2: Affymetrix whole genome custom array (current study), Illumina 6000-gene human array [9], Qiagen 70-mer two channel array [14], Incyte 9, 180-reporter two channel array [13], and Affymetrix GeneChip HU133A&B arrays [4]. More importantly, since the sample sizes for the published studies were all small (n < 200), the power to capture prognosis-associated genes was low. Hence, we applied liberal p-value cutoffs (e.g. 5E-4) in order to capture a majority of the HCC prognosis-associated genes and in turn enhance the comparison to the published signatures (Table 1, 2 and Additional File 5 Table S2). The survival- and DFS-signatures we identified significantly overlapped with all published gene lists (Table 1). For example, Lee et al reported a comprehensive HCC gene signature on a Chinese-Belgium dataset that overlapped our results in a highly significant manner (4.8 fold enrichment; Fisher Exact Test p-value = 1.4E-12 for the tumor tissue DFS signature, Table 1 and 2). As one would expect, when the study design of a published gene signature matches our design, we observed a more extensive overlap with the signatures. For example, Hoshida et al. [9] and Budhu et al. [13] studied adjacent non-tumor liver tissues in HCC patients. Their gene lists overlapped with our normal tissue signature more significantly than with the tumor signature. Alternatively, Lee et al. reported a gene list that overlapped heavily with our tumor tissue signatures. It is noteworthy that the hypergeometric test p-values were driven by both magnitudes of overlaps and the size of the published gene lists. The overlap among the various gene lists were summarized in Additional File 6, 7, 8 and 9, Table S3. The first part of Additional File 5, 6, 7, and 8, Table S3 highlighted genes that reached genome-wide significance in our HCC data. There was no adjustment for clinicopathologic parameters in order to retain consistency with other published signatures. A strict cutoff (Cox p-value ≤ 2e-6) was applied to the identified genes that were genome-wide significant after a Bonferroni correction. The second part of Additional File 6, 7, 8 and 9, Table S3 summarized genes that appeared in at least two other gene lists.
Table 1. Using Independent HCC Studies to Validate HKU Gene Signature Identified at 0.0005 Level*
Table 2. Using Independent HCC Studies to Validate HKU Gene Signature Identified at 0.05 Level
Additional file 5. Supplementary. Supplementary Table 2
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Additional file 6. We integrated the Hong Kong gene list with published HCC gene signatures and create the list of HCC prognosis-associated genes. The first part of the list contains genes that reached genome-wide significance level in our Hong Kong data. Herein, we did not adjust for clinicopathologic parameter in order to remain comparable to published signatures. Strict cutoff (Cox p-value ≤ 2e-6) were applied to our results, therefore, the identified genes were genome-wide significant after Bonferroni correction. The second part of the list contains genes that appeared at least twice in HCC gene lists. Here, we applied a liberal p-value cutoff (Cox p-value ≤ 0.01) to Hong Kong data. The second column of the table presents the Wald's test p-values, where "-" denotes the p-value above 0.01. The columns 3-6 are indicators for published HCC signatures, where "1" denotes present and "-" denotes absent.
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Additional file 7. Supplementary Table 3B
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Additional file 8. Supplementary Table 3C
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Additional file 9. Supplementary Table 3D
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eSNPs underlying differentially connected genes linked to HCC prognosis
To explore the predictive genes in the context of a normal-to-tumor network reconfiguration, we looked at whether the genetic perturbations of the predictive genes were associated with HCC prognosis. Two sets of genes were explored in this way: 1) genes differentially connected between the normal and tumor tissue co-expression networks (gene-set-1), as detailed by Lamb et al [17]; and 2) genes whose expression levels were significantly associated with copy number abnormalities (CAN) in the tumor tissue (gene-set-2).
To explore whether these gene sets were enriched for eSNPs that associate with HCC prognosis, we genotyped DNA isolated from adjacent normal tissues using the Illumina 650Y SNP arrays and characterized the genetic architecture of gene expression based on a previously described method [18]. This genome-wide association study of gene expression resulted in 1, 296 cis expression QTLs (eQTLs) [18] at a 10% FDR (translating to p-value cutoff = 9E-6). We termed the significant SNPs (associated with the corresponding expression trait at a p < 9E-6) underlying the eQTLs as eSNPs. There were 707 and 2, 840 eSNPs for gene-set-1 and gene-set-2, respectively. Further, we examined if the eSNPs linked to gene-set-1 and -2 were enriched for SNPs that associated with clinical endpoints (referred to as clinical SNPs or cSNPs). In brief, the cSNPs were identified using Cox models focusing on survival or DFS. The model was adjusted for clinicopathologic parameters.
At an α level of 0.01, we identified 6, 399 cSNPs associated with HCC survival (referred to as survival-cSNPs). Interestingly, the eSNPs underlying gene-set-1 were 2.1-fold enriched for survival-cSNPs (p = 7E-4); and the eSNPs underlying gene-set-2 were 1.7-fold enriched for survival-cSNPs (p = 2E-5). In parallel, at an α level of 0.01, the SNP screening using a Cox model yielded 5, 246 SNPs associated with DFS (referred to as DFS-cSNPs). We found the eSNPs underlying gene-set-1 were not enriched for DFS cSNPS; in contrast, eSNPs for gene-set 2 were 1.9-fold enriched for DFS cSNPs (p-value = 5E-7). For comparison, we randomized the clinical endpoints and repeated the Cox modeling, and at α level of 0.01, we yielded pseudo-cSNPs, which arose purely from type I errors. The eSNPs underlying gene-set-1 and -2 were not enriched in the pseudo-cSNPs.
Numerous studies have reported the ability of clinicopathologic parameters [2,3,10,19] and gene expression traits [4,9,13,14] to predict HCC prognosis. However, the sample sizes of these previous studies were small, and there were no systematic efforts to compare the performance of these two types of predictors or combine them in one unified model. As we previously showed, several clinicopathologic parameters that are easily and routinely measured, provided excellent predictive power for outcome in HCC [10] and result in predictions that were readily applicable to clinical practice. Given their utility, it is natural to attempt to further enhance the clinicopathology-based prediction model by adding gene expression data. We conducted a head-to-head performance comparison between gene expression predictors derived from normal and tumor tissue (denoted as hgene-expression) vs. predictors derived solely from clinicopathology (hpathology; Materials and Methods) and benchmarked them in a LOO framework (Figure 1, 2 and Additional File 10 Figure S4). Please note, the genes used in the prediction models might be different with regard to normal vs. tumor tissue expression, as well as in each LOO iteration. Overall, hgene-expression and hpathology performed similarly. The hgene-expression of tumor tissue was better than hpathology in predicting DFS, but hgene-expression slightly underperformed hpathology in all other scenarios. Overall, gene expression was not superior to clinicopathology in predicting prognosis. One reason might be that gene selection primarily identified genes correlated with clinicopathologic parameters (e.g. cancer stage). To assess if expression variables could be identified that enhance predictive power, stratified analysis and computed hgene-expression within the good- and poor subgroups that go beyond the clinicopathologic parameters were performed. A combination of these two types of data resulted in the identification of a group of patients with near perfect survival after surgery (blue curve, left panel, Figure 3). These patients had both favorable clinicopathologic and gene expression profiles (they enjoyed a 90% survival rate over 100 months). In contrast, we found that DFS over 30 months for patients with both poor clinicopathologic and gene expression profiles whose was lower than 10%.
Additional file 10. Figure S4. Predicting HCC Prognosis using Gene Expression Profiles of Normal of Tumor Tissue
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The focus of this study is stratified modeling, which is a natural extension of our previous work. Alternatively, we can build a single model incorporating clinicopathologic parameters and gene expression data simultaneously (Additional File 11 Figure S5). The prediction framework is identical to the above analyses except the multivariate Cox model included both the clinicopathologic parameters and the top 6 PCs. In the gene selection step we also included clinicopathologic parameters in the Cox model and then picked 100 genes with the smallest pvalues. The overall prediction was better than using gene expression alone (Additional File 10 Figure S4), indicating clinicopathology captured valuable information beyond gene expression. However, comparing to Figure 1 and 2, adding gene expression only enhanced prediction in one scenario (tumor gene expression improved the prediction of survival). A possible explanation would be that different gene sets were associated with prognosis across the strata defined by clinicopathology, and these gene sets offer various prediction value. For example, shown in Figure 2, normal tissue expression was used in prediction in the good-survival stratum but not the poor-survival stratum. In the single model approach, genes with little prediction value also entered the model, bringing noise and reducing the performance. Lastly, we also evaluated a single model incorporating clinicopathologic parameters, and expression profiles of both normal and tumor tissue (Additional File 12 Figure S6). We reduced the expression profile of each tissue to 6 PCs, therefore, a total of 12 PCs entered the model. Overall, such models did not greatly outperform the models based on clinicopathology alone (Figure 1&2) or models based on clinicopathology and expression profiles (Additional File 11 Figure S5). Again, this lack of improvement could be attributable to noises introduced into the prediction.
Additional file 11. Figure S5. Predicting HCC Prognosis using Clinicopathologic Parameters + Gene Expression Profiles of Normal or Tumor Tissue
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Additional file 12. Figure S6. Predicting HCC Prognosis using Clinicopathologic Parameters + Gene Expression Profiles of Both Normal and Tumor Tissue
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HCC tumor tissue and adjacent non-tumor tissues harbor distinct prognosis-associated signatures and lead to differences in predictive power. Importantly, we noted that the gene signature derived from the tissues significantly overlapped. Consistent findings were also reported on Chinese and Belgium HCC patients [14], Asian [13] and Singapore patients [4]. However, for 82 Japanese patients, Hoshida et al found gene-expression profiles of tumor tissue failed to yield a significant association with survival [9]. This result is inconsistent with the fact that gene expression traits in tumor tissues were correlated with cancer stage, and cancer stage was strongly associated with survival [10]. The failure to detect gene expression traits with predictive power in this instance could be due to the small sample size (N = 82) and the use of formalin-fixed, paraffin-embedded tissues [9].
The mechanistic basis whereby gene expression traits predict the aggressiveness of a tumor remains to be defined. One of the striking features of this analysis and others [4,9,13] was the finding that signatures in normal tissue adjacent to the tumor is highly predictive of prognosis. It had been suggested that mechanistically these signatures represented a so called "field-effect" capturing damage to liver tissue and the state of inflammation related to the likelihood of subsequent tumors arising [9,20]. In other words, the field effect hypothesis implied that the signatures did not relate directly to processes in the tumors per se but rather the environment from which tumors might arise. An alternate hypothesis supported by our results was that the signatures are mechanistically connected to tumor specific events in some way, given the genes associated with survival (p < 2e-159, fold enrichment 31.01) and DFS (p < 5e-152, fold 29.31) in adjacent normal and in tumor tissues significantly overlap.
To address whether the "field effect" or this alternate hypothesis was better supported by the data, we first examined the evidence that tumors directly affect the surrounding normal tissues via secreted factors. If that were the case we would expect that the adjacent normal gene expression patterns would be correlated with DNA copy number abnormalities (CNA) in the tumor tissue, given we previously showed CNA was strongly connected to tumor gene expression [10]. No significant associations beyond what would be expected by chance were found. We were also able to exclude significant invasion of tumor cells into the adjacent normal tissues given we observed no significant associations between normal tissue derived CNA and normal tissue gene expression [10].
Given this result, how might signatures in normal tissues mechanistically relate to tumor events? Herein, we took advantage of previous work on this dataset. We described the massive gene expression network changes that occur during HCC tumorigenesis, and such rearrangements were likely driven by tumor CNA [10]. In brief, we defined gene pairs where the pair was significantly correlated in one setting and significantly less correlated in another [10]. Using stringent cut-offs, there were 8, 736 genes differentially connected between the adjacent normal and tumor tissues with ~86% of cases representing a loss of connectivity in the tumor (LOC) and the remaining ~14% representing a gain of connectivity (GOC) [10]. We therefore tested whether the predictive gene expression traits from the adjacent normal tissue were enriched for differentially connected genes and found that indeed they were. The genes associated with survival in adjacent normal tissue (Cox p < 0.01, Additional File 6, 7, 8 and 9, Table S3) were enriched for genes participating in differential connections (p < 1.98e-80, fold enrichment 2.69). Similarly gene expression traits in adjacent normal tissue associated with DFS (Cox p < 0.01, Additional File 6, 7, 8 and 9, Table S3) were enriched for genes identified as differentially connected in the tumor tissue (p < 5.2e-69, fold 2.52).
Our previous reports also documented that a large fraction of expression variation can be explained by CNA in the tumor tissues [10]. Therefore, we asked if the predictive genes (Additional File 6, 7, 8 and 9, Table S3) were enriched for genes that associated with cis-acting CNAs in tumors. We found that both survival- and DFS-associated genes in normal tissue were enriched for genes associated with CNAs in cis in the tumor tissue (p-values were 2.99e-8 and 1.72e-11, respectively). Since genes in adjacent normal tissues were measured entirely separately from genes in the tumor, there was no a priori reason for them to behave similarly unless there was a mechanistic connection. We found that predictive genes from adjacent normal tissue were selectively enriched in network re-arrangements and enriched for genes that associate with CNA associated tumorigenesis, strongly suggesting that these genes represent important functions targeted for alteration in tumors. Stated in another way, the predictive signatures in adjacent normal tissue are a measure of the ability of the tissue to alter expression networks to enter a more aggressive state.
If the predictive genes were the determinant of the normal-to-tumor network reconfiguration, then we would expect that genetic perturbations of these genes would also be associated with HCC prognosis. We examined the normal liver tissue eSNPs underlying two sets of genes (1) genes that are differentially connected between the normal and tumor states in the HCC cohort, and (2) genes whose expression levels were significantly explained by CNA in the liver tumor tissue. We found that the eSNPs controlling the expression level of these two sets of genes were enriched for association with HCC survival and DFS. This result supports the hypothesis that the mechanisms by which genes in normal tissue are predictive of prognosis reflects their ability to facilitate the transition from a normal tissue network to a tumor network, where this transition determines cancer progression.
We have demonstrated the excellent predictive power of our approach by combining clinicopathologic parameters and gene expression profiles. As a result, we expect that this approach to provide valuable guidance for HCC treatment/management in clinical practice. More importantly, based on our previous work on the architecture of coexpression networks in adjacent normal and tumor tissues [10], we proposed a general mechanism of how predictive genes influence HCC prognosis. The massive rearrangement of expression networks plays a central role in HCC progression, which was reflected in the ability of such genes to predict HCC prognosis. This also explained why the predictive genes significantly overlapped between the adjacent normal and tumor tissues, since such genes would ostensibly continue to reflect the ongoing alterations in network state.
Hepatocellular carcinoma (HCC) is highly lethal, and its prognosis following surgery varies substantially, in a manner which is yet to be explained. Our contributions to understanding the progression of HCC are three fold. (1) We established a comprehensive algorithm to incorporate clinicopathologic and gene expression parameters, which greatly improves the prediction of HCC prognosis. (2) Using a large sample size, we characterize the gene expression alternation in HCC tumor and adjacent normal tissues, and their association to overall survival and disease-free survival. (3) We proposed a general framework explaining why gene expression in both tumor and adjacent normal tissues can predict HCC prognosis. In brief, the gene expression networks undergo massive a transition during tumorigenesis and tumor progression, where normal tissue gene networks are destroyed and tumor gene networks are establish. States of the genes in these key networks determine the likelihood and rate of such massive transition as well as tumor progression and as a result the expression levels of these genes predict HCC prognosis.
Declaration of competing interests
The authors declare that they have no competing interests.
Authors' contributions
All authors read and approved the final manuscript. KH, all figures and tables, experimental design and manuscript preparations. JL, MM, DG, MDF, CM EES, HD and JML, experimental design. CZ, processing the mRNA microarray readings and calculation of the expression values. TX and EC, processing the SNP arrays and calculation of the CNV values. KW, BZ and HZ, construction of the expression networks. NPYL, ION, PCS, RTPP, and JML, collection of tissue samples and clinicopathologic parameters.
The work was supported by Research Grants Council of Hong Kong and Innovation and Technology Fund of the Hong Kong Government to J.M.L. We would like to thank for the technical supports from Ashley Wong and Kit-Yuk Mak of the Queen Mary Hospital. IOL Ng is a Loke Yew Professor in Pathology.
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Pre-publication history
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text:
Verizon Galaxy Note 3 finally gets KitKat update
If you've got a Galaxy Note 3 for Verizon, plug it in! An update is available for you, but won't be pushed to your handset over the air as usual. This one seems to come solely via a wired connection, but doesn't take long and brings you the joy of KitKat with TouchWiz.

subset: commoncrawl


text:
A lithographic process having improved image quality by employing a mask that includes a plurality of opaque elements or transparent elements that are smaller than the resolution of the lighography to be employed in order to control the transmittance of the actinic light exposure area.
1. A lithographic process having improved image quality that comprises: positioning a member including a photosensitive layer at the imaging plane of a projection lens with respect to a lithographic mask that defines areas that are to receive actinic light wherein said lithographic mask includes a plurality of opaque elements or transparent elements, each of which is smaller than the resolution of the projection lens, to be employed for controlling the transmittance of the actinic light defining area, and wherein the concentrations of said elements are varied within an individual mask opening to provide higher transmission in the corners and along the edges of said individual mask opening.
2. The lithographic process of claim 1 wherein said mask includes a plurality of opaque elements.
3. The lithographic process of claim 1 wherein said elements include half-tones, semi-transparent half-tones, or phase shifting regions or a combination of any of them.
4. A lithographic proximity printing process having improved image quality that comprises:
positioning a member including a photosensitive layer in proximity to a lithographic mask that defines areas that are to receive actinic light wherein said lithographic mask includes a plurality of opaque elements or transparent elements, each of which is smaller than the resolution of the proximity printing, to be employed for controlling the transmittance of the actinic light defining area, and wherein the concentrations of said elements are varied within an individual mask opening to provide higher transmission in the corners and along the edges of said individual mask opening.
5. The lithographic process of claim 4 wherein said mask includes a plurality of opaque elements.
6. The lithographic process of claim 4 wherein said elements include half-tones, semi-transparent half-tones, or phase shifting regions or a combination or any of them.
1. Technical Field
The present invention is concerned with a lithographic process that exhibits improved image quality. In particular, the present invention is concerned with lithographic masks that provide regions that at least partially compensate for image degradation caused by the lithographic process itself. The lithographic masks, pursuant to the present invention, have sub-resolution halftones incorporated within the mask patterns for controlling the transmittance of the actinic light exposure area.
2. Background Art
In the fabrication of integrated circuits including integrated circuit chips, one of the most critical and crucial steps is the lithographic processing for providing the desired circuit patterns.
For instance, photolithographic processes involve employing a beam of actinic light, such as U.V. radiation, in order to transfer a pattern from a photolithographic mask onto a photoresist coating through an imaging lens. The mask includes opaque and transparent regions such that the shapes match those of the openings in the resist coating in the desired or predetermined pattern.
In the case of a positive resist coating, the transparent portions of the mask correspond to the desired pattern or image to be provided in the resist coating. When the photoresist coating is a negative resist, the opaque portions or regions of the mask correspond to the subsequent open regions to be provided in the photoresist coating.
However, as the size of the features of the desired pattern approaches the resolution of the photolithographic tool being employed, the contours of the developed regions depart significantly from those in the desired ideal pattern. These departures from, or errors in the pattern, are often pattern-dependent and, accordingly, are difficult to correct with overall changes in the development procedure. Such problems are discussed, for example, in U.S. Pat. No. 4,456,371 to Lin, disclosure of which is incorporated herein by reference.
The present invention provides for improved photolithography and improved image quality. In particular, the present invention substantially compensates for image degradation that is caused by the photolithographic process. The present invention is concerned with correcting pattern-dependent errors in photolithographic processes.
In particular, according to the present invention, improved photolithographic processes are obtained by employing a photolithographic mask that contains half tones. The half-tone regions of the photolithographic mask permit partial compensation for the image degradation that is caused by the photolithographic process itself. The half-tone regions are formed from attenuating arrays of opaque or transparent sub-resolution elements.
In particular, the present invention is concerned with a lithographic process having improved image quality. The process includes positioning a member that is to receive an image of a photolithographic mask that defines areas that are to receive actinic light. The member can be adjacent the mask or separated therefrom by some defined distance such as about 500 mm or more having a lens located between the mask and the member. The photolithographic mask includes a plurality of opaque elements or transparent elements or semi-transparent elements, or combinations, each of which being smaller than the resolution of the photolithography to be employed in the imaging. These opaque elements or transparent elements control the transmittance of the actinic light exposure area. Choice of the type of half-tone employed (e.g., transparent or opaque) will depend upon the practical tradeoffs encountered between the write-time for the mask (i.e., number of half-tones) versus the difficulty of fabrication (i.e., polarity-negative or positive resist) of minimum dimensions.
FIG. 1 is a schematic of a conventional mask containing two objects at about 10� magnification.
FIG. 2 is a schematic of a halftone mask in accordance with the present invention.
FIGS. 3A and 3B represent images provided by the conventional mask of FIG. 1.
FIGS. 3C and 3D illustrate images provided by the halftone mask in accordance with the present invention illustrated in FIG. 2.
FIGS. 4A-4C illustrate the Fourier domain of halftone-corrected mask patterns pursuant to the present invention.
FIG. 4A illustrates the spectrum of spacial frequencies contained in a grating-like array of halftones.
FIG. 4B illustrates the spectrum of an uncorrected mask pattern.
FIG. 4C illustrates the spectrum of the corrected mask.
FIG. 5 is a schematic of a mask containing phase halftones pursuant to the present invention.
The present invention is concerned with obtaining improved photolithography by employing a mask that contains halftones.
The halftone regions that are present in the photolithographic masks employed pursuant to the present invention provide for substantial compensation for the image degradation that is caused by the photolithographic process itself.
The halftone regions provide for a means of correcting the exposure and patterns containing geometry-dependent degradation.
In particular, the presence of opaque elements or transparent elements in the photolithographic mask that are smaller than the resolution of the photolithography to be employed provide for correction of the exposure to the actinic light by adjusting the transmittance of the corresponding mask opening or portion of the mask opening. In particular, when using opaque elements that are smaller than the resolution of the photolithography to be employed, these opaque elements will not be individually reproduced, but instead, will merely reduce the feature exposure. Correspondingly, finite transmittance can be introduced into a nominally opaque mask pattern by selectively deleting small opaque elements of the mask coating that are smaller than the photolithographic resolution to be employed.
Reference to FIG. 1 illustrates a conventional photolithographic mask containing two objects. Black areas (1) represent opaque areas of the mask, and white areas (2) represent transparent portions of the mask. The mask is about a 10� magnification. The dotted circle (3) indicates the approximate lithographic resolution for the particular example represented.
FIG. 2 represents a halftone mask pursuant to the present invention wherein the black portions (1) represent the opaque portions of the mask, the white portions (2) represent the transparent portions of the mask, and the black portions (4) represent the opaque portion being smaller than the resolution of the photolithography to be employed. The dotted circle (3) indicates the approximate photolithographic resolution in the example.
As illustrated in FIGS. 3A-3D, the quality of the photolithographic images is significantly improved by adjustment of the total feature exposure.
In particular, for the particular photolithography illustrated, a three-quarter micron optical photolithography employing a diffraction-limited lens is employed between the masks and the wafer, the wafer being at the imaging side of the lens. The lens numerical aperture (NAwafer) is about 0.28, the wavelength is about 436 nanometers, the reduction is about 10�, and the pupil filling ratio σ is about 0.7. The approximate resolution of the system is rmask =10�rwafer which equals 10�(0.5λ/NAwafer)=7.8 microns. The desired pattern, as illustrated in FIG. 1, consists of two objects (i.e., two clear apertures in a binary mask), a 7.5 micron square opening (contact hole), and a 7.5�25 micron rectangular opening (line). The corresponding wafer-plane dimensions are reduced by a factor of about 10.
In this example, the lens resolution rmask (illustrated as a dotted circle (3) in FIGS. 1 and 2) is comparable to the minimum feature dimension of 7.5 microns. The limited resolution causes a loss in sharpness in exposure latitude for both features. Such also causes a reduction in the exposing intensity actually transmitted to the wafer underlying the mask. It is further noted that the shape of the contact hole is such that it approaches the resolution limit in both dimensions. This, in turn, causes the contact hole exposure to be lower than that of the line when a conventional mask is employed.
FIGS. 3A and 3B illustrate images printed with the conventional mask from FIG. 1. The contours of each printed circuit are calculated using a computer simulation of the image projected by a partially coherent lens system as discussed by Rosenbluth, et al., "A Critical Examination of Sub-micron Optical Lithography Using Simulated Projection Images", Journal Vacuum Science Technology B1(4), p. 1190 (1983), disclosure of which is incorporated herein by reference. Developing of the resist sufficient to bring the diameter of the contact hole to the desired 0.75 micron value results in overdeveloping the line by about 35% in the critical 0.75 micron dimension. On the other hand, using the conventional mask, development of the line to the correct width results in underexposure or underprinting of the contact hole because of its lower exposure, as illustrated in FIG. 3B.
Reference to FIGS. 3C and 3D illustrates simulations of images provided with the halftone mask of the present invention, as illustrated in FIG. 2. The apertures in the 10� mask are divided into 0.8 micron�0.8 micron sub-resolution pixels. Five out of every eight pixels in the line are opaque, while in the contact hole, four are opaque. FIGS. 3C and 3D illustrate that development of either feature of the proper width produces little, if any, error in the other feature. For instance, the smaller proportion of open halftones in the line aperture reduces the exposure of the line image to match that of the contact hole. This exposure correction is obtained by an increase in exposure time.
The opaque halftone can be produced on the mask using standard fabrication processes wherein the resolution of the photolithography used is greater than that to be employed in the subsequent photolithography when the mask is used to develop the desired patterns. However, usually when employing present day state-of-the art lithography, the resolution needed to make the mask is not necessarily any finer than that used to print on the wafer since the mask is demagnified such as about 5-fold to about 10-fold. For instance, the halftone mask can be provided by placing a layer of, for instance, chrome of about 500 angstroms on a transparent glass substrate followed by a layer of photoresist material. The photoresist is then developed to provide the desired halftone pattern and the chrome beneath the photoresist is etched. The photoresist remaining is then removed.
In addition, halftone pixels can be fabricated in masks that are later de-magnified by the lithographic tool, such as employing a reduction stepper. In the event the 2-dimensional mask pattern is Fourier transformed, such an optical reduction system will not reproduce spacial frequencies having a period finer than rmask =0.5Mλ/NAwafer where M is the magnification. In the event the halftone elements are insufficiently small, however, they will generate significant Fourier components at resolvable spacial frequencies, thereby resulting in unacceptable noise in the image. For example, if desired, the halftones can be arrayed in a grating-like pattern. The spacial frequencies in the grating must be chosen to lie outside the imaging bandwidth of the photolithographic tool employed. Ideally, the image cast by the linear or bi-linear optical reduction system would then consist only of the gray-level DC component. However, the corrected mask consists of a multiplication of the high frequency grating with the uncorrected pattern. In particular, noise results from the low frequency harmonics generated by the non-linear multiplication as demonstrated in FIG. 4A. The noise will be localized in the vicinity of feature edges, and is, in fact, equivalent to the intensity change caused by a small shift in the position of the image. The residual noise or intensity change due to the image shift can be made small in comparison to uncorrected optical proximity effects, particularly in cases where the minimum feature size approaches the resolution of the lens employed in the photolithographic tool. In such instances, the halftone pixels are made small in comparison with the lens resolution.
Reference to FIG. 4A illustrates the spectrum of spacial frequencies contained in a grating-like array of halftones. A band-limited optical system will capture only the central DC harmonic, and will then produce the desired uniform image exposure. Reference to FIG. 4B illustrates the spectrum of an uncorrected mask pattern whereby the binary lithographic pattern can not be band-limited. On the other hand, FIG. 4C shows the spectrum of the corrected mask that consists of the convolution of 4A and 4B. A comparison of FIG. 4C with FIG. 4B illustrates the erroneous components in the pattern at resolvable frequencies.
Not only can the present invention and use of halftones be employed to equalize the exposure of different patterns, mask structures in accordance with the present invention can be provided to carry out uniform correction within a pattern itself. For instance, the effective gray level can be varied within an individual mask opening such as for providing higher effective transmission in corners and along edges of an individual mask. This allows for more general improvement in the quality of the image.
The techniques of the present invention can be used not only for binary mask-making processes to be used in the fabrication of half-tone masks as described in detail above, but also in conjunction with more sophisticated mask-making processes such as Levenson's phase-layer processes to fabricate an even more general class of mask (e.g., masks with negative or non-real transmittance). Such phase-layer process is disclosed by Levenson, et al., "Improved Resolution and Photolithography with a Phase-Shifting Mask", IEEE Transaction on Electron Devices, ED-29, page 1828 (1982). For instance, see FIG. 5. The technique could provide a super-position of four basic amplitudes to synthesize an arbitrary amplitude in a complex plane. For instance, four different kinds of halftone elements would be sufficient to define an arbitrary net complex transmittance for each resolution element in the mask. for instance, the four elements could include a pixel (11) with a transparent coating of one-third wave optical thickness, a pixel (12) with coating of two-thirds wave thickness, a pixel (13), and an opaque pixel (14) on the un-coated substrate. In FIG. 5, numeral 13 represents the uncoated substrate, regions of which represent a pixel. The uncoated regions are shown as white. The phase and amplitude transmittances of the resulting masks can have a spacial variation that is arbitrary to within the lens resolution. Such masks form the most general class of two-dimensional optical objects. Accordingly, the mask pattern can be chosen such that it most fully corrects for degradation in the lithographic process.
FIG. 5 is a schematic of a mask containing halftones wherein the effective mask transmittance varies in the y direction, but not in the x direction. The net amplitude transmittance T(y) of each x-oriented strip is indicated with an x on the accompanying plot. The negative transmissions shown could not be obtained with opaque halftones alone. Phase halftones make possible a general complex transmittance.
In addition, according to the present invention, methods for determining the maximum allowed pixel size and criteria for such have been provided.
A simple scheme for placing halftone elements within mask apertures is one in which potential sites for halftones are randomly filled with probability p (so that p is the attenuation factor). Finite pixel size then causes the image to contain random shot noise. The signal-to-noise ratio is approximately the square root of the number of halftone features within one resolution element of the lens. If each chip contains a large number of resolution elements, a nominally random placement procedure should be modified so as to preclude rare noise fluctuations of unusually large magnitude.
Another and more preferable approach is to systematically array the halftone elements in a two-dimensional grating.
The intensity error in the vicinity of an edge of a pattern will have a peak of order ##EQU1## where amask =Mawafer is the size of a single halftone element, M is the magnification, rmask =Mrwafer is the resolution (defined here as 0.5λ/NA), and Io is the baseline exposure level defined as the intensity inside the image of a large object.
In the absence of correction, the degree of interaction between features having a critical dimension d is of order ##EQU2## Eq. 2 may be thought of as the residual lens response at a distance d outside the geometrical boundary of some feature. In contrast, Eq. 1 is essentially the peak lens response to a sub-resolution feature of width a. Eq. 1 is then considerably smaller than Eq. 2 when amask is small compared to rmask (if d and rwafer are comparable).
The increment represented in Eq. 1 will not fluctuate as with randomly dispersed halftone features. In addition, Eq. 1 represents an upper limit to the error introduced by a halftone grating.
In order to estimate the error introduced when a halftone mask is used in place of a mask containing true gray-levels, reference is made to the simple one-dimensional case in which a half-plane is imaged under incoherent illumination. The region x<0 is deemed to be opaque, and the region x>0 to be either a continuous film of 50 percent transmittance, or an equal line-space grating of pitch 2a.
Under these conditions, as discussed by Goodman, "Introduction to Fourier Optics", McGray-Hill, Chapter 6, 1968, the image intensity is given by ##EQU3## where g(Xo) is the mask transmittance, and where, under the assumption of incoherent one-dimensional imaging, the intensity response function is given by ##EQU4## The intensity difference between the true gray-level image and that generated with halftones is ##EQU5## which yields Eq. 1 above. Eq. 6 assumes that the halftone pixels are small enough that h can be approximated by a two-term Taylor expansion within each pixel.
The above approach forms the basis of a general two-dimensional calculation in which the illumination can be partially coherent. A general two-dimensional halftone grating that fills a mask aperture of arbitrary shape can be analyzed.
The image amplitude cast through the halftone object by a single source point as discussed by Born, et al., "Principles of Optics", 5th Ed. (Pergamen, Oxford, (1975), Chapter 10, is ##EQU6## where S(Xs) is the strength of a source point at Xs, h(Xi) is the amplitude impulse response, p(Xo ; Xs) is the amplitude illuminating the object plane due the single source point, and g(Xo) is, as above, the periodic halftone transmittance function. Let the transmittance function in the jth period of the halftone grating be written as ##EQU7## and where Xoj in Eq. 10 is defined implicitly by ##EQU8## (i.e., Xoj is the geometrical center of the jth halftone period).
The halftone period is assumed to be sufficiently small to permit a two term Taylor expansion of the imaging and illuminating fields within each period. Then changing the variable of integration in Eq. 8 from Xo to Xo : ##EQU9## which (using Eqs. 9 and 12 while integrating over the halftone terms, and approximating the resulting sums of h and p terms by integrals) results in ##EQU10## If ds is a differential vector directed along the edge of the aperture, and z is directed normal to the object plane, then using a version of Stoke's theorem, as discussed by Gradshtlyn, et al., "Table of Integrals", Series 1 and Products and Jeffrey, Academic Press, 1980, entrs. #10.723, p. 1091, Eq. 14 reduces to ##EQU11## i.e. dm is an infinitesimal vector directed normal to the aperture edge.
Finally, the product VV* is formed and integrated over all source points Xs. Using the definition of the mutual coherence ##EQU12## and subtracting the image intensity corresponding to a true continuous-tone film of transmittance gg* is obtained ##EQU13##
Eq. 19 indicates that the departure from a true continuous-tone film image may be thought of as an interference between two sources; the continuous-tone film image itself, and an amplitude equivalent to that transmitted by a slit-like opening tracing the feature boundary. The width of this slit is essentially <r>, which is of the order of the width of one halftone. As in the example discussed above, this suggests that the residual error is small compared to uncorrected proximity effects.
Equivalently, one may regard the halftone aperture as a continuous-tone film aperture that has been shifted in position a distance <r> since such a shift changes the transmitted amplitude by an edge-like contribution identical to that in Eq. 16. A similar contribution arises when the aperture does not contain an integral number of periods.
A more general non-periodic halftone object can similarly be regarded as a variable transmittance object that has undergone small internal deformations; in the non-periodic case the deformations are inhomogeneous.
In a similar manner, the distribution of the subresolution elements can be determined in the case when the member to receive the image is positioned in proximity of the mask without a lens in-between. In this situation, h(xi -xo) is replaced with ##EQU14## where λ is the wavelength of the actinic light and z is the distance between the mask and the member. More details on this transfer function h(xi -xo) and better transfer functions can be found in Lin, Polymer Eng. and Sci., Vol. 14, p. 1317, 1975 and J. Opt. Soc. Am., Vol. 62, p. 977, 1972. The subresolution element in the case of proximity printing has now a dimension smaller than ##EQU15##
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Saturn Sedan Reviews
Autobytel has reviews that will walk you around a car, give you a peek under the hood and get you behind the wheel with an industry expert. Browse by category or get into a specific brand to see how well a car does when put to the test.
Showing 7 of 27 reviews for this vehicle
2007 Saturn Aura Photo GallerySaturn drills one deep into Japan's outfield
Saturn Aura – Photo Gallery: It's been some time in coming, but now, Saturn is looking to recapture its squandered brand aura. During the next few...
2007 Saturn Aura First DriveSaturn drills one deep into Japan's outfield
Saturn Aura – First Drive: People buy brands that make positive statements about who they are and how they live their lives. Regardless of socioeconomic...
2007 Saturn Aura PreviewA compelling new American sedan, that speaks with an accent
Having given Saturn up for dead long ago, American consumers buying cars wearing the red-ringed badge today are purchasing 1.) the deal, 2.)...
2007 Saturn Outlook PreviewSaturn seeks to steal sales with a positive Outlook
"Like always. Like never before." That's the new Saturn advertising slogan, meant to invoke memories of a pressure-free no-haggle sales...
Car Brief: 2007 Saturn Vue Green LineSaturn promises a $23,000 SUV that returns 32 mpg
Twelve or more. That's what General Motors executives claim will be available "in time" (translation – don't try to pin them down with any...
2007 Saturn Aura PreviewA better looking Pontiac G6/Chevrolet Malibu
General Motors' Vice President of Design, Ed Welburn, suggests that the Saturn Aura "clearly indicates the dynamic design language for Saturn." And as...
2005 Saturn Ion Quick SpinUpgraded to Average
IRVINE, Calif. – Salt is the bane of automobiles that toil within a day's drive of the 45th parallel. When it snows, this chemical is spread onto roadways to melt frozen...


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The Vampire Diaries: Exclusive Cast Scoop!
We talked to the cast of The Vampire Diaries at Comic-Con. Ready for some Season 6 scoop?
Posted in: Ian Somerhalder
Paul Wesley was born in New Brunswick, New Jersey.
He's appeared on a number of shows, foremost among them: Guiding Light, Smallville, The O.C. and Law & Order: Special Victims Unit.
Wesley has three siblings and was one of The CW's first choices for the role of Stefan on The Vampire Diaries.
|Stefan Salvatore
|The Vampire Diaries


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Ain't No Pain Like A Brett Favre INT
I'd somehow never seen this video before Will Leitch included it in his ranking of the decade's conference championship games. On the off chance you haven't either, remedy that: it's Brett Favre's game-killing interception against the Saints in 2010, spliced in with Vikings fans' histrionic reactions. It's the sort of… »


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Press release from CNW Group
Tuesday, February 15, 2011
INTACT FINANCIAL CORPORATION AGREES TO PURCHASE 140,000 OF ITS SHARES17:58 EST Tuesday, February 15, 2011TORONTO, Feb. 15 /CNW/ - Intact Financial Corporation (TSX : IFC) announced today that it has agreed to purchase for cancellation 140,000 of its outstanding common shares pursuant to a private agreement between Intact and an arm's length third party seller for an aggregate purchase price of $6.6 million which is at a discount to the current market price of Intact's common shares. The purchase was made under an issuer bid exemption order issued by the Ontario Securities Commission. The purchased shares will be included in calculating the maximum number of shares that Intact may purchase under its outstanding normal course issuer bid.About Intact Financial CorporationIntact Financial Corporation (www.intactfc.com) is the largest provider of property and casualty insurance in the country with $4.5 billion in premiums. Its 7,500 employees offer home, auto and business insurance under the Intact Insurance, Novex Group Insurance, belairdirect and Grey Power brands.For further information: Media Inquiries: Gilles Gratton Vice President, Corporate Communications +1 (416) 217-7206 firstname.lastname@example.com Inquiries: Dennis Westfall Director, Investor Relations +1 (416) 341-1464 ext. 45122 firstname.lastname@example.com


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PSA Empowers Integrators With Cybersecurity Solutions ExpertsPerhaps the most notable change to PSA-TEC was the inclusion of a new cybersecurity education track and a series of vendor cybersecurity solutions spotlight sessions. Find out what they had to share.
Latest in Interviews
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How can security dealers/integrators combat margin squeeze and product commoditization? PSA Security Network Vice President of Sales and Customer Service Ric McCullough answers this question and more on wholesale distribution. SSI Staff · February 14, 2014
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Garmin Forerunner 910XT
The Garmin Forerunner 910XT. You swim. You bike. You run. You obsess over data and details. So do we. And we've just perfected your new training partner. Forerunner 910XT is the only all-in-one, GPS-enabled device that provides detailed swim metrics and tracks distance, pace, elevation and heart rate for running and cycling. It sports a sleek profile, comfy wristband and an easy-to-read display.
SPECIFICATIONS of the Garmin Forerunner 910XT
- Unit dimensions: (W x H x D): 2.1" x 2.4" x 0.6" / 5.4 x 6.1 x 1.5 cm
- Display Size: (W x H): 1.3" x 0.8" / 3.3 x 2.0 cm
- Display Resolution: (W x H): 160 x 100 pixels
- Weight: 2.5 oz / 72 g
- Battery: Rechargeable lithium-ion
- Battery life: up to 20 hours
- High-sensitivity receiver
- Lap history: 1000 laps
- Waypoints: 100
- GPS enabled
- virtual racer
- Vibration alert
- Heart rate-based calorie computation
- Swim metrics (stroke type, stroke count and pool lengths
- Training effect
- Shock Resistant
- Water resistant
- Heart rate monitor
- Cadence sensor
- Foot Pod
- Automatic sync
- Garmin Connect compatible
- Virtual Partner
- Courses
- Auto Pause
- Auto Lap
- Auto Scroll
- Multi-sport
- Advanced workouts
- Pace alert
- Time/distance alert
- Interval training
- Customizable screens
- Barometric altimeter
- Power meter compatible
- Additional Specs: Garmin Connect is compatible with Windows XP or newer and PowerPC and Intel-based Mac running OS 10.4 or later with Safari
This item is NOT eligible for High Altitude Rewards Point bonuses, Rewards Promotions, or Affiliate Cash Back. Please don't hate us.
custy reviews
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it is soo nice not having to charge my gps watch every couple days as in the past. This watch lasts for over 20 hours with normal gps recording. The display is bold and readable. The vibration alerts are wonderful.. especially with headphones in. I love how easy it is to program an interval workout on the fly. If you are a runner, you will want to pair it with the footpod for improved instant pace accuracy. This is my only gripe, the instant gps pace isn't as accurate as the fr305 but the 910xt blows it away in every other aspect.
Ships FREE When will I get it?


text: Last year was a good year for building in the city of North Branch. At Monday's City Council meeting, North Branch building official Rich Meyer told the council 41 single-family units — which include houses and townhomes — were constructed in the city last year. That's the most the city has ...Read More