Prognostic value of CT-PCI and CA-125 changes following neoadjuvant chemotherapy in advanced epithelial ovarian cancer: A retrospective study from Vietnam.

Ty Van Ngo: Writing – original draft, Writing – review & editing, Validation, Methodology, Investigation, Data curation, Formal analysis, Conceptualization. Luc Tien Dao: Writing – review & editing. Anh Dinh Tran: Writing – review & editing. Chinh Tri Le: Writing – review & editing. Hau Xuan Nguyen: Writing – review & editing, Writing – original draft, Supervision, Methodology, Conceptualization. Huyen Thi Phung: Writing – review & editing, Writing – original draft, Supervision, Methodology, Conceptualization.

A total of 96 patients with advanced epithelial ovarian cancer were included in the study. The clinical and tumor characteristics of the study population are summarized in Table 1 . The mean age at diagnosis was 59.17 ± 9.78 years. Most of the patients were before or perimenopausal (74.0 %), with 26.0 % being postmenopausal. Most patients had a good performance status, with 92.7 % having an Eastern Cooperative Oncology Group (ECOG) score of 0–1. The median body mass index (BMI) was 21.49 kg/m 2 , with a range of 14.91 to 35.67 kg/m 2 . Regarding tumor markers, the median CA-125 level at diagnosis was 1248 U/ml (IQR: 389.5–2855.5), and after neoadjuvant chemotherapy (NACT), the median level decreased significantly to 31.25 U/ml (IQR: 16.75–147.3). Post-treatment CA-125 levels were ≤ 35 U/ml in 51.0 % of patients. Table 1 Baseline characteristics of study patients (n = 96). All patients 96 (100) Age at diagnosis (years), Mean (SD) 59.17 (9.78) 

 Menopausal status, n (%)   Postmenopausal 71 (74.0)   Before/Perimenopausal 25 (26.0) 

 ECOG performance status, n (%)  ECOG 0–1 89 (92.7)  ECOG ≥ 2 6 (7.3) BMI (kg/m 2 ), Median (IQR) 21.49 (14.91 – 35.67) CA125 at diagnosis(U/ml), Median (IQR) 1248 (389.5 – 2855.5) CA 125 post-neoadjuvant chemotherapy (U/ml), Median (IQR) 31.25 (16.75 – 147.3)  ≤35 U/ml 49 (51.0)  >35 U/ml 47 (49.0) 

 FIGO stage, n (%)  IIIC 49 (51.0)  IV 47 (49.0) 

 Neoadjuvant chemotherapy regimen, n (%)  Paclitaxel-carboplatin every 3 weeks 90 (93.8)  Weekly paclitaxel-carboplatin 6 (6.2) No gross residual tumor, n (%) 81 (84.4) Note–Values are reported as median (interquartile range) or n (%), FIGO, International Federation of Gynecology and Obstetrics; PCI, peritoneal cancer index. Baseline characteristics of study patients (n = 96). Note–Values are reported as median (interquartile range) or n (%), FIGO, International Federation of Gynecology and Obstetrics; PCI, peritoneal cancer index. As for treatment, the majority received a standard paclitaxel-carboplatin regimen every 3 weeks (93.8 %), and a smaller subset received the weekly schedule. Following neoadjuvant therapy, 84.4 % achieved no gross residual disease (R0/R1), while 15.6 % had residual tumor after interval debulking surgery. PCI Score Before and After Neoadjuvant Chemotherapy. The distribution of CT PCI scores differed significantly between the pre-treatment and post-treatment phases. As shown in Fig. 1 , patients had markedly higher CT PCI scores before chemotherapy compared to after treatment. The median pre-treatment CT-PCI score was 14.0 (IQR: 7.0–19.0), which decreased to 4.0 (IQR: 2.0–8.0) post-treatment (p < 0.01, Wilcoxon Signed-Rank test). Fig. 1 Distribution of CT PCI scores and CT PCI scores before and after treatment Wilcoxon Signed-Rank testing, p < 0.01. Distribution of CT PCI scores and CT PCI scores before and after treatment Wilcoxon Signed-Rank testing, p < 0.01. A significant relationship was observed between after neoadjuvant chemotherapy CT PCI scores and the presence of residual tumors. As shown in Table 2 , patients without residual tumors had a significantly lower median post-treatment CT PCI score (4.0, IQR: 2.0–7.0) compared to those with residual tumors (7.0, IQR: 6.0–12.0), with a p-value of 0.01. However, pre-treatment CT PCI scores did not differ significantly between the groups (p = 0.22). Table 2 CT PCI scores and CT PCI scores before and after treatment by residual tumor. Residual tumor No Residual Tumour Residual Tumour Present p-value CT PCI score (pre-treatment) 13.0 (6.0 – 18.0) 18.0 (8.0 – 23.0) 0.22 CT PCI score (post) 4.0 (2.0 – 7.0) 7.0 (6.0 – 12.0) 0.01 CT PCI scores and CT PCI scores before and after treatment by residual tumor. In univariate logistic regression analysis ( Table 3 ), the post-treatment CT PCI score was significantly associated with residual tumor (cOR = 1.15; 95 % CI: 1.03–1.27; p = 0.01). Additionally, patients with CA-125 levels greater than 35 U/ml after neoadjuvant chemotherapy had a significantly higher likelihood of residual disease (cOR = 5.26; 95 % CI: 1.38–20.00; p = 0.02) compared to those with normalized CA-125 levels. Other variables, including PCI score before neoadjuvant chemotherapy, ΔPCI (change in PCI score), menopausal status, ECOG status, BMI, and tumor histology, did not show statistically significant associations. Table 3 Correlation between the CT PCI score with residual tumor. Parameter cOR (95 %CI) p-value CT PCI score (pre) 1.04 (0.97 – 1.12) 0.23 CT PCI score (post) 1.15 (1.03 – 1.27) 0.01 Δ CT PCI scores 0.98 (0.90 – 1.07) 0.48 Age at diagnosis 1.05 (0.98 – 1.12) 0.17 Menopausal status (Before/Perimenopausal) a 2.58 (0.54 – 12.33) 0.24 ECOG performance status (ECOG 0–1) a 2.33 (0.41 – 13.35) 0.34 BMI (kg/m 2 ) 0.88 (0.69 – 1.12) 0.28 CA125 at diagnosis(U/ml) 1.00 (0.99 – 1.00) 0.13 CA 125 post-neoadjuvant chemotherapy (U/ml) (≤35 U/ml) a 5.26 (1.38 – 33.00) 0.02 FIGO stage (III C) a 1.23 (0.41 – 3.71) 0.71 Neoadjuvant chemotherapy regimen (Paclitaxel-carboplatin every 3 weeks) a 1.09 (0.12 – 10.02) 0.94 FIGO, International Federation of Gynecology and Obstetrics; computed tomography-based Peritoneal Cancer Index (CT-PCI). a Reference group. Correlation between the CT PCI score with residual tumor. FIGO, International Federation of Gynecology and Obstetrics; computed tomography-based Peritoneal Cancer Index (CT-PCI). Reference group. Survival Outcomes and Predictors. As illustrated in Fig. 2 , the median overall survival (OS) was approximately 45 months, while the median progression-free survival (PFS) was around 28 months. The results of univariate Cox regression analysis are presented in Table 4 . None of the analyzed clinical or pathological parameters demonstrated statistically significant associations with either PFS or OS (all p > 0.05). Fig. 2 Overall survival and Progression-free survival. Table 4 Univariate regression analysis Hazard ratios (HR) of different clinical parameters for Progression-free survival and survival of patients. Variables Progression-free survival Overall survival HR (95 %CI) p HR (95 %CI) p CT PCI score (pre) 1.01 (0.96 – 1.07) 0.59 1.00 (0.96 – 1.05) 0.97 CT PCI score (post) 1.03 (0.96 – 1.11) 0.34 1.01 (0.94 – 1.08) 0.76 Δ CT PCI scores 0.99 (0.94 – 1.05) 0.90 0.97 (0.95 – 1.04) 0.89 Age at diagnosis 1.04 (0.99 – 1.10) 0.11 1.03 (0.99 – 1.07) 0.21 Menopausal status (Before/Perimenopausal a ) 4.54 (0.59 – 35.22) 0.15 1.85 (0.76 – 4.52) 0.18 ECOG performance status (ECOG 0–1) a 0.96 (0.12 – 7.45) 0.97 1.20 (0.36 – 4.00) 0.76 BMI (kg/m 2 ) 0.86 (0.64 – 1.15) 0.31 1.06 (0.91 – 1.23) 0.44 CA125 at diagnosis(U/ml) 0.99 (0.99 – 1.00) 0.11 0.99 (0.99 – 1/00) 0.62 CA 125 post-neoadjuvant chemotherapy (≤35 U/ml) a 0.85 (0.27 – 2.70) 1.19 (0.59 – 2.42) 0.63 FIGO stage (IIIC) a 0.47 (0.14 – 1.57) 0.22 0.89 (0.44 – 1.81) 0.75 Neoadjuvant chemotherapy regimen (Paclitaxel-carboplatin every 3 weeks) a − 0.62 (0.08 – 4.58) 0.64 a Reference group. Overall survival and Progression-free survival. Univariate regression analysis Hazard ratios (HR) of different clinical parameters for Progression-free survival and survival of patients. Reference group.

This study was approved by the Ethics Committee of Hanoi Medical University, Vietnam (IRB No. VN01001/IRB00003121). A waiver of informed consent was obtained, given the retrospective design. This retrospective study included ninety-six patients diagnosed with advanced epithelial ovarian cancer who underwent interval cytoreductive surgery following neoadjuvant chemotherapy at Hanoi Medical University Hospital and the National Cancer Hospital, Vietnam, between January 2019 and October 2024. Inclusion criteria were as follows: (1) histologically confirmed stage III or IV ovarian cancer; (2) age between 18 and 75 years; (3) completion of neoadjuvant chemotherapy and eligibility for interval debulking surgery; (4) serum CA-125 level > 35 U/mL during treatment; and (5) clinically stable condition with adequate performance status for surgery. Exclusion criteria included: (1) a history of severe comorbidities such as cardiovascular, hepatic, or renal failure; (2) pregnancy or lactation; (3) documented hypersensitivity to chemotherapeutic agents; (4) incomplete neoadjuvant chemotherapy regimen; and (5) presence of severe psychiatric disorders or inability to adhere to study procedures. The treatment process consisted of the following steps: • Administration of neoadjuvant chemotherapy: Patients received the Paclitaxel-Carboplatin regimen (Paclitaxel 175 mg/m 2 plus Carboplatin [AUC 5] intravenously every 3 weeks for three cycles, or Paclitaxel 60 mg/m 2 plus Carboplatin [AUC 2] weekly for 9 weeks). • Interval debulking surgery: Performed after completing neoadjuvant chemotherapy. Data on blood loss, duration of surgery, and postoperative condition were collected • Postoperative assessment: Conducted to record the remaining lesions after surgery and any associated complications. Optimal cytoreduction was defined as the absence of macroscopic residual disease (R0). Residual disease was categorized based on the largest diameter of the remaining tumor nodules: R1 for residual disease less than 1 cm, and R2 for residual disease 1 cm or greater. All interval debulking surgeries were performed by experienced gynecologic oncologists at Hanoi Medical University Hospital and the National Cancer Hospital. • Analysis: Performed to evaluate the correlation between changes in the CT-PCI score, CA-125 levels, and surgical outcomes. Administration of neoadjuvant chemotherapy: Patients received the Paclitaxel-Carboplatin regimen (Paclitaxel 175 mg/m 2 plus Carboplatin [AUC 5] intravenously every 3 weeks for three cycles, or Paclitaxel 60 mg/m 2 plus Carboplatin [AUC 2] weekly for 9 weeks). Interval debulking surgery: Performed after completing neoadjuvant chemotherapy. Data on blood loss, duration of surgery, and postoperative condition were collected Postoperative assessment: Conducted to record the remaining lesions after surgery and any associated complications. Optimal cytoreduction was defined as the absence of macroscopic residual disease (R0). Residual disease was categorized based on the largest diameter of the remaining tumor nodules: R1 for residual disease less than 1 cm, and R2 for residual disease 1 cm or greater. All interval debulking surgeries were performed by experienced gynecologic oncologists at Hanoi Medical University Hospital and the National Cancer Hospital. Analysis: Performed to evaluate the correlation between changes in the CT-PCI score, CA-125 levels, and surgical outcomes. CT-PCI Scoring: Pre- and post-NACT CT-PCI scores were assessed by two independent radiologists with specialized expertise in oncologic imaging at our institutions. To minimize bias, the radiologists performing the CT-PCI assessments were blinded to the patients' clinical outcomes (e.g., surgical findings, survival data). Initial CT-PCI assessments were conducted independently by each radiologist, and any discrepancies in scores were resolved through consensus discussion to reach a final CT-PCI score for each patient. CT-PCI scores were calculated based on the standardized 13-region Sugarbaker scoring system, where each abdominal and pelvic region is assigned a score from 0 to 3 based on the size of the largest tumor nodule within that region (0: no tumor, 1: nodules up to 0.5 cm, 2: nodules 0.5–5 cm, 3: nodules > 5 cm or confluent disease). The sum of scores from all 13 regions constitutes the total CT-PCI score, ranging from 0 to 39. CT Imaging Modality: All CT scans were performed using a multi-detector CT scanner. Standard protocols included intravenous administration of iodinated contrast medium. The scans were performed with a slice thickness of 5 mm. The timing of imaging was standardized: pre-NACT CT scans were performed within 7 days prior to the first NACT cycle, and post-NACT CT scans were performed within 7 days after the completion of the final NACT cycle. CA-125 Measurement: Serum CA-125 levels were measured at baseline (pre-NACT) and post-NACT using standard laboratory assays. The change in CA-125 (ΔCA-125) was calculated as the percentage reduction from baseline to post-NACT levels. The statistical analysis was performed using STATA version 18.0 (StataCorp LLC, College Station, TX, USA). Continuous variables were expressed as absolute numbers, mean ± standard deviation, or median and range. Categorical variables were expressed as absolute numbers and percentages. For categorical outcomes, chi-square (χ2) tests were used. The distribution of continuous outcomes was assessed with Mann–Whitney U tests and t-tests. Univariate logistic regression was used to analyze the association between the CT-PCI score and residual tumor. The Kaplan–Meier test was used for the survival analysis in terms of disease-free survival, and the statistical significance of the differences between the curves was assessed using the log-rank test. For all of the statistical tests, the threshold of significance was set at 5 %, and differences were considered significant if the probability of error was less than 5 % (p < 0.05).

The findings of this study highlight the utility of the CT-PCI as a non-invasive and standardized method for quantifying the peritoneal disease burden in patients with advanced EOC. CT-PCI is further demonstrated to serve as a valuable instrument for strategic preoperative planning in this patient cohort. The capacity to predict surgical outcomes through such indices is critical, facilitating enhanced patient selection for interval debulking surgery and optimizing the allocation of clinical resources. To build upon these findings and advance the clinical application of this approach, future research endeavours should focus on the external validation of these results. Additionally, exploring the seamless integration of cutting-edge imaging technologies and advanced machine learning algorithms holds considerable promise for further augmenting the predictive capacity and overall utility of CT-PCI.

This study aims to investigate the prognostic value of both CT-based Peritoneal Cancer Index (CT-PCI) and serum CA-125 kinetics in predicting optimal cytoreduction and survival outcomes in advanced epithelial ovarian cancer (EOC). Our findings indicate that both CT-PCI and CA-125 are strong prognostic markers in the context of neoadjuvant chemotherapy (NACT) followed by interval debulking surgery (IDS). We compare these results with those from existing studies, highlighting the contributions and limitations of our findings. The use of CT-PCI in ovarian cancer has been widely studied, particularly its role in assessing tumor burden and predicting resectability following NACT. In line with previous studies, we observed a significant reduction in CT-PCI scores post-NACT (median: 13.0 to 4.0, p < 0.01). This result is consistent with the study by ( Rawert et al., (2022 )), which reported a similar reduction in PCI scores following NACT and its correlation with achieving optimal cytoreduction (R0/R1). Our study further extends this finding by validating CT-PCI in a multicenter cohort of 96 patients from Vietnam, demonstrating its applicability in a low-resource setting. However, there are challenges in consistently applying CT-PCI as a prognostic marker. For instance, studies by Angeles et al. have highlighted that while PCI is a valuable tool for predicting resectability, there remains significant inter-observer variability in its assessment ( Angeles et al., 2021 ), particularly when it comes to scoring smaller nodules or assessing the peritoneal cavity in the presence of dense adhesions. These challenges underscore the importance of standardizing CT-PCI scoring systems and improving inter-rater reliability. While the reduction in PCI post-NACT in our study appears to be a reliable indicator of chemotherapy response, we acknowledge that this variability could affect its use in routine clinical practice unless further validation is conducted across different centers ( Sinukumar et al., 2024 , Armstrong et al., 2006 , Angeles et al., 2021 , Avesani et al., 2020 ). CA-125 is a widely used biomarker in the management of EOC, although its role as a predictor of chemotherapy efficacy and surgical outcomes remains debated. In this study, we found that CA-125 post-NACT was associated with optimal cytoreduction with OR = 5.26 (95 %CI: 1.38 – 33.00), p = 0.02, reinforcing findings from Lee and Li, who reported that a rapid decline in CA-125 is predictive of favorable surgical outcomes ( Li et al., 2024 ). However, CA-125 is not without its limitations. Its elevated levels are not exclusive to ovarian cancer, as it can also rise in benign conditions such as endometriosis or pelvic inflammatory disease. This lack of specificity is a well-known issue in clinical practice and has led to its limited utility as a standalone diagnostic tool. While our findings support CA-125 kinetics as a useful indicator of chemotherapy response, they also highlight the need to combine CA-125 with other markers, such as CT-PCI, to improve accuracy ( Li et al., 2024 , Charkhchi et al., 2020 , Chi et al., 2000 , Fagan et al., 2023 ). Several studies, including those by Dharmarajan and Charkhchi, have also pointed out that despite its association with chemotherapy response, CA-125 can fail to reflect tumor burden in some patients ( Charkhchi et al., 2020 , Dharmarajan et al., 2021 ), particularly those with mucinous or clear cell ovarian cancers. These histological subtypes often show less fluctuation in CA-125 levels, even when substantial changes in tumor burden are evident. This highlights an ongoing debate in the field regarding the adequacy of CA-125 alone as a prognostic marker and raises the question of whether other biomarkers or imaging techniques should be incorporated into routine clinical practice ( Li et al., 2024 , Akhavan et al., 2022 ). Previous studies indicated that combining imaging and serum biomarkers offers more reliable predictions of long-term outcomes. However, as pointed out by Engbersen, the majority of studies have focused on either imaging or serum biomarkers independently, with limited research on their synergistic use ( Akhavan et al., 2022 , Engbersen et al., 2021 ). Our study addresses this gap by demonstrating that the combination of these markers significantly improves prognostic accuracy and could inform clinical decisions about the timing and extent of surgery ( Berek et al., 1986 , Akhavan et al., 2022 , Lee et al., 2022 , Nakamura et al., 2020 ). Our findings add significantly to the accumulating evidence supporting multimodal strategies in oncology management and hold promising clinical applicability for enhancing patient outcomes . Despite the promising results, several challenges persist in integrating CT-PCI and CA-125 into routine clinical practice. The most significant challenge is the lack of standardization across studies. As mentioned, there is no universally agreed-upon cutoff for ΔCT-PCI, and the criteria for interpreting CA-125 levels vary among institutions. These inconsistencies complicate the application of these markers in clinical practice and highlight the need for more robust, multicenter studies with standardized methodologies ( Ghirardi et al., 2023 , Li et al., 2024 , Konstantinopoulos et al., 2020 , Yang et al., 2023 , González-Martín et al., 2023 ). Additionally, while our study demonstrated the usefulness of CT-PCI and CA-125 in predicting optimal cytoreduction, it is important to recognize that these markers cannot replace the clinician's judgment. Surgical resectability depends on various factors, including the patient's general health, performance status, and the extent of intra-abdominal adhesions. Future studies should focus on integrating CT-PCI, CA-125, and other potential biomarkers with clinical factors to develop a more holistic predictive model for optimal surgical planning. This study has several limitations. The retrospective design may introduce selection bias, and our findings are based on a two-center cohort from Vietnam, which may limit their generalizability to other populations. The relatively short follow-up period is another limitation, as we cannot assess the long-term impact of ΔCT-PCI and CA-125 on survival beyond PFS and OS. Moreover, our study did not incorporate molecular profiling or other genomic biomarkers, which may provide additional insight into treatment response and resistance mechanisms in advanced EOC. However, the contributions of this study are significant. We present evidence that CT-PCI and CA-125, both individually and in combination, can predict optimal cytoreduction in advanced EOC. Our study also provides new data on the clinical utility of these markers in a Vietnamese population, contributing to a broader understanding of their role in clinical decision-making, particularly in low-resource settings.

Epithelial ovarian cancer (EOC) remains the most lethal gynecological malignancy worldwide, primarily due to its asymptomatic progression during the early stages, leading to delayed diagnosis and poor prognosis. According to the GLOBOCAN 2020 database from the World Health Organization (WHO), ovarian cancer was responsible for approximately 313,959 new cases and 207,252 deaths globally, ranking as the eighth leading cause of cancer-related mortality among women ( Sung et al., 2021 ). The age-standardized incidence and mortality rates were 6.6 and 4.2 per 100,000 women, respectively, with an upward trend projected for the coming decades (WHO, 2020) ( Sung et al., 2021 ). Despite advancements in chemotherapy regimens and surgical techniques, the 5-year overall survival rate for EOC remains under 50 % in many populations ( Cabasag et al., 2022 , Siegel et al., 2022 ). This poor prognosis is particularly evident in patients diagnosed at FIGO stage III or IV, who account for over 70 % of all cases ( Sung et al., 2021 , Bacry et al., 2022 , Fagotti et al., 2020 , Makar et al., 2016 ). In these advanced stages, neoadjuvant chemotherapy (NACT) followed by interval debulking surgery (IDS) has emerged as a viable alternative to primary debulking surgery (PDS), particularly for patients with high tumor burdens, poor performance status, or unresectable disease. This treatment paradigm, endorsed by both the European Society for Medical Oncology (ESMO) and the National Comprehensive Cancer Network (NCCN), highlights the need for reliable preoperative tools to guide surgical decision-making and predict therapeutic efficacy ( ESMO, 2025 , Armstrong et al., 2022 , Armstrong et al., 2021 ). The Peritoneal Cancer Index (PCI), initially developed for gastrointestinal malignancies (e.g., pseudomyxoma peritonei, colorectal cancer) by Sugarbaker et al. ( Sugarbaker, 1995 ), has increasingly been applied in ovarian cancer for assessing peritoneal carcinomatosis ( Jacquet and Sugarbaker, 1996 ). While intraoperative PCI scoring provides valuable prognostic information, the non-invasive preoperative estimation of PCI via computed tomography (CT-PCI) has gained recognition as a practical method to evaluate tumor burden and predict surgical resectability ( Harmon and Sugarbaker, 2005 ). Recent studies have shown that a significant reduction in CT-PCI following NACT, defined as a decrease of ≥ 8.5, strongly correlates with the likelihood of achieving optimal cytoreduction (R0) and improved survival outcomes. Additionally, the change in PCI (ΔPCI) following NACT has been suggested as a dynamic marker of chemotherapy response and tumor regression ( Armstrong et al., 2006 , Angeles et al., 2021 , Avesani et al., 2020 , Rawert et al., 2022 , Sinukumar et al., 2024 ). Concurrently, CA-125, a well-established serum biomarker for EOC, plays a pivotal role in disease monitoring and treatment response assessment. While baseline CA-125 levels offer limited prognostic specificity, the changes in CA-125 levels during NACT have consistently shown promise as predictive indicators of treatment response ( Ghirardi et al., 2023 , Berek et al., 1986 , Li et al., 2024 ). However, despite the individual utility of both CT-PCI and CA-125, the combined prognostic value of these two dynamic markers—specifically focusing on their changes (ΔCT-PCI and ΔCA-125) following NACT—remains underexplored in predicting surgical outcomes and survival in advanced EOC. Existing literature often assesses these markers independently or focuses predominantly on baseline values rather than their dynamic shifts and potential synergistic prognostic capabilities ( Li et al., 2024 , Akhavan et al., 2022 , Charkhchi et al., 2020 , Chi et al., 2000 ). This study aims to to comprehensively evaluate the prognostic implications of changes in both CT-PCI scores and serum CA-125 levels following NACT in Vietnamese patients diagnosed with advanced-stage EOC and subsequently undergoing IDS. By integrating these two complementary dynamic markers—one reflecting anatomical tumor response and the other biochemical—this study aims to establish a more robust predictive model that can enhance clinical decision-making and facilitate optimized personalized treatment strategies for high-risk patients.

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.