An Analysis of Finite Difference and Galerkin Techniques Applied to the Simulation of Advection and Diffusion of Air Pollutants from a Line Source

A finite difference and a Galerkin type scheme are compared with reference to a very accurate solution describing time dependent advection and diffusion of air pollutants from a line source in an atmosphere vertically stratified and limited by an inversion layer. The accurate solution was achieved by applying the finite difference scheme on a very refined grid with a very small time step. Grid size and time step were defined according to stability and accuracy criteria discussed in the text. It is found that for the problem considered, the two methods can be considered equally accurate. However, the Galerkin method gives larger areas of small errors close to the source, This was assumed to be partly due to the different way the source term is taken into account by the two methods. An improvement of the accuracy of the finite difference scheme was achieved by approximating, at every step, the contribution of the source term by a Gaussian puff moving and diffusing with velocity and diffusivity of the source location, instead of utilizing a stepwise function for the numerical approximation of the delta function representing the source term

El antígeno de células neoplásicas escamosas (SCCA) solo o formando el complejo SCCA-igM es un biomarcador precoz de carcinoma hepatocelular.

Background: Hepatocellular carcinoma (HCC) represents more than 90% of primary liver cancers and is a major health problem. Every year more than 6.7 million deaths and 10.9 million new cancer cases were diagnosed. Early detection of HCC still is difficult due to the lack of adequate biomarkers that show high sensitivity and specificity. Currently, alpha-fetoprotein (AFP) is the most commonly used biomarker, but only 50-70% of patients affected by HCC have high levels of AFP, which is also difficult to distinguish HCC early stage of other diseases. The SerpinB3, the squamous cell carcinoma antigen (SCCA) is overexpressed in liver cancer and circulating SCCA-IgM complexes have been described in patients with HCC. Current screening programs for all cirrhotics are controversial and a personalized screening is an unmet need in the precision medicine era. Aim: To know long-term predictive accuracy of SCCA and SCCA-IgM alone or together with AFP in early diagnosis of HCC. To determine the role of SCCA-IgM predicting long-term appearance of HCC. Methods: After a systematic review of the relevant studies, the sensitivity, specificity, positive and negative likelihood ratios, diagnostic odds ratio (DOR) and area under curve (AUC) for the diagnosis of HCC were pooled using bivariate meta-analysis. Hierarchic summary receiver operating characteristic curves were used to summarize the overall test performance. Bivariate boxplots were used to confirm whether the threshold effect existed. A Fagan nomogram was used to assess the clinical utility. Heterogeneity was explored by sensitivity analysis, univariable meta-regression and subgroup analysis. Patients: Two-hundred and three cirrhotic patients (Child A 74.9%, B 21.2%, C 3.9%) were followed-up prospectively every six months to screen HCC by ultrasound and AFP according to EASL guidelines. The estimation cohort was obtained from Italy (30.5%; 62/203) and validation cohort from Spain (69.5%; 141/203). Patients underwent to evaluate SCCA-IgM by ELISA (Hepa-IC, Xeptagen, Venice, Italy). Patients were followed-up for 60 months, being censored at the time of the appearance of HCC. Results: Eleven studies that had HCC diagnosis as their purpose were ultimately included in the quantitative analysis. The summary estimates were as follows: SCCA [AUC: 0.80 (95% CI: 0.76 - 0.83)] and SCCA-IgM [AUC: 0.77 (95% CI: 0.74 - 0.83)] demonstrated similar diagnostic performance, while a combination of AFP and SCCA-IgM had an AUC of 0.90 (95% CI: 0.87 - 0.92) and a DOR of 22.87 (95% CI: 8.38 – 62.40). Meta-regression showed that patient selection, cut-off values, reference standards and tumor biopsy as the diagnostic method significantly influenced the heterogeneity of the included studies. There were 10.8% and 23.1% of two- and five-year follow up of HCC development. Patients with HCC showed higher levels of SCCA-IgM than those without it (425.72 ± 568.33 AU/ml vs. 195.93 ± 188.40 AU/ml, p = 0.009) during the five-year follow-up. In multivariate analysis, after adjusting by age, sex and AST, the following factors were independently associated with HCC: SCCA-IgM (HR 1.001 95% CI 1.000 - 1.002; p = 0.003), AFP (HR 1.028 95% CI 1.009 - 1.046; p = 0.003) and creatinine (HR 1.564 95% CI 1.151 - 2.124; p = 0.004). The log-rank test of the combination resulted in a 7.488 (p = 0.024) in the estimation cohort and 11.061 (p = 0.004) in the validation cohort, and 100% of correctly classified rate in both cohorts to identify low-risk group patients in two-year of follow-up. Conclusion: Both SCCA and SCCA-IgM showed a moderate diagnostic accuracy for HCC screening; the combination of SCCA-IgM and AFP is the best diagnostic option. We have constructed a predictive model based on the combination of SCCA-IgM and AFP that enhanced the predictive value for detecting HCC followed by tailored HCC surveillance for individual patients, especially to identify patients with low-risk.Antecedentes: El carcinoma hepatocelular (CHC) representa más del 90% de los cánceres primarios de hígado y constituye un problema de salud mundial. La detección temprana de CHC todavía es difícil debido a la falta de biomarcadores adecuados que muestren una alta sensibilidad y especificidad. En la actualidad, la alfa-fetoproteína (AFP) es el biomarcador más utilizado, pero solo el 50-70% de los pacientes afectados por CHC presentan niveles elevados de AFP. El antígeno de carcinoma de células escamosas (SCCA) se sobre-expresa en el cáncer de hígado e inmuno-complejos circulantes SCCA-IgM se han descrito en pacientes con CHC. El actual programa de vigilancia de CHC recomendado por la guía de práctica clínica "one-size fits all" para la detección temprana de tumores es controvertido en la era de la medicina de precisión. Objetivos: 1) Realizamos un meta-análisis para evaluar el rendimiento diagnóstico de SCCA y SCCA-IgM y de ambos combinados con alfa-fetoproteína. 2) Validamos el papel de la SCCA-IgM en la predicción del riesgo de hepatocarcinoma a largo plazo en pacientes con cirrosis hepática. Métodos: Después de una revisión sistemática de los estudios pertinentes, se combinaron la sensibilidad, la especificidad, las razones de verosimilitud positiva y negativa, la odds ratio de diagnóstico (DOR) y el área debajo de la curva (AUC) para el diagnóstico de CHC mediante el meta-análisis bivariado. Las curvas características operativas del receptor resumido jerárquico se usaron para resumir el rendimiento general de la prueba. Los diagramas de caja bivariados se usaron para confirmar si el efecto umbral existía. Se utilizó un nomograma de Fagan para evaluar la utilidad clínica. La heterogeneidad se exploró mediante análisis de sensibilidad, meta-regresión univariante y análisis de subgrupos. Pacientes: Se incluyeron 203 pacientes cirróticos (Child A 74,9%, B 21,2%, C 3,9%) seguidos prospectivamente cada seis meses para detectar el CHC por ultrasonido de acuerdo con las guías EASL. La cohorte de estimación se obtuvo de Italia (30,5%; 62/203) y la cohorte de validación de España (69,5%; 141/203). Los pacientes fueron sometidos a evaluación de SCCA-IgM por ELISA (Hepa-IC, Xeptagen, Venecia, Italia). Los pacientes fueron seguidos durante 60 meses, siendo censurados en el momento de la aparición del CHC. Resultados: Once estudios que tenían el diagnóstico de CHC como objetivo principal se incluyeron finalmente en el análisis cuantitativo. Las estimaciones resumidas fueron las siguientes: SCCA [AUC: 0,80 (IC 95%: 0,76-0,83)] y SCCA-IgM [AUC: 0,77 (IC 95%: 0,74-0,83)] mostraron un rendimiento diagnóstico similar, mientras que una combinación de AFP y SCCA-IgM tuvieron un AUC de 0,90 (IC del 95%: 0,87-0,92) y un DOR de 22,87 (IC del 95%: 8,38 - 62,40). La meta regresión mostró que la selección del paciente, los valores de corte, los estándares de referencia y la biopsia tumoral como método de diagnóstico influyeron significativamente en la heterogeneidad de los estudios incluidos. Hubo un 10.8% y 23,1% de desarrollo de CHC a dos y cinco años de seguimiento. Los pacientes con CHC mostraron niveles más altos de SCCA-IgM que los que no (425,72 ± 568,33 AU / ml frente a 195,93 ± 188,40 AU / ml, p = 0,009) durante el seguimiento de cinco años. En el análisis multivariado, después de ajustar por edad, sexo y AST, los siguientes factores se asociaron independientemente con CHC: SCCA-IgM (HR 1,001 IC 95% 1,000 - 1,002; p = 0,003), AFP (HR 1,028 IC 95% 1,009 - 1,046; p = 0,003) y creatina (HR 1,564 IC 95% 1,151 - 2,124; p = 0,004). La prueba de log-rank de la combinación mostró un valor de 7,488 (p = 0,024) en la cohorte de estimación y 11,061 (p = 0,004) en la cohorte de validación y una tasa del 100% de pacientes correctamente clasificados al identificar el grupo de bajo riesgo a dos años de seguimiento. Conclusión: Tanto los niveles de SCCA como de SCCA-IgM mostraron una precisión diagnóstica moderada para el cribado de CHC; la combinación de SCCA-IgM y AFP es la mejor opción de diagnóstico. SCCA-IgM podría representar un nuevo biomarcador para CHC a largo plazo. Hemos construido un modelo predictivo de la combinación de SCCA-IgM y AFP que mejoró el valor predictivo para detectar CHC seguido de una vigilancia de CHC adaptada para pacientes individuales, especialmente para identificar pacientes con bajo riesgo