A unified Bayesian inversion approach for a class of tumor growth models with different pressure laws

In this paper, we use the Bayesian inversion approach to study the data assimilation problem for a family of tumor growth models described by porous-medium type equations. The models contain uncertain parameters and are indexed by a physical parameter $m$, which characterizes the constitutive relation between density and pressure. Based on these models, we employ the Bayesian inversion framework to infer parametric and nonparametric unknowns that affect tumor growth from noisy observations of tumor cell density. We establish the well-posedness and the stability theories for the Bayesian inversion problem and further prove the convergence of the posterior distribution in the so-called incompressible limit, $m \rightarrow \infty$. Since the posterior distribution across the index regime $m\in[2,\infty)$ can thus be treated in a unified manner, such theoretical results also guide the design of the numerical inference for the unknown. We propose a generic computational framework for such inverse problems, which consists of a typical sampling algorithm and an asymptotic preserving solver for the forward problem. With extensive numerical tests, we demonstrate that the proposed method achieves satisfactory accuracy in the Bayesian inference of the tumor growth models, which is uniform with respect to the constitutive relation.Comment: 29 pages, 14 figure

Screening the Drug Sensitivity Genes Related to GEM and CDDP in the Lung Cancer Cell-lines

Background and objective Screening of small-cell lung cancer (SCLC) and non-small cell lung cancer (NSCLC) cell lines with gemcitabine hydrochloride (GEM) and cisplatin (CDDP) related to drug sensitivity gene might clarify the action mechanism of anti-cancer drugs and provide a new clue for overcoming drug resistance and the development of new anti-cancer drugs, and also provide theoretical basis for the clinical treatment of individual. Methods The drug sensitivity of CDDP and GEM in 4 SCLC cell lines and 6 NSCLC cell lines was determined using MTT colorimetric assay, while the cDNA macroarray was applied to detect the gene expression state related to drug sensitivity of 10 lung cancer cell line in 1 291, and the correlation between the two was analysized. Results There were 6 genes showing significant positive correlation (r≥0.632, P < 0.05) with GEM sensitivity; 45 genes positively related to CDDP; another 41 genes related to both GEM and CDDP (r≥± 0.4). Lung cancer with GEM and CDDP sensitivity of two types of drugs significantly related genes were Metallothinein (Signal transduction molecules), Cathepsin B (Organization protease B) and TIMP1 (Growth factor); the GEM, CDDP sensitivity associated genes of lung cancer cell lines mainly distributed in Metallothinein, Cathepsin B, growth factor TIMP1 categories. Conclusion There existed drug-related sensitive genes of GEM, CDDP in SCLC and NSCLC cell lines; of these genes, Metallothinein, Cathepsin B and TIMP1 genes presented a significant positive correlation with GEM drug sensitivity, a significant negative correlation with CDDP drug sensitivity