An asymptotic preserving scheme for a tumor growth model of porous medium type

Mechanical models of tumor growth based on a porous medium approach have been attracting a lot of interest both analytically and numerically. In this paper, we study the stability properties of a finite difference scheme for a model where the density evolves down pressure gradients and the growth rate depends on the pressure and possibly nutrients. Based on the stability results, we prove the scheme to be asymptotic preserving (AP) in the incompressible limit. Numerical simulations are performed in order to investigate the regularity of the pressure. We study the sharpness of the $L^4$-uniform bound of the gradient, the limiting case being a solution whose support contains a bubble which closes-up in finite time generating a singularity, the so-called focusing solution.

Treatment of Bone Marrow Cancer Based on Model Predictive Control

Bone marrow is a spongy tissue that contains stem cells that are found inside some bones, including the hip and femur. Bone marrow cancer is a type of cancer that is caused by stem cells that make up the blood cells in the bone marrow. Sometimes these cells grow too fast or abnormally, which is called bone marrow cancer. Bone tissue cells are mainly composed of osteoblasts and osteoclasts. Osteoblast cells constantly build new bone throughout the life of each bone, and other cells called osteoclasts constantly absorb pieces of bone, so the bone is constantly being renewed. In this paper, mathematical models of tumors, the effect of the body on the drug, and the drug on the body are introduced, and then the appropriate dose of the drug to reduce tumor density is calculated using the model predictive control (MPC) algorithm. To obtain an adaptive MPC strategy, the extended least squares (ELS) method developed to learn the parameters of the tumor growth model is used. Finally, the simulation in MATLAB, assuming the model is correct, shows that the tumor is gone, and the bone mass improves over a period of time. The results demonstrate that the proposed method is effective for the treatment of bone marrow cancer.

SPDEF suppresses head and neck squamous cell carcinoma progression by transcriptionally activating NR4A1

SAM pointed domain containing E26 transformation-specific transcription factor (SPDEF) plays dual roles in the initiation and development of human malignancies. However, the biological role of SPDEF in head and neck squamous cell carcinoma (HNSCC) remains unclear. In this study, the expression level of SPDEF and its correlation with the clinical parameters of patients with HNSCC were determined using TCGA-HNSC, GSE65858, and our own clinical cohorts. CCK8, colony formation, cell cycle analysis, and a xenograft tumor growth model were used to determine the molecular functions of SPDEF in HNSCC. ChIP-qPCR, dual luciferase reporter assay, and rescue experiments were conducted to explore the potential molecular mechanism of SPDEF in HNSCC. Compared with normal epithelial tissues, SPDEF was significantly downregulated in HNSCC tissues. Patients with HNSCC with low SPDEF mRNA levels exhibited poor clinical outcomes. Restoring SPDEF inhibited HNSCC cell viability and colony formation and induced G0/G1 cell cycle arrest, while silencing SPDEF promoted cell proliferation in vitro. The xenograft tumor growth model showed that tumors with SPDEF overexpression had slower growth rates, smaller volumes, and lower weights. SPDEF could directly bind to the promoter region of NR4A1 and promoted its transcription, inducing the suppression of AKT, MAPK, and NF-κB signaling pathways. Moreover, silencing NR4A1 blocked the suppressive effect of SPDEF in HNSCC cells. Here, we demonstrate that SPDEF acts as a tumor suppressor by transcriptionally activating NR4A1 in HNSCC. Our findings provide novel insights into the molecular mechanism of SPDEF in tumorigenesis and a novel potential therapeutic target for HNSCC.

Water-Soluble Total Flavonoids Isolated from Isodon lophanthoides var. gerardianus (Benth.) H. Hara Promote Hepatocellular Carcinoma Sensitivity to 5-Fluorouracil

Isodon lophanthoides var. gerardianus (Benth.) H. Hara, a native medicinal plant produced chiefly across Southern China, is one of the mainstream varieties of Xihuangcao, which has long been applied in preventing and treating some common liver or gall diseases. Water-soluble total flavonoids (WSTF) extracted from folk herbal medicine have many pharmacological effects. The objective of the paper is to investigate the synergy of WSTF with 5-fluorouracil (5-FU) on HCC and the related mechanisms. Cells were exposed to WSTF alone or combination treatment with 5-FU. Then, in this study, we conducted cell viability test, cell cycle and clone forming test, apoptosis assay, reactive oxygen species (ROS), Western blotting, immunohistochemistry, and a xenograft tumor growth model for investigating the role of WSTF in HCC in vivo and in vitro. It was discovered that WSTF caused cell cycle arrest at the G0/G1 phase while increasing the ROS contents. The generation of ROS levels could cause cell apoptosis and inhibit colony formation. WSTF decreased the Bcl-2 level but promoted the Bax level. These showed the mitochondrial dependence of WSTF-mediated apoptosis. WSTF combined with 5-FU have a synergistic effect to significantly inhibit carcinogenicity in vivo and in vitro. The reduced ROS changed the synergy of WSTF with 5-FU. At last, WSTF inhibit the growth of HCC and promote the HCC sensitivity to 5-FU through ROS accumulation. WSTF-increased ROS levels may partially or completely contribute to enhanced toxicity. WSTF combined with 5-FU in HCC can play a synergistic effect when applied in the clinical setting.

Second-order analysis of an optimal control problem in a phase field tumor growth model with singular potentials and chemotaxis

This paper concerns a distributed optimal control problem for a tumor growth model of Cahn–Hilliard type including chemotaxis with possibly singular potentials, where the control and state variables are nonlinearly coupled. First, we discuss the weak well-posedness of the system under very general assumptions for the potentials, which may be singular and nonsmooth. Then, we establish the strong well-posedness of the system in a reduced setting, which however admits the logarithmic potential: this analysis will lay the foundation for the study of the corresponding optimal control problem. Concerning the optimization problem, we address the existence of minimizers and establish both first-order necessary and second-order sufficient conditions for optimality. The mathematically challenging second-order analysis is completely performed here, after showing that the solution mapping is twice continuously differentiable between suitable Banach spaces via the implicit function theorem. Then, we completely identify the second-order Fr ́echet derivative of the control-to-state operator and carry out a thorough and detailed investigation about the related properties.