Parallel splitting solvers for the isogeometric analysis of the Cahn-Hilliard equation

Abstract

Modeling tumor growth in biological systems is a challenging problem with important consequences for diagnosis and treatment of various forms of cancer. This growth process requires large simulation complexity due to evolving biological and chemical processes in living tissue and interactions of cellular and vascular constituents in living organisms. Herein, we describe with a phase-field model, namely the Cahn-Hilliard equation the intricate interactions between the tumors and their host tissue. The spatial discretization uses highly-continuous isogeometric elements. For fast simulation of the time-dependent Cahn-Hilliard equation, we employ an alternating directions implicit methodology. Thus, we reduce the original problems to Kronecker products of 1?D matrices that can be factorized in a linear computational cost. The implementation enables parallel multi-core simulations and shows good scalability on shared-memory multi-core machines. Combined with the high accuracy of isogeometric elements, our method shows high efficiency in solving the Cahn-Hilliard equation on tensor-product meshes.     

C-terminal fragments of parathyroid hormone-related protein,PTHrP-(107-111) and (107-139), and the N-terminal PTHrP-(1-40) fragment stimulate membrane-associated protein kinase C activity in rat spleen lymphocytes

Membrane-associated protein kinase C (PKC) activity in lymphocytes freshly isolated from rat spleen was stimulated by the C-terminal parathyroid hormonerelated protein fragments, PTHrP-(107–111) and PTHrP-(107–139), at concentrations from 10^?3 to 10⁴ pM. By contrast, the same concentrations of PTHrP-(120–139), Without the 107–111 TRSAW (-Thr-Arg-Ser-Ala-Trp-) sequence of the other C terminal fragments, did not stimulate spleen lymphocyte PKC. Low concentrations of the N-terminal PTHrP-(1–40) fragment also stimulated membrane-associated PKC activity in the spleen lymphocytes. These results suggest that PTHrP might be an important physiological regulator of the immune response. Published 1994 Wiley-Liss, Inc.     

Permeabilization of the mitochondrial outer membrane by Bax/truncated Bid (tBid) proteins as sensitized by cardiolipin hydroperoxide translocation: mechanistic implications for the intrinsic pathway of oxidative apoptosis

Cytochrome c (cyt c) release upon oxidation of cardiolipin (CL) in the mitochondrial inner membrane (IM) under oxidative stress occurs early in the intrinsic apoptotic pathway. We postulated that CL oxidation mobilizes not only cyt c but also CL itself in the form of hydroperoxide (CLOOH) species. Relatively hydrophilic CLOOHs could assist in apoptotic signaling by translocating to the outer membrane (OM), thus promoting recruitment of the pro-apoptotic proteins truncated Bid (tBid) and Bax for generation of cyt c-traversable pores. Initial testing of these possibilities showed that CLOOH-containing liposomes were permeabilized more readily by tBid plus Ca(2+) than CL-containing counterparts. Moreover, CLOOH translocated more rapidly from IM-mimetic to OM-mimetic liposomes than CL and permitted more extensive OM permeabilization. We found that tBid bound more avidly to CLOOH-containing membranes than to CL counterparts, and binding increased with increasing CLOOH content. Permeabilization of CLOOH-containing liposomes in the presence of tBid could be triggered by monomeric Bax, consistent with tBid/Bax cooperation in pore formation. Using CL-null mitochondria from a yeast mutant, we found that tBid binding and cyt c release were dramatically enhanced by transfer acquisition of CLOOH. Additionally, we observed a pre-apoptotic IM-to-OM transfer of oxidized CL in cardiomyocytes treated with the Complex III blocker, antimycin A. These findings provide new mechanistic insights into the role of CL oxidation in the intrinsic pathway of oxidative apoptosis.     

Using spin-label electron paramagnetic resonance (EPR) to discriminate and characterize the cholesterol bilayer domain

Electron paramagnetic resonance (EPR) spin-labeling methods make it possible not only to discriminate the cholesterol bilayer domain (CBD) but also to obtain information about the organization and dynamics of cholesterol molecules in the CBD. The abilities of spin-label EPR were demonstrated for Chol/POPC (cholesterol/1-palmitoyl-2-oleoylphosphatidylcholine) membranes, with a Chol/POPC mixing ratio that changed from 0 to 3. Using the saturation-recovery (SR) EPR approach with cholesterol analogue spin labels, ASL and CSL, and oxygen or NiEDDA relaxation agents, it was confirmed that the CBD was present in all membrane suspensions when the mixing ratio exceeded the cholesterol solubility threshold (CST). Conventional EPR spectra of ASL and CSL in the CBD were similar to those in the surrounding POPC bilayer (which is saturated with cholesterol), indicating that in both domains, cholesterol exists in the lipid-bilayer-like structures. The behavior of ASL and CSL (and, thus, the behavior of cholesterol molecules) in the CBD was compared with that in the surrounding POPC-cholesterol domain (PCD). In the CBD, ASL and CSL molecules are better ordered than in the surrounding PCD. This difference is small and can be compared to that induced in the surrounding domain by an ∼10 °C decrease in temperature. Thus, cholesterol molecules are unexpectedly dynamic in the CBD, which should enhance their interaction with the surrounding domain. The polarity of the water/membrane interface of the CBD is significantly greater than that of the surrounding PCD, which significantly enhances penetration of the water-soluble relaxation agent, NiEDDA, into that region. Hydrophobicity measured in the centers of both domains is similar. The oxygen transport parameter (oxygen diffusion-concentration product) measured in the center of the CBD is about ten times smaller than that measured in the center of the surrounding domain. Thus, the CBD can form a significant barrier to oxygen transport. The results presented here point out similarities between the organization and dynamics of cholesterol molecules in the CBD and in the surrounding PCD, as well as significant differences between CBDs and cholesterol crystals.     

Effects of heme oxygenase-1 on induction and development of chemically induced squamous cell carcinoma in mice

Heme oxygenase-1 (HO-1) is an antioxidative and cytoprotective enzyme, which may protect neoplastic cells against anticancer therapies, thereby promoting the progression of growing tumors. Our aim was to investigate the role of HO-1 in cancer induction. Experiments were performed in HO-1^+/+, HO-1^+/−, and HO-1^−/− mice subjected to chemical induction of squamous cell carcinoma with 7,12-dimethylbenz[a]anthracene and phorbol 12-myristate 13-acetate. Measurements of cytoprotective genes in the livers evidenced systemic oxidative stress in the mice of all the HO-1 genotypes. Carcinogen-induced lesions appeared earlier in HO-1^−/− and HO-1^+/− than in wild-type animals. They also contained much higher concentrations of vascular endothelial growth factor and keratinocyte chemoattractant, but lower levels of tumor necrosis factor-α and interleukin-12. Furthermore, tumors grew much larger in HO-1 knockouts than in the other groups, which was accompanied by an increased rate of animal mortality. However, pathomorphological analysis indicated that HO-1^−/− lesions were mainly large but benign papillomas. In contrast, in mice expressing HO-1, most lesions displayed dysplastic features and developed to invasive carcinoma. Thus, HO-1 may protect healthy tissues against carcinogen-induced injury, but in already growing tumors it seems to favor their progression toward more malignant forms.     

Is it a good idea to train fillies and colts separately?

This study compared the physiological response to novel situations in sex-separated and sex-mixed groups of horses, as measured by heart rate (HR). The study evaluated the possibility of training horses in a mixed-sex system. The study included 41 Purebred Arabian 2?-year-olds during their first walk on an automated horse walker. Four groups, divided by manner of care and training, consisted of 10 colts and 10 fillies kept in separate stables and trained in separate male or female groups and 12 colts and 9 fillies kept in the same stable and trained together. The study measured HR when horses were at rest before exercise, while moving from stable to walker, during 30 min of exercise on walker, while moving from walker to stable, and at rest after exercise. Mean HR scores recorded from training on the walker were higher in sex-mixed groups. Results obtained while horses were moving from stable to walker, then from walker to stable, were significantly higher in the sex-mixed groups. The study did not recommend training young horses in sex-mixed groups.