The Semi Implicit Gradient Augmented Level Set Method

Here a semi-implicit formulation of the gradient augmented level set method is presented. By tracking both the level set and it's gradient accurate subgrid information is provided,leading to highly accurate descriptions of a moving interface. The result is a hybrid Lagrangian-Eulerian method that may be easily applied in two or three dimensions. The new approach allows for the investigation of interfaces evolving by mean curvature and by the intrinsic Laplacian of the curvature. In this work the algorithm, convergence and accuracy results are presented. Several numerical experiments in both two and three dimensions demonstrate the stability of the scheme.Comment: 19 Pages, 14 Figure

Biofilm-induced bioclogging produces sharp interfaces in hyporheic flow, redox conditions, and microbial community structure

Riverbed sediments host important biogeochemical processes that play a key role in nutrient dynamics. Sedimentary nutrient transformations are mediated by bacteria in the form of attached biofilms. The influence of microbial metabolic activity on the hydrochemical conditions within the hyporheic zone is poorly understood. We present a hydrobiogeochemical model to assess how the growth of heterotrophic and autotrophic biomass affects the transport and transformation of dissolved nitrogen compounds in bedform-induced hyporheic zones. Coupling between hyporheic exchange, nitrogen metabolism, and biomass growth leads to an equilibrium between permeability reduction and microbial metabolism that yields shallow hyporheic flows in a region with low permeability and high rates of microbial metabolism near the stream-sediment interface. The results show that the bioclogging caused by microbial growth can constrain rates and patterns of hyporheic fluxes and microbial transformation rate in many streams

MRI of Neuronal Recovery After Low-Dose Methamphetamine Treatment of Traumatic Brain Injury in Rats

We assessed the effects of low dose methamphetamine treatment of traumatic brain injury (TBI) in rats by employing MRI, immunohistology, and neurological functional tests. Young male Wistar rats were subjected to TBI using the controlled cortical impact model. The treated rats (n = 10) received an intravenous (iv) bolus dose of 0.42 mg/kg of methamphetamine at eight hours after the TBI followed by continuous iv infusion for 24 hrs. The control rats (n = 10) received the same volume of saline using the same protocol. MRI scans, including T2-weighted imaging (T2WI) and diffusion tensor imaging (DTI), were performed one day prior to TBI, and at 1 and 3 days post TBI, and then weekly for 6 weeks. The lesion volumes of TBI damaged cerebral tissue were demarcated by elevated values in T2 maps and were histologically identified by hematoxylin and eosin (H&E) staining. The fractional anisotropy (FA) values within regions-of-interest (ROI) were measured in FA maps deduced from DTI, and were directly compared with Bielschowsky’s silver and Luxol fast blue (BLFB) immunohistological staining. No therapeutic effect on lesion volumes was detected during 6 weeks after TBI. However, treatment significantly increased FA values in the recovery ROI compared with the control group at 5 and 6 weeks after TBI. Myelinated axons histologically measured using BLFB were significantly increased (p,0.001) in the treated group (25.8461.41%) compared with the control group (17.0562.95%). Significant correlations were detected between FA and BLFB measures in the recovery ROI (R = 0.54, p,0.02). Methamphetamine treatment significantly reduced modified neurological severity scores from 2 to 6 weeks (p,0.05) and foot-fault errors from 3 days to 6 weeks (p,0.05) after TBI. Thus, the FA data suggest that methamphetamine treatment improves white matter reorganization from 5 to 6 weeks after TBI in rats compared with saline treatment, which may contribute to the observed functional recovery

Mesenchymal stromal cells’ therapy for polyglutamine disorders: where do we stand and where should we go?

Polyglutamine (polyQ) diseases are a group of inherited neurodegenerative disorders caused by the expansion of the cytosine-adenine-guanine (CAG) repeat. This mutation encodes extended glutamine (Q) tract in the disease protein, resulting in the alteration of its conformation/physiological role and in the formation of toxic fragments/aggregates of the protein. This group of heterogeneous disorders shares common molecular mechanisms, which opens the possibility to develop a pan therapeutic approach. Vast efforts have been made to develop strategies to alleviate disease symptoms. Nonetheless, there is still no therapy that can cure or effectively delay disease progression of any of these disorders. Mesenchymal stromal cells (MSC) are promising tools for the treatment of polyQ disorders, promoting protection, tissue regeneration, and/or modulation of the immune system in animal models. Accordingly, data collected from clinical trials have so far demonstrated that transplantation of MSC is safe and delays the progression of some polyQ disorders for some time. However, to achieve sustained phenotypic amelioration in clinics, several treatments may be necessary. Therefore, efforts to develop new strategies to improve MSC's therapeutic outcomes have been emerging. In this review article, we discuss the current treatments and strategies used to reduce polyQ symptoms and major pre-clinical and clinical achievements obtained with MSC transplantation as well as remaining flaws that need to be overcome. The requirement to cross the blood-brain-barrier (BBB), together with a short rate of cell engraftment in the lesioned area and low survival of MSC in a pathophysiological context upon transplantation may contribute to the transient therapeutic effects. We also review methods like pre-conditioning or genetic engineering of MSC that can be used to increase MSC survival in vivo, cellular-free approaches-i.e., MSC-conditioned medium (CM) or MSC-derived extracellular vesicles (EVs) as a way of possibly replacing the use of MSC and methods required to standardize the potential of MSC/MSC-derived products. These are fundamental questions that need to be addressed to obtain maximum MSC performance in polyQ diseases and therefore increase clinical benefits.Portuguese Foundation for Science and Technology: SFRH/BD/148877/2019; CENTRO01-0145-FEDER-000008 CENTRO-01-0145FEDER-022095 POCI-01-0145-FEDER-016719 POCI-01-0145-FEDER-029716 POCI01-0145-FEDER-016807 POCI-01-0145-FEDER016390 UID4950/2020 CENTRO-01-0145-FEDER-022118info:eu-repo/semantics/publishedVersio

Another look at velocity extensions in the level set method

Abstract. The level set method [8] has become a widely used numerical method for moving interfaces, e.g. see the many examples in [11, 7]. For many applications, the velocity of the interface is known only on the interface, while the level set method requires information about the interface speed at least in a neighborhood of grid points near the interface. To address this issue, velocity extensions are used to map the velocity information on the interface into the rest of the computational domain [2]. This allows the level set method to proceed. The velocity extension method presented in [2] uses the fast marching method [12, 13], and is only a first order approximation for the velocity field near the interface. Furthermore, it can lead to unexpected behavior in some cases. This is primarily due to the strictly local solution for the characteristics of the flow near the interface. In this paper, we look more closely at the characteristics near the interface, and then present a modified velocity extension method, also based on the fast marching method, which handles the characteristcs more accurately. In turn, this new method will lead to some interesting new possibilities for the fast marching method

Flow under Curvature: Singularity Formation, Minimal Surfaces, and Geodesics

this paper extends the technology in several directions. In Section 3.1 we study the collapse of a surface under motion by mean curvature. In [Sethian 1989] it was shown experimentally that the handle of a dumbbell pinches off, splitting the dumbbell into two surfaces, each of which collapses to a point. Here we show that an extension of this problem produces an interesting result: a multi-armed dumbbell leaves a separate, residual closed object at the center after the singularity forms. We verify this by studying a series of similar numerical problems, each showing this detached surface. In Section 3.2 we briefly consider flow under Gaussian curvature. In Section 4 we use the level set approach to generate minimal surfaces attached to a given onedimensional closed curve (wire frame) in

Modeling how soluble microbial products (SMP) support heterotrophic bacteria in autotroph-based biofilms

International audienceMulti-species biofilm modeling has been used for many years to understand the interactions between species in different biofilm systems, but the complex symbiotic relationship between species is sometimes overlooked, because models do not always include all relevant species and components. In this paper, we develop and use a mathematical model to describe a model biofilm system that includes autotrophic and heterotrophic bacteria and the key products produced by the bacteria. The model combines the methods of earlier multi-species models with a multi-component biofilm model in order to explore the interaction between species via exchange of soluble microbial products (SMP). We show that multiple parameter sets are able to describe the findings of experimental studies, and that heterotrophs growing on autotrophically produced SMP may pursue either r- or K-strategies to sustain themselves when SMP is their only substrate. We also show that heterotrophs can colonize some distance from the autotrophs and still be sustained by autotrophically produced SMP. This work defines the feasible range of parameters for utilization of SMP by heterotrophs and the nature of the interactions between autotrophs and heterotrophs in multi-species, multi-component biofilms