Trigonometry of spacetimes: a new self-dual approach to a curvature/signature (in)dependent trigonometry

A new method to obtain trigonometry for the real spaces of constant curvature and metric of any (even degenerate) signature is presented. The method encapsulates trigonometry for all these spaces into a single basic trigonometric group equation. This brings to its logical end the idea of an absolute trigonometry, and provides equations which hold true for the nine two-dimensional spaces of constant curvature and any signature. This family of spaces includes both relativistic and non-relativistic homogeneous spacetimes; therefore a complete discussion of trigonometry in the six de Sitter, minkowskian, Newton--Hooke and galilean spacetimes follow as particular instances of the general approach. Any equation previously known for the three classical riemannian spaces also has a version for the remaining six spacetimes; in most cases these equations are new. Distinctive traits of the method are universality and self-duality: every equation is meaningful for the nine spaces at once, and displays explicitly invariance under a duality transformation relating the nine spaces. The derivation of the single basic trigonometric equation at group level, its translation to a set of equations (cosine, sine and dual cosine laws) and the natural apparition of angular and lateral excesses, area and coarea are explicitly discussed in detail. The exposition also aims to introduce the main ideas of this direct group theoretical way to trigonometry, and may well provide a path to systematically study trigonometry for any homogeneous symmetric space.Comment: 51 pages, LaTe

Influence of chronic ocular hypertension on emmetropia: Refractive, structural and functional study in two rat models

Chronic ocular hypertension (OHT) influences on refraction in youth and causes glaucoma in adulthood. However, the origin of the responsible mechanism is unclear. This study analyzes the effect of mild-moderate chronic OHT on refraction and neuroretina (structure and function) in young-adult Long-Evans rats using optical coherence tomography and electroretinography over 24 weeks. Data from 260 eyes were retrospectively analyzed in two cohorts: an ocular normotension (ONT) cohort (20 mmHg), in which OHT was induced either by sclerosing the episcleral veins (ES group) or by injecting microspheres into the anterior chamber. A trend toward emmetropia was found in both cohorts over time, though it was more pronounced in the OHT cohort (p < 0.001), especially in the ES group (p = 0.001) and males. IOP and refraction were negatively correlated at week 24 (p = 0.010). The OHT cohort showed early thickening in outer retinal sectors (p < 0.050) and the retinal nerve fiber layer, which later thinned. Electroretinography demonstrated early supranormal amplitudes and faster latencies that later declined. Chronic OHT accelerates emmetropia in Long–Evans rat eyes towards slowly progressive myopia, with an initial increase in structure and function that reversed over time. © 2021 by the authors. Licensee MDPI, Basel, Switzerland

Neonatal brain-directed gene therapy rescues a mouse model of neurodegenerative CLN6 Batten disease

The neuronal ceroid lipofuscinoses (NCLs), more commonly referred to as Batten disease, are a group of inherited lysosomal storage disorders that present with neurodegeneration, loss of vision and premature death. There are at least 13 genetically distinct forms of NCL. Enzyme replacement therapies and pre-clinical studies on gene supplementation have shown promising results for NCLs caused by lysosomal enzyme deficiencies. The development of gene therapies targeting the brain for NCLs caused by defects in transmembrane proteins has been more challenging and only limited therapeutic effects in animal models have been achieved so far. Here, we describe the development of an adeno-associated virus (AAV)-mediated gene therapy to treat the neurodegeneration in a mouse model of CLN6 disease, a form of NCL with a deficiency in the membrane-bound protein CLN6. We show that neonatal bilateral intracerebroventricular injections with AAV9 carrying CLN6 increase lifespan by more than 90%, maintain motor skills and motor coordination and reduce neuropathological hallmarks of Cln6-deficient mice up to 23 months post vector administration. These data demonstrate that brain-directed gene therapy is a valid strategy to treat the neurodegeneration of CLN6 disease and may be applied to other forms of NCL caused by transmembrane protein deficiencies in the future

Novel use of plga microspheres to create an animal model of glaucoma with progressive neuroretinal degeneration

Progressive degeneration of neuroretinal tissue with maintained elevated intraocular pressure (IOP) to simulate chronic glaucoma was produced by intracameral injections of poly (lactic-co-glycolic) acid (PLGA) microspheres (Ms) in rat eyes. The right eye of 39 rats received different sizes of PLGA-Ms (2 µL suspension; 10% w/v): 14 with 38–20 µm Ms (Ms38/20 model) and 25 with 20–10 µm particles (Ms20/10 model). This novel glaucoma animal model was compared to the episcleral vein sclerosis (EPI) model (25 eyes). Injections were performed at baseline, two, four and six weeks. Clinical signs, IOP, retina and optic nerve thicknesses (using in vivo optical coherence tomography; OCT), and histological studies were performed. An IOP increment was observed in all three groups, however, the values obtained from the PLGA-Ms injection resulted lower with a better preservation of the ocular surface. In fact, the injection of Ms20/10 created a gentler, more progressive, and more sustained increase in IOP. This IOP alteration was correlated with a significant decrease in most OCT parameters and in histological ganglion-cell count for the three conditions throughout the eight-week follow-up. In all cases, progressive degeneration of the retina, retinal ganglion cells and optic nerve, simulating chronic glaucoma, was detected by OCT and corroborated by histological study. Results showed an alternative glaucoma model to the well-known episcleral vein model, which was simpler to perform, more reproducible and easier to monitor in vivo

Chronic glaucoma using biodegradable microspheres to induce intraocular pressure elevation. Six-month follow-up

Background: To compare two prolonged animal models of glaucoma over 24 weeks of follow-up. A novel pre-trabecular model of chronic glaucoma was achieved by injection of biodegradable poly lactic-co-glycolic acid (PLGA) microspheres (10–20 µm) (Ms20/10) into the ocular anterior chamber to progressively increase ocular hypertension (OHT). Methods: Rat right eyes were injected to induce OHT: 50% received a suspension of Ms20/10 in the anterior chamber at 0, 2, 4, 8, 12, 16 and 20 weeks, and the other 50% received a sclerosing episcleral vein injection biweekly (EPIm). Ophthalmological clinical signs, intraocular pressure (IOP), neuroretinal functionality measured by electroretinography (ERG), and structural analysis of the retina, retinal nerve fiber layer (RNFL) and ganglion cell layer (GCL) protocols using optical coherence tomography (OCT) and histological exams were performed. Results: Both models showed progressive neuroretinal degeneration (p < 0.05), and contralateral eye affectation. The Ms20/10 model showed a more progressive increase in IOP and better preservation of ocular surface. Although no statistical differences were found between models, the EPIm showed a tendency to produce thicker retinal and thinner GCL thicknesses, slower latency and smaller amplitude as measured using ERG, and more aggressive disturbances in retinal histology. In both models, while the GCL showed the greatest percentage loss of thickness, the RNFL showed the greatest and earliest rate of thickness loss. Conclusions: The intracameral model with biodegradable microspheres resulted more like the conditions observed in humans. It was obtained by a less-aggressive mechanism, which allows for adequate study of the pathology over longer periods. © 2021 by the authors. Licensee MDPI, Basel, Switzerland

CRB2 completes a fully expressed Crumbs complex in the Retinal Pigment Epithelium

The CRB proteins CRB1, CRB2 and CRB3 are members of the cell polarity complex Crumbs in mammals that together with Scribble and Par complexes stablish the polarity of a variety of cell types. Although many members of the Crumbs complex proteins are expressed in the retinal pigment epithelium (RPE), and even though the mRNA of CRB2 has been detected in ARPE-19 cells and in the RPE/Choroid, to date no CRB protein has yet been found in this tissue. To investigate this possibility, we generated an antibody that specifically recognize the mouse CRB2 protein, and we demonstrate the expression of CRB2 in mouse RPE. Confocal analysis shows that CRB2 is restricted to the apicolateral membrane of RPE cells, and more precisely, in the tight junctions. Our study identified CRB2 as the member of the CRB protein family that is present together with the rest of the components of the Crumbs complex in the RPE apico-lateral cell membrane. Considering that the functions of CRB proteins are decisive in the establishment and maintenance of cell-cell junctions in several epithelial-derived cell types, we believe that these findings are a relevant starting point for unraveling the functions that CRB2 might perform in the RPE

Quimioterapia complementaria del cáncer de mama; experiencia de la Clínica Universitaria de Navarra

Desde 1982 a 1989 se han tratado 68 pacientes con carcinoma de mama. 57 han sido premenopáusicas y 11 postmenopáusicas. El estadio tumoral más frecuente ha sido T2N1 (44,1 %) seguido de T1N1 (20,6 %). La dosis media de quimioterapia recibida ha sido de 91,2 %, 88 % y 94 % para la ciclofosfamida, metotrexate y 5-fluorouracilo respectivamente. El tratamiento ha sido bien tolerado, siendo la toxicidad más frecuente la hematológica (leucopenia). Las pacientes premenopáusicas han presentado un intervalo libre de enfermedad de 89,4 % a 96 meses y las postmenopáusicas de 63,3 % a 68 meses. No se han observado diferencias en el intervalo libre de enfermedad según el tamaño del primario o la positividad del tumor a receptores de estrógeno o progesterona. Los factores pronósticos más importantes de esta serie han sido el número de ganglios axilares afectos y la dosis de quimioterapia recibid