Bolytrope orders

Bolytropes are bounded subsets of an affine building that consist of all points that have distance at most $r$ from some polytrope. We prove that the points of a bolytrope describe the set of all invariant lattices of a bolytrope order, generalizing the correspondence between polytropes and graduated orders.Comment: Minor revisions according to referee's suggestions. To appear in International Journal of Number Theor

Tropical invariants for binary quintics and reduction types of Picard curves

In this paper, we express the reduction types of Picard curves in terms of tropical invariants associated to binary quintics. These invariants are connected to Picard modular forms using recent work by Cl{\'e}ry and van der Geer. We furthermore give a general framework for tropical invariants associated to group actions on arbitrary varieties. The previous problem fits in this general framework by mapping the space of binary forms to symmetrized versions of the Deligne--Mumford compactification $\bar{M}_{0,n}$. We conjecture that the techniques introduced here can be used to find tropical invariants for binary forms of any degree

Valued rank-metric codes

In this paper, we study linear spaces of matrices defined over discretely valued fields and discuss their dimension and minimal rank drops over the associated residue fields. To this end, we take first steps into the theory of rank-metric codes over discrete valuation rings by means of skew algebras derived from Galois extensions of rings. Additionally, we model projectivizations of rank-metric codes via Mustafin varieties, which we then employ to give sufficient conditions for a decrease in the dimension.Comment: 33 page

Vertical bone regeneration with synthetic biomimetic calcium phosphate onto the calvaria of rats

Bone regeneration is often required to provide adequate oral rehabilitation before dental implants. Vertical ridge augmentation is the most challenging of all situations, and often requires the use of autologous bone grafting. However, autologous bone grafting induces morbidity, and the harvestable bone is limited in quantity. Alternatives to autologous bone grafting include bovine-bone-derived biomaterials, which provide good clinical results and synthetic bone substitutes that still fail to provide a reliable clinical outcome. Synthetic biomimetic calcium phosphate (SBCP) biomaterials, consisting of precipitated apatite crystals that resemble in composition and crystallinity to the mineral phase of bone, arise as alternatives to both bovine bone and the current sintered bone substitutes. This study aims to compare the vertical bone regeneration capacity of the SBCP (MimetikOss, Mimetis Biomaterials) with that of a deproteinized bovine bone matrix (DBBM, Bio-Oss®; Geistlich Biomaterials) on the calvaria of rats. To model vertical bone augmentation, hemispherical cups were filled with the two types of biomaterial granules and implanted onto the skull of rats, while empty cups were used as controls. After 4 and 8 weeks of healing, bone growth was determined by microcomputed tomography and histomorphometry. After 4 weeks of implantation, a significantly higher bone growth was found in the case of SBCP compared with DBBM and left empty controls. At 8 weeks, no statistically significant differences were found between the two bone substitutes. These results are promising since vertical bone regeneration was faster in the case of SBCP than for DBBM.Peer ReviewedPostprint (author's final draft

Computed tomography and histological evaluation of xenogenic and biomimetic bone grafts in three-wall alveolar defects in minipigs

Objectives This study aimed to compare the performance of a xenograft (XG) and a biomimetic synthetic graft (SG) in three-wall alveolar defects in minipigs by means of 3D computerised tomography and histology. Materials and methods Eight minipigs were used. A total of eight defects were created in the jaw of each animal, three of which were grafted with XGs, three with SGs, and two were left empty as a negative control. The allocation of the different grafts was randomised. Four animals were euthanised at 6 weeks and four at 12 weeks. The grafted volume was then measured by spiral computed tomography to assess volume preservation. Additionally, a histological analysis was performed in undecalcified samples by backscattered scanning electron microscopy and optical microscopy after Masson’s trichrome staining. Results A linear mixed-effects model was applied considering four fixed factors (bone graft type, regeneration time, anatomic position, and maxilla/mandible) and one random factor (animal). The SG exhibited significantly larger grafted volume (19%) than the XG. The anterior sites preserved better the grafted volume than the posterior ones. Finally, regeneration time had a positive effect on the grafted volume. Histological observations revealed excellent osseointegration and osteoconductive properties for both biomaterials. Some concavities found in the spheroidal morphologies of SGs were associated with osteoclastic resorption. Conclusions Both biomaterials met the requirements for bone grafting, i.e. biocompatibility, osseointegration, and osteoconduction. Granule morphology was identified as an important factor to ensure a good volume preservation. Clinical relevance Whereas both biomaterials showed excellent osteoconduction, SGs resulted in better volume preservation.Peer ReviewedPostprint (author's final draft

Accelerated hardening of nanotextured 3D-plotted self-setting calcium phosphate inks

Direct ink writing (DIW) techniques open up new possibilities for the fabrication of patient-specific bone grafts. Self-setting calcium phosphate inks, which harden at low temperature, allow obtaining nanostructured scaffolds with biomimetic properties and enhanced bioactivity. However, the slow hardening kinetics hampers the translation to the clinics. Different hydrothermal treatments for the consolidation of DIW scaffolds fabricated with an a-tricalcium phosphate /pluronic F127 ink were explored, comparing them with a biomimetic treatment. Three different scaffold architectures were analysed. The hardening process, associated to the conversion of a-tricalcium phosphate to hydroxyapatite was drastically accelerated by the hydrothermal treatments, reducing the time for complete reaction from 7¿days to 30 minutes, while preserving the scaffold architectural integrity and retaining the nanostructured features. ß-tricalcium phosphate was formed as a secondary phase, and a change of morphology from plate-like to needle-like crystals in the hydroxyapatite phase was observed. The binder was largely released during the treatment. The hydrothermal treatment resulted in a 30% reduction of the compressive strength, associated to the residual presence of ß-tricalcium phosphate. Biomimetic and hydrothermally treated scaffolds supported the adhesion and proliferation of rat mesenchymal stem cells, indicating a good suitability for bone tissue engineering applications. Statement of Significance 3D plotting has opened up new perspectives in the bone regeneration field allowing the customisation of synthetic bone grafts able to fit patient-specific bone defects. Moreover, this technique allows the control of the scaffolds’ architecture and porosity. The present work introduces a new method to harden biomimetic hydroxyapatite 3D-plotted scaffolds which avoids high-temperature sintering. It has two main advantages: i) it is fast and simple, reducing the whole fabrication process from the several days required for the biomimetic processing to a few hours; and ii) it retains the nanostructured character of biomimetic hydroxyapatite and allows controlling the porosity from the nano- to the macroscale. Moreover, the good in vitro cytocompatibility results support its suitability for cell-based bone regeneration therapiesPeer ReviewedPostprint (author's final draft

Regeneration of segmental defects in metatarsus of sheep with vascularized and customized 3D-printed calcium phosphate scaffolds

Although autografts are considered to be the gold standard treatment for reconstruction of large bone defects resulting from trauma or diseases, donor site morbidity and limited availability restrict their use. Successful bone repair also depends on sufficient vascularization and to address this challenge, novel strategies focus on the development of vascularized biomaterial scaffolds. This pilot study aimed to investigate the feasibility of regenerating large bone defects in sheep using 3D-printed customized calcium phosphate scaffolds with or without surgical vascularization. Pre-operative computed tomography scans were performed to visualize the metatarsus and vasculature and to fabricate customized scaffolds and surgical guides by 3D printing. Critical-sized segmental defects created in the mid-diaphyseal region of the metatarsus were either left empty or treated with the 3D scaffold alone or in combination with an axial vascular pedicle. Bone regeneration was evaluated 1, 2 and 3 months post-implantation. After 3 months, the untreated defect remained non-bridged while the 3D scaffold guided bone regeneration. The presence of the vascular pedicle further enhanced bone formation. Histology confirmed bone growth inside the porous 3D scaffolds with or without vascular pedicle inclusion. Taken together, this pilot study demonstrated the feasibility of precised pre-surgical planning and reconstruction of large bone defects with 3D-printed personalized scaffolds.Peer ReviewedPostprint (published version

Osteoinduction by foamed and 3D-printed calcium phosphate scaffolds: effect of nanostructure and pore architecture

Some biomaterials are osteoinductive, that is, they are able to trigger the osteogenic process by inducing the differentiation of mesenchymal stem cells to the osteogenic lineage. Although the underlying mechanism is still unclear, microporosity and specific surface area (SSA) have been identified as critical factors in material-associated osteoinduction. However, only sintered ceramics, which have a limited range of porosities and SSA, have been analyzed so far. In this work, we were able to extend these ranges to the nanoscale, through the foaming and 3D-printing of biomimetic calcium phosphates, thereby obtaining scaffolds with controlled micro- and nanoporosity and with tailored macropore architectures. Calcium-deficient hydroxyapatite (CDHA) scaffolds were evaluated after 6 and 12 weeks in an ectopic-implantation canine model and compared with two sintered ceramics, biphasic calcium phosphate and ß-tricalcium phosphate. Only foams with spherical, concave macropores and not 3D-printed scaffolds with convex, prismatic macropores induced significant ectopic bone formation. Among them, biomimetic nanostructured CDHA produced the highest incidence of ectopic bone and accelerated bone formation when compared with conventional microstructured sintered calcium phosphates with the same macropore architecture. Moreover, they exhibited different bone formation patterns; in CDHA foams, the new ectopic bone progressively replaced the scaffold, whereas in sintered biphasic calcium phosphate scaffolds, bone was deposited on the surface of the material, progressively filling the pore space. In conclusion, this study demonstrates that the high reactivity of nanostructured biomimetic CDHA combined with a spherical, concave macroporosity allows the pushing of the osteoinduction potential beyond the limits of microstructured calcium phosphate ceramics.Peer ReviewedPostprint (author's final draft

Cementos de fosfato tricálcico sustituidos con silicio: estudio de la bioactividad y de la liberacion de iones

Doble titulacióEl presente proyecto, que estudia un cemento de fosfato de calcio dopado con silicio y lo compara con el cemento análogo sin dopar, se divide en dos partes. En la primera, se evalúa la bioactividad de ambos cementos in vitro, y en la segunda se estudia la liberación de iones de dichos cementos en distintos medios ampliamente utilizados en el campo de los biomateriales para realizar estudios in vitro. En todo el proyecto se ha hecho especial hincapié en el papel que juega el silicio en los procesos estudiados. Ambos cementos han sido preparados a partir de fosfato tricálcico alfa (α-TCP), cuya reacción de fraguado resulta en la formación de hidroxiapatita. En el caso del cemento dopado con silicio, el fosfato tricálcico alfa contiene este ión (Si-α-TCP) y la hidroxiapatita resultante puede incorporar parcialmente el silicio en su estructura (Si-HA). El estudio de bioactividad in vitro consiste en evaluar si los materiales cumplirían uno de los requisitos principales para que puedan crear un enlace directo con el hueso en el momento de ser implantados in vivo. Dicho requisito consiste en la formación de una capa de apatita, similar a la del hueso, en la superficie del material después de su implantación un ser vivo. Para predecir este fenómeno, los cementos fraguados fueron sumergidos en un fluido corporal simulado (SBF) durante distintos tiempos, entre 6 horas y 68 días, con la intención de observar la evolución de la capa de apatita en su superficie. Se observó la evolución del cemento fraguado y la formación la capa apatítica formada en cuanto a las fases cristalinas presentes, la cristalinidad de la capa, la variación de peso, la morfología de las superficies y la composición atómica. Se ha observado que, a partir de los 14 días de inmersión en el fluido corporal simulado, se forma una capa de apatita con una menor cristalinidad que el cemento fraguado en el caso de la Si-HA. En cambio, no se ha podido identificar claramente la formación de la capa de apatita en el caso de la HA, a pesar que su variación de peso indique un proceso de precipitación o adsorción de materia, probablemente minerales que podrían depositarse en la porosidad abierta del material. En resumen, se ha comprobado que el cemento de Si-HA tiene una mayor bioactividad que el cemento de HA. En la segunda parte del proyecto se ha realizado un estudio in vitro de la liberación de iones de ambos cementos fraguados, empleando cuatro medios que son comúnmente utilizados para realizar estudios in vitro con biomateriales. Dichos medios son: fluido corporal simulado (SBF), solución tampón de fosfatos (PBS), medio de cultivos celulares (McCoys) y agua destilada. Los cementos fraguados estuvieron inmersos en cada uno de los medios entre 6h y 21 días, y se cuantificaron las concentraciones de iones de Ca2+, P5+ y Si4+. Se destacó que ambos cementos tienen un comportamiento muy similar respecto a las concentraciones de Ca2+ y P5+. Con respecto al ion silicio se observó concentraciones muy similares en el caso de los reactivos y de la Si-HA lo que despierta una sospecha en cuanto a la integración parcial del silicio en la red cristalina de la Si-HA. Este hecho parece indicar la presencia de un compuesto similar al SiO2 de partida. Finalmente comentar que la presencia de Si4+ argumenta a favor de un mecanismo activo de mejora de la bioactividad teniendo un efecto sobre las células del entorno y que parece favorecer la formación de la capa apatítica