Bone remodeling as a spatial evolutionary game

Ryser, Marc D.; Murgas, Kevin A.

doi:10.1016/j.jtbi.2017.01.021

Cited by 19 publications

(27 citation statements)

References 58 publications

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“…Este proceso equilibrado, permite la renovación tanto el cortical como el trabecular (Ryser & Murgas, 2017). Para iniciar la renovación, se cuenta con un mecanismo capaz de detectar y localizar las partes dañadas para removerlas y reemplazarlas con tejido óseo nuevo, restaurando su micro y macro arquitectura (Qing & Wang, 2012).…”

Section: La Remodelación óSeaunclassified

“…Esto sugiere que la remodelación ósea responde a mantener su resistencia, reemplazando al hueso dañado por nuevo para prevenir la acumulación de daños (Badilatti, Christen, & Parkinson, 2016) el propósito del remodelado es la reparación del hueso, entonces las células deben responder a señales debido al daño que se está presentando. Uno de los enfoques más aceptado indica que el hueso, por medio del remodelado óseo, se adapta a las condiciones de carga a las cuales es expuesto, lo cual implica que tiene sensores internos que miden las cargas internas traduciéndolas en señales que activan a células capaces de reabsorber o formar hueso, desde hace ya algunos años se ha demostrado como las células pueden detectar las cargas mecánicas y como estas son trasformadas en señales celulares (Ayati, Edwards, & Webb, 2010), (Ryser & Murgas, 2017). Existen evidencias experimentales mostrando que independientemente de los puntos de vista sobre la remodelación ósea, existe un estímulo que incita a la remodelación.…”

Section: La Remodelación óSeaunclassified

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La mecánica del hueso. Una revisión de los modelos de remodelación óseo

Rentería

Domı́nguez

Cruz-Avilés

et al. 2018

ESCS

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ResumenEl hueso, al igual que las demás estructuras biológicas se adaptan continuamente a su entorno físico, se ha aceptado ampliamente que el tejido óseo responde a la estimulación mecánica, se reabsorbe en regiones expuestas a estímulos mecánicos de baja intensidad, mientras que se renueva donde estos son altos. Se cree que el proceso de adaptación permite al hueso realizar sus funciones mecánicas con un mínimo de masa. A partir de esta idea muchos modelos teóricos para la remodelación ósea utilizan este concepto como parte de la estrategia para simular la adaptación estructural ósea. Lo que implican la existencia de un estado de equilibrio donde la estructura ósea se adapta al medio ambiente. Esto ha dado origen al desarrollo de modelos computacionales que, por una parte, suponen una estructura trabecular isotrópica, cuyos resultados muestran las similitudes en la distribución de densidad del hueso in vivo, aun así se considera que no es posible obtener una solución convergente, por otra parte se han desarrollado modelos considerando la naturaleza anisotrópica del hueso trabecular en el nivel continuo haciendo uso de los principios de optimización; Sin embargo, a pesar de las similitudes con el comportamiento real, los modelos, representan simplemente una abstracción matemática de la arquitectura trabecular. El objetivo de este trabajo es mostrar los modelos de adaptación ósea que emplean una aproximación matemáticos para caracterizar las propiedades mecánicas de la estructura del hueso.Palabras clave: Hueso, estímulo, remodelado óseo, densidad de energía de deformación AbstractThe bone as biological structure is continually adapting to changes in their physical environment, it has been widely accepted that bone respond to mechanical stimulation, tissue is resorbed in regions exposed to low mechanical stimulus, whereas new bone is deposited where the stimulus is high. This process of adaptation is thought to enable bone to perform its mechanical functions with a minimum of mass. From this idea, many theoretical models for bone remodeling use this concept as part of the strategy to simulate bone structural adaptation. What implies the existence of an equilibrium state where the bone structure is adapted to the environment. That is the origin to develop of computational models were, on one hand, the assumption of isotropy of the trabecular structure is made. The results show the similarities in density distribution with in vivo bone, as well as a convergent solution cannot be obtained. To another part, models have been developed to consider the anisotropic nature of the trabecular bone in the continuum level making use of optimization principles;

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Section: La Remodelación óSeaunclassified

La mecánica del hueso. Una revisión de los modelos de remodelación óseo

Rentería

Domı́nguez

Cruz-Avilés

et al. 2018

ESCS

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“…10. In many cases the behavior of the spatial game differs from that of the replicator equation, so it is important to consider the impact of spatial structure in order to obtain correct conclusions.…”

Section: Ecology Applied Mathematicsmentioning

confidence: 99%

Spatial evolutionary games with weak selection

Nanda

Durrett

2017

Proc. Natl. Acad. Sci. U.S.A.

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Recently, a rigorous mathematical theory has been developed for spatial games with weak selection, i.e., when the payoff differences between strategies are small. The key to the analysis is that when space and time are suitably rescaled, the spatial model converges to the solution of a partial differential equation (PDE). This approach can be used to analyze all 2 × 2 games, but there are a number of 3 × 3 games for which the behavior of the limiting PDE is not known. In this paper, we give rules for determining the behavior of a large class of 3 × 3 games and check their validity using simulation. In words, the effect of space is equivalent to making changes in the payoff matrix, and once this is done, the behavior of the spatial game can be predicted from the behavior of the replicator equation for the modified game. We say predicted here because in some cases the behavior of the spatial game is different from that of the replicator equation for the modified game. For example, if a rock-paper-scissors game has a replicator equation that spirals out to the boundary, space stabilizes the system and produces an equilibrium.cancer modeling | public goods game | bone cancer | rock-paper-scissors E volutionary games are often studied by assuming that the population is homogeneously mixing, i.e., each individual interacts equally with all the others. In this case, the frequencies of strategies evolve according to the replicator equation. See, e.g., Hofbauer and Sigmund's book (1). If ui is the frequency of players using strategy i, thenwhere Fi = j Gi,j uj is the fitness of strategy i, Gi,j is the payoff for playing strategy i against an opponent who plays strategy j , andF = i ui Fi is the average fitness. The homogeneous mixing assumption is not satisfied for the evolutionary games that arise in ecology or modeling solid cancer tumors, so it is important to understand how spatial structure changes the outcome of games. The goal of this paper is to facilitate applications of spatial evolutionary games by giving rules to determine the limiting behavior of a large class of 3 × 3 games. Our spatial games will take place on the 3D integer lattice Z 3 . The theory (2, 3) has been developed under the assumption that the interactions between an individual and its neighbors are given by an irreducible probability kernel p(x ) on Z 3 with p(0) = 0, that is finite range, symmetric p(x ) = p(−x ), and has covariance matrix σ 2 I . Here we will restrict our attention to the nearest neighbor case, in which p(x ) = 1/6 for x = (1, 0, 0), (−1, 0, 0), . . . (0, 0, −1).To describe the dynamics we let ξt (x ) be the strategy used by the individual at x at time t and letbe the fitness of x at time t. In birth-death dynamics, site x gives birth at rate ψt (x ) and sends its offspring to replace the individual at y with probability p(y − x ). In death-birth dynamics, the individual at x dies at rate 1 and is replaced by a copy of the one at y with probability proportional to p(y − x )ψt (y). The theory developed in ref. 3 can be applied...

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“…A remodelação óssea é um processo fisiológico contínuo, complexo e necessário para a manutenção e adaptação do esqueleto saudável que envolve interações multicelulares, sinalização bioquímica e estímulos mecânicos (Robling et al, 2006;Ryser;Murgas, 2017).…”

Section: Lista De Abreviaturas E Siglasunclassified

“…Os osteoblastos são células de origem mesenquimal, responsáveis pela síntese e secreção dos componentes orgânicos da matriz óssea (Mackie, 2003;Arana-Chavez;Bradaschia, 2012). Além disso, funcionam como transmissores de sinais para a remodelação, um fenômeno que engloba formação e reabsorção óssea McDonald, 2011;Ryser;Murgas, 2017).…”

Section: Introductionunclassified

Análise in vitro da citotoxicidade em osteoblastos de dispositivos poliméricos incorporados com antimicrobianos para uso local

Lage¹

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Lage TC. In vitro analysis of cytotoxicity in osteoblasts of polymer devices incorporated with antimicrobials for local use [dissertation] São Paulo: Universidade de São Paulo, Faculdade de Odontologia; 2017. Versão Corrigida. Osteoblasts are mesenquima originated cells, which are involved in the bone formation. These cells may suffer alterations due to traumas, interventions and infeccions. The infections can be minimized by the handling of antimicrobials. Poly (L-lactide) or PLLA is a synthetic polymer known for its biocompatibility and absorption, which can be used as a local pharmacological releaser, as an alternative to the systemic antimicrobial therapy. This polymer also can be frequently used as a supporting structure to cellular matrix in the bone tissue engineering as it can be used for support in repair and regeneration. The particle incorporation in this polymer can create side effects, therefore, we need to certificate that the polymeric device incorporated with antimicrobials are not cytotoxic. Proposition: Analyse the structure and cytotoxicity in osteoblasts of PLLA polymeric devices associated with antimicrobials, being them: Amoxicillin, Azithromycin, Clindamycin and Metronidazole. Methods: For this study 270 polymerical devices were manufactured with 6mm diameter of PLLA with a 20% antimicrobials incorporation of Amoxicillin (AM), Azithromycin (AZ), Clindamycin (CL) and Metronidazole (ME) that have been produced through two methods: eletrospinning (mesh) or casting (film). Afterwards a MTT cytotoxicity test was made over the periods of 24, 48 and 72 hours of experiment. To make a structural analysis of the device a macroscopic analysis was performed through photographs and microscopic imaging with scanning electron microscope (SEM). Results: The cytotoxicity reaction exhibited that meshes and films incorporated with antimicrobials are comparable with the osteoblasts culture, indicating that there was no cytotoxicity in any moment (p < 0.05). In the phothograph we could observe that the devices showed a similar coloration among the meshes and different coloration for the films depending on the incorporated antimicrobial. The SEM analysis displayed a difference in the surface appearance of the films. The AM films displayed an irregular and porous appearance, meanwhile, AZ looked smooth with few grains, the CL and ME have rough surfaces and PLLA presents smooth surfaces. As for the meshes, we noticed that all the samples had microfibers and pores that mimic the extracellular matrix, differing only in the thickness of the fibers. Osteoblasts were present in all films but AM did not induce proliferation, with only isolated cells emerging. In meshes osteoblasts were only found in AM, ME and PLLA. Conclusion: Polymeric devices made with PLLA incorporated with antimicrobials can be used in bone repair and regeneration given that they did not offer cytotoxicity for osteoblasts.

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Bone remodeling as a spatial evolutionary game

Cited by 19 publications

References 58 publications

La mecánica del hueso. Una revisión de los modelos de remodelación óseo

La mecánica del hueso. Una revisión de los modelos de remodelación óseo

Spatial evolutionary games with weak selection

Análise in vitro da citotoxicidade em osteoblastos de dispositivos poliméricos incorporados com antimicrobianos para uso local

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