TY - JOUR A1 - Omori, Toshihiro A1 - Winter, Katja A1 - Shinohara, Kyosuke A1 - Hamada, Hiroshi A1 - Ishikawa, Takuji T1 - Simulation of the nodal flow of mutant embryos with a small number of cilia BT - comparison of mechanosensing and vesicle transport hypotheses JF - Royal Society Open Science N2 - Left-right (L-R) asymmetry in the body plan is determined by nodal flow in vertebrate embryos. Shinohara et al. (Shinohara K et al. 2012 Nat. Commun. 3, 622 (doi:10.1038/ncomms1624)) used Dpcd and Rfx3 mutant mouse embryos and showed that only a few cilia were sufficient to achieve L-R asymmetry. However, the mechanism underlying the breaking of symmetry by such weak ciliary flow is unclear. Flow-mediated signals associated with the L-R asymmetric organogenesis have not been clarified, and two different hypotheses-vesicle transport and mechanosensing-are now debated in the research field of developmental biology. In this study, we developed a computational model of the node system reported by Shinohara et al. and examined the feasibilities of the two hypotheses with a small number of cilia. With the small number of rotating cilia, flow was induced locally and global strong flow was not observed in the node. Particles were then effectively transported only when they were close to the cilia, and particle transport was strongly dependent on the ciliary positions. Although the maximum wall shear rate was also influenced by ciliary position, the mean wall shear rate at the perinodal wall increased monotonically with the number of cilia. We also investigated the membrane tension of immotile cilia, which is relevant to the regulation of mechanotransduction. The results indicated that tension of about 0.1 mu Nm(-1) was exerted at the base even when the fluid shear rate was applied at about 0.1 s(-1). The area of high tension was also localized at the upstream side, and negative tension appeared at the downstream side. Such localization may be useful to sense the flow direction at the periphery, as time-averaged anticlockwise circulation was induced in the node by rotation of a few cilia. Our numerical results support the mechanosensing hypothesis, and we expect that our study will stimulate further experimental investigations of mechanotransduction in the near future. KW - nodal flow KW - left-right asymmetry KW - boundary element method KW - fluid-structure interaction Y1 - 2018 U6 - https://doi.org/10.1098/rsos.180601 SN - 2054-5703 VL - 5 IS - 8 PB - Royal Society CY - London ER - TY - GEN A1 - Omori, Toshihiro A1 - Winter, Katja A1 - Shinohara, Kyosuke A1 - Hamada, Hiroshi A1 - Ishikawa, Takuji T1 - Simulation of the nodal flow of mutant embryos with a small number of cilia BT - comparison of mechanosensing and vesicle transport hypotheses T2 - Postprints der Universität Potsdam : Mathematisch Naturwissenschaftliche Reihe N2 - Left-right (L-R) asymmetry in the body plan is determined by nodal flow in vertebrate embryos. Shinohara et al. (Shinohara K et al. 2012 Nat. Commun. 3, 622 (doi:10.1038/ncomms1624)) used Dpcd and Rfx3 mutant mouse embryos and showed that only a few cilia were sufficient to achieve L-R asymmetry. However, the mechanism underlying the breaking of symmetry by such weak ciliary flow is unclear. Flow-mediated signals associated with the L-R asymmetric organogenesis have not been clarified, and two different hypotheses-vesicle transport and mechanosensing-are now debated in the research field of developmental biology. In this study, we developed a computational model of the node system reported by Shinohara et al. and examined the feasibilities of the two hypotheses with a small number of cilia. With the small number of rotating cilia, flow was induced locally and global strong flow was not observed in the node. Particles were then effectively transported only when they were close to the cilia, and particle transport was strongly dependent on the ciliary positions. Although the maximum wall shear rate was also influenced by ciliary position, the mean wall shear rate at the perinodal wall increased monotonically with the number of cilia. We also investigated the membrane tension of immotile cilia, which is relevant to the regulation of mechanotransduction. The results indicated that tension of about 0.1 mu Nm(-1) was exerted at the base even when the fluid shear rate was applied at about 0.1 s(-1). The area of high tension was also localized at the upstream side, and negative tension appeared at the downstream side. Such localization may be useful to sense the flow direction at the periphery, as time-averaged anticlockwise circulation was induced in the node by rotation of a few cilia. Our numerical results support the mechanosensing hypothesis, and we expect that our study will stimulate further experimental investigations of mechanotransduction in the near future. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1056 KW - nodal flow KW - left-right asymmetry KW - boundary element method KW - fluid-structure interaction Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-468734 SN - 1866-8372 IS - 1056 ER - TY - THES A1 - Metz, Malte T1 - A quasi-dynamic and self-consistent rupture model to simulate earthquake ruptures N2 - Dynamic earthquake rupture modeling provides information on the rupture physics as the rupture velocity, frictions or tractions acting during the rupture process. Nevertheless, as often based on spatial gridded preset geometries, dynamic modeling is depending on many free parameters leading to both a high non-uniqueness of the results and large computation times. That decreases the possibilities of full Bayesian error analysis. To assess the named problems we developed the quasi-dynamic rupture model which is presented in this work. It combines the kinematic Eikonal rupture model with a boundary element method for quasi-static slip calculation. The orientation of the modeled rupture plane is defined by a previously performed moment tensor inversion. The simultanously inverted scalar seismic moment allows an estimation of the extension of the rupture. The modeled rupture plane is discretized by a set of rectangular boundary elements. For each boundary element an applied traction vector is defined as the boundary value. For insights in the dynamic rupture behaviour the rupture front propagation is calculated for incremental time steps based on the 2D Eikonal equation. The needed location-dependent rupture velocity field is assumed to scale linearly with a layered shear wave velocity field. At each time all boundary elements enclosed within the rupture front are used to calculate the quasi-static slip distribution. Neither friction nor stress propagation are considered. Therefore the algorithm is assumed to be “quasi-static”. A series of the resulting quasi-static slip snapshots can be used as a quasi-dynamic model of the rupture process. As many a priori information is used from the earth model (shear wave velocity and elastic parameters) and the moment tensor inversion (rupture extension and orientation) our model is depending on few free parameters as the traction field, the linear factor between rupture and shear wave velocity and the nucleation point and time. Hence stable and fast modeling results are obtained as proven from the comparison to different infinite and finite static crack solutions. First dynamic applications show promissing results. The location-dependent rise time is automatically derived by the model. Different simple kinematic models as the slip-pulse or the penny-shaped crack model can be reproduced as well as their corresponding slip rate functions. A source time function (STF) approximation calculated from the cumulative sum of moment rates of each boundary element gives results similar to theoretical and empirical known STFs. The model was also applied to the 2015 Illapel earthquake. Using a simple rectangular rupture geometry and a 2-layered traction regime yields good estimates of both the rupture front propagation and the slip patterns which are comparable to literature results. The STF approximation shows a good fit with previously published STFs. The quasi-dynamic rupture model is hence able to fastly calculate reproducable slip results. That allows to test full Bayesian error analysis in the future. Further work on a full seismic source inversion or even a traction field inversion can also extend the scope of our model. N2 - Die dynamische Bruchmodellierung eines Erdbebens erlaubt Rückschlüsse auf Parameter der Bruchphysik, z. B. die Bruchgeschwindigkeit, die Reibung oder die Scherspannungsänderungen auf der Bruchfläche. Die meisten dynamischen Ansätze basieren dabei auf einem vorab definierten räumlichen Gitter. Dies führt zu einer großen Anzahl freier Modellparameter. Dynamische Modellierungen sind darum oft rechenaufwändig und hochgradig mehrdeutig im Ergebnis. Dies erschwert eine gute bayesische Fehleranalyse. Die benannnten Probleme und Schwierigkeiten werden durch das in dieser Arbeit präsentierte quasi-dynamische Bruchmodell angegangen. Es basiert auf der Kombination des Eikonal-Bruchmodells mit einer eigens entwickelten Randelementmethode zur Bestimmung der quasi-statischen Verschiebung. Dabei wird die Orientierung der Bruchfläche vorab über eine Momententensorinversion bestimmt. Das ebenfalls invertierte skalare seismische Moment dient zur Abschätzung der Bruchgröße. Die so bestimmte Bruchfläche wird in rechteckige Randelemente unterteilt. Als Randwerte werden die auf jedem Randelement angreifenden Spannungsänderungen vorgegeben. Um das dynamische Bruchverhalten zu studieren, wird die Bruchfrontausbreitung für inkrementelle Zeitschritte auf Grundlage der 2D-Eikonalgleichung berechnet. Die Bruchgeschwindigkeit wird dabei als linear zur Scherwellengeschwindigkeit skalierendes Feld angenommen, basierend auf einem geschichteten 1D-Untergrundmodell. Die von der Bruchfront eingeschlossenen Randelemente werden für eine quasi-statische Verschiebungsinversion genutzt. Dabei werden weder Reibung noch Spannungsmigrierung berücksichtigt (deswegen “quasi-statisch”). Eine Serie aus mehreren Verschiebungsbestimmungen ergibt dabei das quasi-dynamisches Bruchmodell. Da viele a priori Informationen aus dem Erdmodell beziehungsweise der Momententensorinversion genutzt werden, gibt es nur wenige freie Modellparameter (Nukleationspunkt und -Zeit, Linearfaktor zwischen Scher- und Bruchgeschwindigkeit sowie das Spannungsänderungsfeld). Das ermöglicht stabile und schnelle Modellierungen. Dies belegen durchgeführte Vergleiche mit finiten und infiniten analytischen, statischen Bruchlösungen. Zudem wurden erste dynamische Anwendungen erprobt. Dabei ergibt sich die ortsabhängige Zeit der Slipänderung jedes Randelementes (“rise time”) automatisch aus der Modellierung. Selbst die Reproduktion verschiedener kinematischer Modelle wie dem “slip-pulse” oder dem “penny-shaped crack” Modell ist möglich. Die spezifischen Slipratenfunktionen werden dabei automatisch erzeugt. Zudem lässt sich eine so genannte äquivalente Herdzeitfunktion aus der Summe der Momentenänderungen aller Randelemente bestimmen. Diese ist vergleichbar mit verschiedenen theoretischen und empirischen Herdzeitfunktionen. Unser Modell wurde zudem auf das 2015 Illapel Erdbeben angewandt. Basierend auf einer einfachen, rechteckigen Bruchgeometrie und einem zweigeteilten geschichteten Spannungsänderungsfeldes konnten sowohl die Bruchfrontausbreitung als auch das Verschiebungsfeld mit bekannten Werten aus der Literatur in Übereinstimmung gebracht werden. Die Herdzeitapproximation zeigt dabei einen Verlauf, der vergleichbar zu bereits veröffentlichten Herdzeitfunktionen ist. Das quasi-dynamische Bruchmodell kann schnell reproduzierbare Verschiebungsfelder und deren zeitliche Veränderung bestimmen. Damit ermöglicht es bayesische Fehlerabschätzungen. Auch für komplette seismische Quellinversion sowie eine Integration der Spannungsänderungen auf der Bruchfläche kann das Modell in Zukunft genutzt werden. T2 - Ein quasi-dynamisches und selbst-ähnliches Bruchmodel zur Erdbebenbruchmodelierung KW - earthquake modeling KW - source inversion KW - boundary element method KW - Erdbebenquellinversion KW - Randelementmethode KW - Erdbebenmodelierung Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-473100 ER -