Continuum Modeling of Biological Network Formation

2017 ◽  
pp. 1-48 ◽  
Author(s):  
Giacomo Albi ◽  
Martin Burger ◽  
Jan Haskovec ◽  
Peter Markowich ◽  
Matthias Schlottbom
Keyword(s):  
Network Formation ◽  
Biological Network ◽  
Continuum Modeling

scholarly journals Notes on a PDE system for biological network formation

2016 ◽  
Vol 138 ◽  
pp. 127-155 ◽  
Author(s):  
Jan Haskovec ◽  
Peter Markowich ◽  
Benoît Perthame ◽  
Matthias Schlottbom
Keyword(s):  
Network Formation ◽  
Biological Network

Biological transportation networks: Modeling and simulation

2016 ◽  
Vol 14 (01) ◽  
pp. 185-206 ◽  
Author(s):  
Giacomo Albi ◽  
Marco Artina ◽  
Massimo Foransier ◽  
Peter A. Markowich
Keyword(s):  
Network Formation ◽  
Biological Network ◽  
Transportation Networks ◽  
Transportation Network ◽  
Gradient Flow ◽  
Model Parameters ◽  
Biological Transport ◽  
Leaf Venation ◽  
Numerical Finite Element ◽  
The Impact

We present a model for biological network formation originally introduced by Cai and Hu [Adaptation and optimization of biological transport networks, Phys. Rev. Lett. 111 (2013) 138701]. The modeling of fluid transportation (e.g., leaf venation and angiogenesis) and ion transportation networks (e.g., neural networks) is explained in detail and basic analytical features like the gradient flow structure of the fluid transportation network model and the impact of the model parameters on the geometry and topology of network formation are analyzed. We also present a numerical finite-element based discretization scheme and discuss sample cases of network formation simulations.

scholarly journals Mathematical Analysis of a PDE System for Biological Network Formation

2015 ◽  
Vol 40 (5) ◽  
pp. 918-956 ◽  
Author(s):  
Jan Haskovec ◽  
Peter Markowich ◽  
Benoit Perthame
Keyword(s):  
Mathematical Analysis ◽  
Network Formation ◽  
Biological Network

Platelet Microtubules in Clot Structure Formation and Contractile Force Generation: Investigation of a Controversy

1986 ◽  
Vol 56 (01) ◽  
pp. 023-027 ◽  
Author(s):  
C J Jen ◽  
L V McIntire
Keyword(s):  
Network Formation ◽  
Contractile Force ◽  
Second Phase ◽  
Clot Retraction ◽  
Forming Process ◽  
Microtubule Organization ◽  
Physiological Processes ◽  
Fibrin Network ◽  
Two Parameters

SummaryWhether platelet microtubules are involved in clot retraction/ contraction has been controversial. To address this question we have simultaneously measured two clotting parameters, clot structural rigidity and isometric contractile force, using a rheological technique. For recalcified PRP clots these two parameters began rising together at about 15 min after CaCl2 addition. In the concentration range affecting microtubule organization in platelets, colchicine, vinca alkaloids and taxol demonstrated insignificant effects on both clotting parameters of a recalcified PRP clot. For PRP clots induced by adding small amounts of exogenous thrombin, the kinetic curves of clot rigidity were biphasic and without a lag time. The first phase corresponded to a platelet-independent network forming process, while the second phase corresponded to a platelet-dependent process. These PRP clots began generating contractile force at the onset of the second phase. For both rigidity and force parameters, only the second phase of clotting kinetics was retarded by microtubule affecting reagents. When PRP samples were clotted by adding a mixture of CaCl2 and thrombin, the second phase clotting was accelerated and became superimposed on the first phase. The inhibitory effects of micro tubule affecting reagents became less pronounced. Thrombin clotting of a two-component system (washed platelets/ purified fibrinogen) was also biphasic, with the second phase being microtubule-dependent. In conclusion, platelet microtubules are important in PRP clotted with low concentrations of thrombin, during which fibrin network formation precedes platelet-fibrin interactions. On the other hand they are unimportant if a PRP clot is induced by recalcification, during which the fibrin network is constructed in the presence of platelet-fibrin interactions. The latter is likely to be more analogous to physiological processes in vivo.

High rate continuum modeling mesh reduction methodologies and advanced applications

2006 ◽  
Author(s):  
E. L. Baker ◽  
D. Pfau ◽  
J. M. Pincay ◽  
T. Vuong ◽  
K. W. Ng
Keyword(s):  
High Rate ◽  
Continuum Modeling ◽  
Advanced Applications
Sign in / Sign up

Export Citation Format

Share Document