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Lattice
FAQ
Modeling
Neighborhoods
‘How are neighborhoods defined?’
Courses
From PDE to Tissue
1D PDE Barkley Model
Derived from the seminal Hodgkin-Huxley and FitzHugh-Nagumo models, the Barkley model is probably the simplest continuous model for excitable media. It replaces the cubic term in the FitzHugh-Nagumo model with a piece-wise linear term as a simplification that enables fast simulation.
Courses
From PDE to Tissue
Convert to 2D
Converting the model from the previous chapter into a 2D model is trivial in Morpheus. In the Space section, you only need to change the Size of the Lattice to e.
Courses
From PDE to Tissue
Convert to 3D
Now we finally arrive at the 3D model. As an example, we further develop the coupled PDE and CPM model with mechanical interaction. Similar to the 1D to 2D case, it is straighforward to extend the dimensionality to 3D.
Models
Built-in Examples
ODE
Coupled ODE Lattice: Lateral Signaling
Morpheus Model ID:
M0004
Introduction This example model cell fate decisions during early patterning of the pancreas (de Back et al., 2012). The simple gene regulatory network of each cell is coupled to adjacent cells by lateral (juxtacrine) signaling.
W. de Back
,
J. X. Zhou
,
L. Brusch
(Authors)
Models
Published Models
Zebrafish
Guidance by Followers
Morpheus Model ID:
M0006
The migration of zebrafish polster cells is oriented by the migration of follower cells, allowing robust long-range coordination of different cell populations. Introduction Collective cell migration is an important process during biological development and tissue repair.
A. Boutillon
,
S. Escot
,
A. Elouin
,
D. Jahn
,
S. González-Tirado
,
J. Starruß
,
L. Brusch
,
N. B. David
(Authors)
D. Jahn
(Contributor)
DOI:10.1016/j.devcel.2022.05.001
Models
Contributed Examples
PDE
Scaled Diffusion Coefficient to Obtain Identical Results in Physical Units Independent of Lattice Discretization
Morpheus Model ID:
M7992
This example model demonstrates how to obtain consistent results in physical units together with the freedom to choose arbitrary lattice and time discretizations. Introduction Often, one starts to build a model with a particular lattice size and time scaling.
R. Müller
(Author)
L. Brusch
(Contributor)
Models
Contributed Examples
PDE
Actin Waves
Morpheus Model ID:
M2013
Spatial relaxation oscillator produces spatial dynamics and spiral waves Introduction We consider a full spatial variant of the Morpheus Model ID: M2012"model of a F-actin negative feedback to GTPase system.
L. Edelstein-Keshet
(Author)
Y. Xiao
(Contributor)
L. Edelstein-Keshet: Mathematical Models in Cell Biology
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