### Continuous time stochastic model for neurite branching (van Elburg 2011)

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Accession:129071
"In this paper we introduce a continuous time stochastic neurite branching model closely related to the discrete time stochastic BES-model. The discrete time BES-model is underlying current attempts to simulate cortical development, but is difficult to analyze. The new continuous time formulation facilitates analytical treatment thus allowing us to examine the structure of the model more closely. ..."
Reference:
1 . van Elburg R (2011) Stochastic Continuous Time Neurite Branching Models with Tree and Segment Dependent Rates Journal of Theoretical Biology 276(1):159-173 [PubMed]
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Model Information (Click on a link to find other models with that property)
 Model Type: Axon; Dendrite; Brain Region(s)/Organism: Cell Type(s): Channel(s): Gap Junctions: Receptor(s): Gene(s): Transmitter(s): Simulation Environment: C or C++ program; MATLAB; Model Concept(s): Development; Implementer(s): van Elburg, Ronald A.J. [R.van.Elburg at ai.rug.nl];
 / ContinuousTimeDendriticBranchingModel figures mat-files mexhandle readme.html cBEModel.m mexSDependenceCalculator.cpp mexSDependenceCalculator.mexglx ObjectHandle.h plotBEModelCurves.m SDependenceCalculation.m SDependenceCalculator.cpp SDependenceCalculator.h SDependenciesPlot.m
```function [T,Y,mun,sigman,validPoints]=cBEModel(b,E)

% Internal parameters
probability_leak_tolerance = 1e-6; % Maximum amount of probability that we allow to leave the system of differential equations.
P=1-E;                             % Power
tspan = [0 25];
dim=1000;                          % Number of p(n,t)'s used, n=1:dim

% Initial condition
y0 = zeros(1,dim);
y0(1) = 1;

% Terminal segment count
ngamma=1:dim;

% Define transition rate matrix ...
Rho = b.*sparse(-diag(ngamma.^P)+diag((ngamma(1:end-1)).^P,-1));
Rho(dim,dim) = 0;                                               % Gather all lost probility in remainder
Sparsity=spones(Rho);

% ...  and solve the problem using ode15s
options = odeset('Jacobian',Rho,'JPattern',Sparsity);
[T,Y]=ode15s(@RhoModel,tspan,y0, options);

% Calculate mean and variance of the number of terminal segments
mun=ngamma*Y';
sigman=sqrt(ngamma.^2*Y'-mun.^2);

% Determine points for which we are within the probability leak tolerance
validPoints= (Y(:,end)<probability_leak_tolerance );

function dydt=RhoModel(t,y) %#ok<INUSL>
dydt = Rho*y;
end

end ```