BibTeX
@ARTICLE{
Khuvis2015Tst,
author = "Samuel Khuvis and Matthias K. Gobbert and Bradford E. Peercy",
title = "Timestepping techniques to enable the simulation of bursting behavior in a
physiologically realistic computational islet",
journal = "Mathematical Biosciences",
volume = "263",
pages = "117",
year = "2015",
issn = "00255564",
doi = "10.1016/j.mbs.2015.02.001",
url = "http://www.sciencedirect.com/science/article/pii/S0025556415000334",
keywords = "Computational islet, Beta cells, Stiff ordinary differential equations, Numerical
differentiation formulas, Automatic differentiation",
abstract = "Physiologically realistic simulations of computational islets of beta cells require
the longtime solution of several thousands of coupled ordinary differential equations (ODEs),
resulting from the combination of several \{ODEs\} in each cell and realistic numbers of
several hundreds of cells in an islet. For a reliable and accurate solution of complex nonlinear
models up to the desired final times on the scale of several bursting periods, an appropriate
\{ODE\} solver designed for stiff problems is eventually a necessity, since other solvers
may not be able to handle the problem or are exceedingly inefficient. But stiff solvers are
potentially significantly harder to use, since their algorithms require at least an approximation of
the Jacobian matrix. For sophisticated models, systems of several complex \{ODEs\} in each
cell, it is practically unworkable to differentiate these intricate nonlinear systems analytically
and to manually program the resulting Jacobian matrix in computer code. This paper demonstrates that
automatic differentiation can be used to obtain code for the Jacobian directly from code for the
\{ODE\} system, which allows a full accounting for the sophisticated model equations. This
technique is also feasible in sourcecode languages Fortran and C, and the conclusions apply to a
wide range of systems of coupled, nonlinear reaction equations. However, when we combine an
appropriately supplied Jacobian with slightly modified memory management in the \{ODE\}
solver, simulations on the realistic scale of one thousand cells in the islet become possible that
are several orders of magnitude faster than the original solver in the software Matlab, a language
that is particularly user friendly for programming complicated model equations. We use the efficient
simulator to analyze electrical bursting and show nonmonotonic average burst period between fast
and slow cells for increasing coupling strengths. We also find that interestingly, the arrangement
of the connected fast and slow heterogeneous cells impacts the peak bursting period monotonically.",
ad_area = "Biomedicine",
ad_tools = "ADiMat"
}
