@article {23999,
	title = {High-order finite element methods for cardiac monodomain simulations},
	journal = {Frontiers in Physiology},
	year = {2015},
	month = {08/2015},
	publisher = {Frontiers Media S.A.},
	abstract = {Computational modeling of tissue-scale cardiac electrophysiology requires numerically converged solutions to avoid spurious artifacts. The steep gradients inherent to cardiac action potential propagation necessitate fine spatial scales and therefore a substantial computational burden. The use of high-order interpolation methods has previously been proposed for these simulations due to their theoretical convergence advantage. In this study, we compare the convergence behavior of linear Lagrange, cubic Hermite, and the newly proposed cubic Hermite-style serendipity interpolation methods for finite element simulations of the cardiac monodomain equation. The high-order methods reach converged solutions with fewer degrees of freedom and longer element edge lengths than traditional linear elements. Additionally, we propose a dimensionless number, the cell Thiele modulus, as a more useful metric for determining solution convergence than element size alone. Finally, we use the cell Thiele modulus to examine convergence criteria for obtaining clinically useful activation patterns for applications such as patient-specific modeling where the total activation time is known a priori.},
	doi = {10.3389/fphys.2015.00217},
	url = {http://journal.frontiersin.org/article/10.3389/fphys.2015.00217/abstract},
	author = {K. P. {Vincent} and M. J. {Gonzales} and Andrew K. {Gillette} and C. T. {Villongco} and Pezzuto, Simone and J. H. {Omens} and M. J. {Holst} and Andrew D. {McCulloch}}
}
@article {Simula.simula.2284,
	title = {Molecular and Subcellular-Scale Modeling of Nucleotide Diffusion in the Cardiac Myofilament Lattice},
	journal = {Biophysical Journal},
	volume = {105},
	number = {9},
	year = {2013},
	pages = {2130},
	doi = {10.1016/j.bpj.2013.09.020},
	author = {Peter M. {Kekenes-Huskey} and Liao, Tao and Andrew K. {Gillette} and Johan Elon {Hake} and Zhang, Yongjie and Anushka P. {Michailova} and Andrew D. {McCulloch} and Andrew J. {McCammon}}
}
@article {Simula.simula.1664,
	title = {Finite-Element Estimation of Protein-ligand Association Rates With Post-Encounter Effects: Applications to Calcium Binding in Troponin C and SERCA},
	journal = {Computational Science \& Discovery},
	volume = {5},
	number = {1},
	year = {2012},
	pages = {014015},
	abstract = {We introduce a computational pipeline and suite of software tools for the approximation of diffusion-limited binding based on a recently developed theoretical framework. Our approach handles molecular geometries generated from high-resolution structural data and can account for active sites buried within the protein or behind gating mechanisms. Using tools from the FEniCS library and the APBS solver, we implement a numerical code for our method and study two Ca2+-binding proteins: troponin C and the sarcoplasmic reticulum Ca2+ ATPase. We find that a combination of diffusional encounter and internal {\textquoteright}buried channel{\textquoteright} descriptions provides superior descriptions of association rates, improving estimates by orders of magnitude.},
	author = {Peter M. {Kekenes-Huskey} and Andrew K. {Gillette} and Johan Elon {Hake} and Andrew J. {McCammon}}
}
