@article{betts_campbell_thompson_2016, title={Solving optimal control problems with control delays using direct transcription}, volume={108}, ISSN={["1873-5460"]}, DOI={10.1016/j.apnum.2015.12.008}, abstractNote={The numerical treatment of optimal control problems with state and control delays is important in a wide variety of scientific and technical applications. Solutions to these types of problems are difficult to obtain via analytic techniques since the system may be nonlinear and subjected to complicated inputs and constraints. There are several numerical methods available to compute the solutions of optimal control problems without delays. One such popular method is direct transcription. Although the numerical solutions of optimal control delay problems are important, less literature and software exists in this area. A general purpose industrial grade direct transcription code that can handle optimal control problems with both state and control constraints and delays is under development. Control delays pose a special challenge. A new technique for treating control delays when using a direct transcription approach is investigated in this paper.}, journal={APPLIED NUMERICAL MATHEMATICS}, author={Betts, John T. and Campbell, Stephen L. and Thompson, Karmethia C.}, year={2016}, month={Oct}, pages={185–203} }
 @article{betts_campbell_thompson_2015, title={Lobatto IIIA methods, direct transcription, and DAEs with delays}, volume={69}, ISSN={["1572-9265"]}, DOI={10.1007/s11075-014-9896-y}, number={2}, journal={NUMERICAL ALGORITHMS}, author={Betts, John T. and Campbell, Stephen L. and Thompson, Karmethia}, year={2015}, month={Jun}, pages={291–300} }
 @article{haider_olander_arnold_marous_mclamb_thompson_woodruff_haugh_2011, title={A phenomenological mixture model for biosynthesis and linking of cartilage extracellular matrix in scaffolds seeded with chondrocytes}, volume={10}, ISSN={1617-7959 1617-7940}, url={http://dx.doi.org/10.1007/s10237-010-0282-y}, DOI={10.1007/s10237-010-0282-y}, abstractNote={A phenomenological mixture model is presented for interactions between biosynthesis of extracellular matrix (ECM) constituents and ECM linking in a scaffold seeded with chondrocytes. A system of three ordinary differential equations for average apparent densities of unlinked ECM, linked ECM and scaffold is developed along with associated initial conditions for scaffold material properties. Equations for unlinked ECM synthesis and ECM linking include an inhibitory mechanism where associated rates decrease as unlinked ECM concentration in the interstitial fluid increases. Linking rates are proposed to depend on average porosity in the evolving tissue construct. The resulting initial value problem contains nine independent parameters that account for scaffold biomaterial properties and interacting mechanisms in the engineered system. Effects of parameter variations on model variables are analyzed relative to a baseline case with emphasis on the evolution of solid phase apparent density, which is often correlated with the compressive elastic modulus of the tissue construct. The new model provides an additional quantitative framework for assessing and optimizing the design of engineered cell-scaffold systems and guiding strategies for articular cartilage tissue engineering.}, number={6}, journal={Biomechanics and Modeling in Mechanobiology}, publisher={Springer Science and Business Media LLC}, author={Haider, Mansoor A. and Olander, Jeffrey E. and Arnold, Rachel F. and Marous, Daniel R. and McLamb, April J. and Thompson, Karmethia C. and Woodruff, William R. and Haugh, Janine M.}, year={2011}, month={Jan}, pages={915–924} }