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Current Research

​My graduate research in the field of mathematical biology involves modeling cardiovascular dynamics. See the website dedicated to the Cardiovascular Dynamics Group at NCSU here. In particular, my dissertation has focused on assesing the state of the cardiovascular system for individuals suffering from orthostatic intolerance (OI). The ultimate goals of my research are to apply techniques of mathematical modeling, parameter identification, numerical optimization, and control theory to understand how disorders alter the biological function of the cardiovascular system, and to use these methods to aid clinical professionals to assess the state of the cardiovascular system. My current research focuses on applying a mathematical model, coupled with an optimal control problem formulation to regulate certain efferents. I wish to analyze data-sets within and between different groups of subjects. The goal is to predict differences in regulated quantities so that we may assess the state of a subject's cardiovascular system.



​I would love to continue to use mathematical models and parameter identication techniques to understand the cardiovascular system and aid clinical professionals in determining answers to their medical questions. I am also interested in studying related aspects of the human body involving not only the cardiovascular system, but the renal, reproductive, respiratory, and immune systems. My ultimate desire is to use mathematics in research to study biological systems so that I may contribute to enhancing the life of people all over the world, whether it involves rather simple disorders or deadly diseases.



Selected Presentations

  • ​An Optimal Control Approach for Modeling the Response to HUT
        SIAM Life Sciences Conference, San Diego, CA, August 2012 
        Biomath Seminar, Roskilde University, Denmark, October 2012
        Joint Math Meetins 2013 San Diego, CA, January 2013

  • Modeling Baroreflex Regulation of Blood Pressure in Rats (poster), The Virtual Physiological â€‹Rat Project Annual Meeting, Milwaukee, WI, July 2012

  • Patient Specific Modeling of Head-Up Tilt
        Applied Mathematics Graduate Student Seminar,NC State University, November 2011
        Corrdinating Research Centre, Frederiksburg Hospital, Denmark, October 2012

 

Publications

  • N.D. Williams, M.S. Olufsen, H. Tran, Modeling Cardiovascular Dynamics during Head-Up

    Tilt via a Non-Pulsatile Model with Optimal Control, in process

  • N.D. Williams, M.S. Olufsen, H. Tran, Patient Specific Pulsatile and Non-pulsatile Modeling

    of Cardiovascular Dynamics During Head-Up Tilt, in process

  • N.D.Williams, M.S. Olufsen, H. Tran, An Optimal Control Approach for Modeling HUT, Proc

    The International Workshop on Innovative Simulation for Healthcare (IWISH), 2013 (6 pages)

  • N.D. Williams, M.S. Olufsen, H. Tran, Cardiovascular Dynamics During Head-up Tilt Assessed

    via a Pulsatile and Non-pulsatile Model, Proc Special Session on Modeling and Simulation

    in Biology and Medicine of the International Conference on Simulation and Modeling

    Methodologies, Technologies and Applications (SIMULTECH), 2013 (8 pages)

  • N.D. Williams, O. Wind-Willassen, REU Program, J. Mehlsen, J.T. Ottesen, M.S. Olufsen; Patient Specific Modeling of Head-Up Tilt, Mathematical Medicine and Biology: A Journal of the IMA, revised & re-submitted December 2012.

  • B. Matzuka, J. Mehlsen, M.S, Olufsen, H. Tran, N. Williams, A Kalman Filtering Based Approach for the Modeling of the Cardiovascular Regualtion System, The International Workshop on Innovative Simulation for Healthcare (IWISH), July 2012

 

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