Research
I am currently a fifth-year Ph.D. student in applied mathematics at University of Delaware. I am working under the supervision of Dr. Richard J. Braun and expect to receive my Ph.D. in May 2018. My research focuses on the mathematical modeling of a specific type of dry eye, where eyes dry abnormally fast.
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My research involves biophysical modeling, fluid dynamics in thin film, numerical methods for PDE and image processing. Here are copies of my CV and my research statement .
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Ph.D. candidate
Department of Mathematical Sciences
University of Delaware
108 Ewing Hall, Newark, DE, 19716
Email: lanzhong@udel.edu
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L. Zhong, C. Ketelaar, R. J. Braun, PE. King-Smith, CG. Begley. Mathematica Modelling for Glob-Driven Tear Film Breakup, Mathematical Medicine Biology, accepted, 2017.
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L. Zhong, R. J. Braun, PE. King-Smith, CG. Begley. Dynamics of Fluorescent Imaging in Glob-Driven Breakup, Meeting Highlights Article, Journal for Modeling in Ophthalmology, accepted 2017.
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C. Anghel, K. Archer, J. Chang, A. Cochran, A. Radulescu, K. Y. Djima, R. Turner, L. Zhong. Simulations of the Vascular Network Growth Process for Studying Placenta Structure and Function Associated with Autism, Submitted to the Proceedings of the Conference on Understanding Complex Biological Systems with Mathematics, November, 2017
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C. Anghel, K. Archer, J. Chang, A. Cochran, A. Radulescu, K. Y. Djima, R. Turner, L. Zhong. Placental Vessel Extraction using Shearlets, Laplacian Eigenmaps and a Conditional Generative Adversarial Network, Submitted to the Proceedings of the Conference on Understanding Complex Biological Systems with Mathematics, November, 2017
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L. Zhong, R. J. Braun, PE. King-Smith, CG. Begley. Modeling Fluorescent Imaging in Rapid Tear Thinning, in preparation.
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L. Zhong, Deborah Antwi, R. J. Braun, PE. King-Smith, CG. Begley. Comparing Fluorescent Imaging and Mathematical Model in Tear Breakup , in preparation.
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L. Zhong, A. Cochran, R. Turner, A. Radulescu, C. Anghel, J. Chang, Markers of Autism from Functional Properties of Placental Vascular Networks, in preparation.
We have a group that models human tear film at the Department of Mathematical Sciences (more informations here ). My problem mainly focuses on simulating rapid tear thinning, where the eye thins dramatically right after the first blink. The thinning of the eye is visualized by fluorescent imaging, where the darker region indicates thinner tear film (or drier eye). The models we developed simulate the tear film thickness as well as the pixel value in fluorescent imaging (fluorescent intensity). By comparing the experimental data with the models' results, we study the mechanism of the tear thinning. Here's a three minutes video for a brief introduction to my research.
0.14s after first blink
1.01s after first blink
2.01s after first blink
The dark spots formed 0.14 seconds after the first blink. Dark regions became darker in the next few seconds with unmoved centers. The simultaneous images for other similar cases of rapid thinning indicate that a thinning region corresponds to a thicker lipid layer. Mathematical models are proposed to explain this phenomenon; a thicker lipid (glob) spreads to its surrounding area and drives flow which thins the aqueous layer.
Simultaneous images for rapid thinning. Left: fluorescent image, darker = thinner film. Right: Tear film lipid layer image, brighter = thicker lipid [1].
Schematic of the mechanism of glob-driven tear thinning. Blue circles with tails indicate the concentration of lipid. 1. From the upper image to the lower image, the glob with higher concentration in the center spreads to its surrounding region via the Marangoni effect. 2. The aqueous layer is thinned by the driven tangential flow (Marangoni flow).
Comparison of the experimental data (left) with simulated model results (right).
Validation of the model
Mathematical model after nondimensionalization using lubrication theory.
Mathematical modeling
Background
The following sequential images show the thinning process.
Publication
More research in simulating blood flow in the vascular network on the surface of placenta
I also worked on a project which studies how the growth of the vascular network on the surface of placenta relates to Autism; the blood flow in the vascular network delivers oxygen and necessary nutrients from mother to infants. Not enough oxygen or nutrition might correspond to Autism. (1) We use Monte-Carlo simulations to mimic the growth process of an arterial vascular network controlled by different mechanisms. (2) The simulated arterial vascular network is mirrored to be a venous one. Connecting them, we have a complete vascular network . Diffusion of oxygen and nutrients is assumed to occur in the connecting region. (3) Following the conservation laws and Poiseuille’s law of blood flow, we are able to calculate the blood flow, flow through the whole network and some other parameters to study the differences between healthy and unhealthy vascular networks.
