MMPB Subgroup Contributed Talks

Ahmed Abdelhamid

"Computational modeling of external versus internal fibrinolysis in contracted blood clots"

Abstract to be determined. Please check back later.

Minseo Kim

Arnold O. Beckman High School

"Revealing the Effect of Hydration on Kidney Stone Formation Through Singular Perturbation Analysis"

Kidney stones, also known as renal calculi, are hard deposits of salts and minerals that form in the kidney. When the stones get stuck in the urinary tract and obstruct the path of urine, they may cause excruciating pain in the lower abdomen. The most common type of kidney stones is made of calcium and oxalate, and they form during the bodily process of creating urine, especially when the urine becomes supersaturated and does not allow minerals to dissolve. In fact, recent studies have shown that drinking plenty of water dilutes the substances in urine and thereby reduces the likelihood of contracting kidney stones. Overall, this project devises two mathematical models that accurately and systematically determine the behavior of chemicals in the system. Then, we present a quantitative mechanism, namely the method of matched asymptotic expansions, and different modeling techniques to explain how an increase in fluid consumption decreases the amount of calcium-oxalate complex in the body and consequently the risk of contracting kidney stones.

Valeri Barsegov

Department of Chemistry, University of Massachusetts, Lowell

"Biomechanics, Thermodynamics and Mechanisms of Rupture of Fibrin Clots"

Fibrin is the main determinant of the mechanical stability of blood clots and thrombi. Here, we explored the rupture of blood clots, emulating thrombus breakage by stretching fibrin gels with single-edge cracks. The stress-strain profiles display the weakly non-linear regime I of the gel due to alignment of fibrin fibers; linear elastic regime II owing to reversible stretching of fibers; and the rupture regime III for large deformations, during which irreversible breakage of fibers occurs. These dynamic mechanical regimes correlate with structural changes in the fibrin network. To model the stress-strain curves, we developed the Fluctuating Spring model, which maps the fibrin alignment, elastic network stretching, and cooperative rupture of coupled fibrin fibers into a mathematical framework to obtain a formula for stress as a function of strain. Cracks render network rupture stochastic. The free energy change for fiber deformation and rupture decreases with the crack size, thereby making the network rupture more spontaneously, but mechanical cooperativity due to the inter-fiber coupling strengthens the fibrin network. These results provide a basis for understanding of blood clot breakage that underlies thrombotic embolization. The mathematical Fluctuating Spring model can be used to characterize the dynamics of mechanical deformation of other protein networks.