Mathematical Sciences
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Mathematical research at MSU is focused primarily on related topics in pure and applied mathematics. Research programs complement each other and are often applied to problems in science and engineering. Research in statistics encompasses a broad range of theoretical and applied topics. Because the statisticians are actively engaged in interdisciplinary work, much of the statistical research is directed toward practical problems. Mathematics education faculty are active in both qualitative and quantitative experimental research areas. These include teacher preparation, coaching and mentoring for in-service teachers, online learning and curriculum development.
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Item Surface micropattern reduces colonization and medical device-associated infections(2017-11) Xu, Binjie; Wei, Qiuhua; Mettetal, M. Ryan; Han, Jie; Rau, Lindsey; Tie, Jinfeng; May, Rhea M.; Pathe, Eric T.; Reddy, Shravanthi T.; Sullivan, Lauren; Parker, Albert E.; Maul, Donald H.; Brennan, Anthony B.; Mann, Ethan E.PURPOSE: Surface microtopography offers a promising approach for infection control. The goal of this study was to provide evidence that micropatterned surfaces significantly reduce the potential risk of medical device-associated infections. METHODOLOGY: Micropatterned and smooth surfaces were challenged in vitro against the colonization and transference of two representative bacterial pathogens - Staphylococcus aureus and Pseudomonas aeruginosa. A percutaneous rat model was used to assess the effectiveness of the micropattern against device-associated S. aureus infections. After the percutaneous insertion of silicone rods into (healthy or immunocompromised) rats, their backs were inoculated with S. aureus. The bacterial burdens were determined in tissues under the rods and in the spleens. RESULTS: The micropatterns reduced adherence by S. aureus (92.3 and 90.5 % reduction for flat and cylindrical surfaces, respectively), while P. aeruginosa colonization was limited by 99.9 % (flat) and 95.5 % (cylindrical). The micropatterned surfaces restricted transference by 95.1 % for S. aureus and 94.9 % for P. aeruginosa, compared to smooth surfaces. Rats with micropatterned devices had substantially fewer S. aureus in subcutaneous tissues (91 %) and spleens (88 %) compared to those with smooth ones. In a follow-up study, immunocompromised rats with micropatterned devices had significantly lower bacterial burdens on devices (99.5 and 99.9 % reduction on external and internal segments, respectively), as well as in subcutaneous tissues (97.8 %) and spleens (90.7 %) compared to those with smooth devices. CONCLUSION: Micropatterned surfaces exhibited significantly reduced colonization and transference in vitro, as well as lower bacterial burdens in animal models. These results indicate that introducing this micropattern onto surfaces has high potential to reduce medical device-associated infections. KEYWORDS: hospital-acquired infections; infections; medical devices; micropatternsItem Micropatterned Endotracheal Tubes Reduce Secretion-Related Lumen Occlusion(2016-12) Mann, Ethan E.; Magin, Chelsea M.; Mettetal, M. Ryan; May, Rhea M.; Henry, MiKayla M.; DeLoid, Heather; Prater, Justin; Sullivan, Lauren; Thomas, John G.; Twite, Mark D.; Parker, Albert E.; Brennan, Anthony B.; Reddy, Shravanthi T.Tracheal intubation disrupts physiological homeostasis of secretion production and clearance, resulting in secretion accumulation within endotracheal tubes (ETTs). Novel in vitro and in vivo models were developed to specifically recapitulate the clinical manifestations of ETT occlusion. The novel Sharklet™ micropatterned ETT was evaluated, using these models, for the ability to reduce the accumulation of both bacterial biofilm and airway mucus compared to a standard care ETT. Novel ETTs with micropattern on the inner and outer surfaces were placed adjacent to standard care ETTs in in vitro biofilm and airway patency (AP) models. The primary outcome for the biofilm model was to compare commercially-available ETTs (standard care and silver-coated) to micropatterned for quantity of biofilm accumulation. The AP model's primary outcome was to evaluate accumulation of artificial airway mucus. A 24-h ovine mechanical ventilation model evaluated the primary outcome of relative quantity of airway secretion accumulation in the ETTs tested. The secondary outcome was measuring the effect of secretion accumulation in the ETTs on airway resistance. Micropatterned ETTs significantly reduced biofilm by 71% (p = 0.016) compared to smooth ETTs. Moreover, micropatterned ETTs reduced lumen occlusion, in the AP model, as measured by cross-sectional area, in distal (85%, p = 0.005), middle (84%, p = 0.001) and proximal (81%, p = 0.002) sections compared to standard care ETTs. Micropatterned ETTs reduced the volume of secretion accumulation in a sheep model of occlusion by 61% (p < 0.001) after 24 h of mechanical ventilation. Importantly, micropatterned ETTs reduced the rise in ventilation peak inspiratory pressures over time by as much as 49% (p = 0.005) compared to standard care ETTs. Micropatterned ETTs, demonstrated here to reduce bacterial contamination and mucus occlusion, will have the capacity to limit complications occurring during mechanical ventilation and ultimately improve patient care.Item Micro-patterned surfaces reduce bacterial colonization and biofilm formation in vitro: Potential for enhancing endotracheal tube designs(2014-04) May, Rhea M.; Hoffman, Matt G.; Sogo, M.; Parker, Albert E.; O'Toole, George A.; Brennan, Anthony B.; Reddy, Shravanthi T.Ventilator-associated pneumonia (VAP) is a leading hospital acquired infection in intensive care units despite improved patient care practices and advancements in endotracheal tube (ETT) designs. The ETT provides a conduit for bacterial access to the lower respiratory tract and a substratum for biofilm formation, both of which lead to VAP. A novel microscopic ordered surface topography, the Sharklet micro-pattern, has been shown to decrease surface attachment of numerous microorganisms, and may provide an alternative strategy for VAP prevention if included on the surface of an ETT. To evaluate the feasibility of this micro-pattern for this application, the microbial range of performance was investigated in addition to biofilm studies with and without a mucin-rich medium to simulate the tracheal environment in vitro.