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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Author: search.filters.author.Parker, Albert E.Subject: search.filters.subject.Beer's Law

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    Imaging and plate counting to quantify the effect of an antimicrobial: A case study of a photo‐activated chlorine dioxide treatment
    (Wiley, 2022-09) Parker, Albert E.; Miller, Lindsey; Adams, Jacob; Pettigrew, Charles; Buckingham‐Meyer, Kelli; Summers, Jennifer; Christen, Andres; Goeres, Darla
    Aim. To assess removal versus kill efficacies of antimicrobial treatments against thick biofilms with statistical confidence. Methods and results. A photo-activated chlorine dioxide treatment (Photo ClO2) was tested in two independent experiments against thick (>100 μm) Pseudomonas aeruginosa biofilms. Kill efficacy was assessed by viable plate counts. Removal efficacy was assessed by 3D confocal scanning laser microscope imaging (CSLM). Biovolumes were calculated using an image analysis approach that models the penetration limitation of the laser into thick biofilms using Beer's Law. Error bars are provided that account for the spatial correlation of the biofilm's surface. The responsiveness of the biovolumes and plate counts to the increasing contact time of Photo ClO2 were quite different, with a massive 7 log reduction in viable cells (95% confidence interval [CI]: 6.2, 7.9) but a more moderate 73% reduction in biovolume (95% CI: [60%, 100%]). Results are leveraged to quantitatively assess candidate CSLM experimental designs of thick biofilms. Conclusions. Photo ClO2 kills biofilm bacteria but only partially removes the biofilm from the surface. To maximize statistical confidence in assessing removal, imaging experiments should use fewer pixels in each z-slice, and more importantly, at least two independent experiments even if there is only a single field of view in each experiment. Significance and impact of study There is limited penetration depth when collecting 3D confocal images of thick biofilms. Removal can be assessed by optimally fitting Beer's Law to all of the intensities in a 3D image and by accounting for the spatial correlation of the biofilm's surface. For thick biofilms, other image analysis approaches are biased or do not provide error bars. We generate unbiased estimates of removal and assess candidate CSLM experimental designs of thick biofilms with different pixilations, numbers of fields of view and number of experiments using the included design tool.
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