How do classroom-turnover times depend on lecture-hall size?

Academic spaces in colleges and universities span classrooms for 10 students to lecture halls that hold over 600 people. During the break between consecutive classes, students from the first class must leave and the new class must find their desks, regardless of whether the room holds 10 or 600 people. Here we address the question of how the size of large lecture halls affects classroom-turnover times, focusing on non-emergency settings. By adapting the established social-force model, we treat students as individuals who interact and move through classrooms to reach their destinations. We find that social interactions and the separation time between consecutive classes strongly influence how long it takes entering students to reach their desks, and that these effects are more pronounced in larger lecture halls. While the median time that individual students must travel increases with decreased separation time, we find that shorter separation times lead to shorter classroom-turnover times overall. This suggests that the effects of scheduling gaps and lecture-hall size on classroom dynamics depends on the perspective-individual student or whole class-that one chooses to take.

A Hybrid Model of Cartilage Regeneration Capturing the Interactions Between Cellular Dynamics and Porosity.

To accelerate the development of strategies for cartilage tissue engineering, models are necessary to investigate the interactions between cellular dynamics and the local microenvironment. We use a discrete framework to capture the individual behavior of cells, modeling experiments where cells are seeded in a porous scaffold or hydrogel and over the time course of a month, the scaffold slowly degrades while cells divide and synthesize extracellular matrix constituents. The movement of cells and the ability to proliferate is a function of the local porosity, defined as the volume fraction of fluid in the surrounding region. A phenomenological approach is used to capture a continuous profile for the degrading scaffold and accumulating matrix, which will then change the local porosity throughout the construct. We parameterize the model by first matching total cell counts in the construct to chondrocytes seeded in a polyglycolic acid scaffold (Freed et al. in Biotechnol Bioeng 43:597-604, 1994). We investigate the influence of initial scaffold porosity on the total cell count and spatial profiles of cell and ECM in the construct. Cell counts were higher at day 30 in scaffolds of lower initial porosity, and similar cell counts were obtained using different models of scaffold degradation and matrix accumulation (either uniform or cell-specific). Using this modeling framework, we study the interplay between a phenomenological representation of scaffold architecture and porosity as well as the potential continuous application of growth factors. We determine parameter regimes where large cellular aggregates occur, which can hinder matrix accumulation and cellular proliferation. The developed modeling framework can easily be extended and can be used to identify optimal scaffolds and culture conditions that lead to a desired distribution of extracellular matrix and cell counts throughout the construct.

Waveform parameters of retrobulbar vessels in glaucoma patients with different demographics and disease severity.

INTRODUCTION: To identify novel velocity waveform parameters of the ophthalmic artery and central retinal artery by computer-aided image processing of Doppler ultrasonography measurements, and to evaluate correlations between the waveform parameters and different demographics and disease severity of open-angle glaucoma patients. METHODS: Thirty-six images of 36 open-angle glaucoma patients were considered. A semiautomated image processing code was used to detect the digitalized ophthalmic artery and central retinal artery velocity waveforms and to extract the waveform parameters. Concordance correlation coefficient, two-sample t-test, and Pearson's correlation coefficient were used to test for similarities, differences, and associations among variables. RESULTS: Female glaucoma patients showed a statistically higher ophthalmic artery normalized distance between ascending and descending limb (p = 0.004), hypertensive glaucoma patients a statistically higher ophthalmic artery peak systolic velocity time (p = 0.025), glaucoma patients with hyperlipidemia a statistically higher ophthalmic artery resistivity index (p = 0.023) and a statistically higher ophthalmic artery peak systolic velocity acceleration (p = 0.025), glaucoma patients with cardiovascular diseases a statistically lower central retinal artery normalized distance between ascending and descending limb of the wave (p = 0.033) and a statistically higher central retinal artery period (p = 0.028), and patients with different body mass index a statistically different central retinal artery normalized distance between ascending and descending limb of the wave (p = 0.016). Groups with different disease severity, classified following the Brusini glaucoma staging system 2, showed statistically different central retinal artery normalized distance between ascending and descending limb of the wave (p < 0.001) and central retinal artery period (p = 0.016). No statistical differences were found in regard to race, diabetes status, glaucoma family history, and smoking. DISCUSSION: Ophthalmic artery and central retinal artery computer-aided analysis of velocity waveforms could identify novel waveform parameters capable of differentiating among different demographics and disease severity of open-angle glaucoma patients.

Intraocular pressure, blood pressure, and retinal blood flow autoregulation: a mathematical model to clarify their relationship and clinical relevance.

PURPOSE: This study investigates the relationship between intraocular pressure (IOP) and retinal hemodynamics and predicts how arterial blood pressure (BP) and blood flow autoregulation (AR) influence this relationship. METHODS: A mathematical model is developed to simulate blood flow in the central retinal vessels and retinal microvasculature as current flowing through a network of resistances and capacitances. Variable resistances describe active and passive diameter changes due to AR and IOP. The model is validated by using clinically measured values of retinal blood flow and velocity. The model simulations for six theoretical patients with high, normal, and low BP (HBP-, NBP-, LBP-) and functional or absent AR (-wAR, -woAR) are compared with clinical data. RESULTS: The model predicts that NBPwAR and HBPwAR patients can regulate retinal blood flow (RBF) as IOP varies between 15 and 23 mm Hg and between 23 and 29 mm Hg, respectively, whereas LBPwAR patients do not adequately regulate blood flow if IOP is 15 mm Hg or higher. Hemodynamic alterations would be noticeable only if IOP changes occur outside of the regulating range, which, most importantly, depend on BP. The model predictions are consistent with clinical data for IOP reduction via surgery and medications and for cases of induced IOP elevation. CONCLUSIONS: The theoretical model results suggest that the ability of IOP to induce noticeable changes in retinal hemodynamics depends on the levels of BP and AR of the individual. These predictions might help to explain the inconsistencies found in the clinical literature concerning the relationship between IOP and retinal hemodynamics.

Mathematical modeling approaches in the study of glaucoma disparities among people of African and European descents.

Open angle glaucoma (OAG) is a severe ocular disease characterized by progressive and irreversible vision loss. While elevated intraocular pressure (IOP) is a well-established risk factor for OAG, the progression of OAG in many cases, despite IOP treatment, suggests that other risk factors must play significant roles in the development of the disease. For example, various structural properties of the eye, ocular blood flow properties, and systemic conditions have been identified as risk factors for OAG. Ethnicity has also been indicated as a relevant factor that affects the incidence and prevalence of OAG; in fact, OAG is the leading cause of blindness among people of African descent. Numerous clinical studies have been designed to examine the possible correlation and causation between OAG and these factors; however, these studies are met with the challenge of isolating the individual role of multiple interconnected factors. Over the last decade, various mathematical modeling approaches have been implemented in combination with clinical studies in order to provide a mechanical and hemodynamical description of the eye in relation to the entire human body and to assess the contribution of single risk factors to the development of OAG. This review provides a summary of the clinical evidence of ocular structural differences, ocular vascular differences and systemic vascular differences among people of African and European descent, describes the mathematical approaches that have been proposed to study ocular mechanics and hemodynamics while discussing how they could be used to investigate the relevance to OAG of racial disparities, and outlines possible new directions of research.