La matematica最新文献

Retinal Venous Vulnerability in Primary Open Angle Glaucoma: The Combined Effects of Intraocular Pressure and Blood Pressure with Application to the Thessaloniki Eye Study. 原发性开角型青光眼的视网膜静脉易感性：眼压和血压的联合作用及其在塞萨洛尼基眼科研究中的应用。

La matematica Pub Date : 2025-03-01 Epub Date: 2024-12-23 DOI: 10.1007/s44007-024-00144-8

Rajat Rai, Giovanna Guidoboni, Christopher K Wikle, Fotis Topouzis, Brent Siesky, Alice Verticchio Vercellin, Gal Antman, Alon Harris

{"title":"Retinal Venous Vulnerability in Primary Open Angle Glaucoma: The Combined Effects of Intraocular Pressure and Blood Pressure with Application to the Thessaloniki Eye Study.","authors":"Rajat Rai, Giovanna Guidoboni, Christopher K Wikle, Fotis Topouzis, Brent Siesky, Alice Verticchio Vercellin, Gal Antman, Alon Harris","doi":"10.1007/s44007-024-00144-8","DOIUrl":"https://doi.org/10.1007/s44007-024-00144-8","url":null,"abstract":"Primary open angle glaucoma (POAG) is a leading cause of irreversible blindness with risk factors including elevated intraocular pressure (IOP), and both high and low blood pressure (BP). This study investigates the joint influence of IOP and BP on retinal hemodynamics, emphasizing venous circulation. A synthetic dataset comprising 2500 eyes with varied IOP [5-45] mmHg, systolic BP (SBP) [90-200] mmHg and diastolic BP (DBP) [40-120] mmHg was created. Mean pressure <math><mo>(</mo> <mover><mrow><mi>P</mi></mrow> <mi>‾</mi></mover> <mo>)</mo></math> , mean flow <math><mo>(</mo> <mover><mrow><mi>Q</mi></mrow> <mi>‾</mi></mover> <mo>)</mo></math> , and mean resistance <math><mo>(</mo> <mover><mrow><mi>R</mi></mrow> <mi>‾</mi></mover> <mo>)</mo></math> , were estimated using a validated mathematical model. The values of these hemodynamic output variables were then analyzed in relation to different values of IOP and mean arterial pressure (MAP; MAP = 1/3 SBP + 2/3 DBP). Clinical data from a population-based Greek study were similarly analyzed. Differences in the simulated hemodynamic output variables and clinical markers between healthy and POAG eyes were then measured. Synthetic dataset analysis revealed that <math> <mover><mrow><mi>R</mi></mrow> <mi>‾</mi></mover> </math> and <math> <mover><mrow><mi>P</mi></mrow> <mi>‾</mi></mover> </math> vary significantly depending on different IOP-MAP combinations. Notably, eyes with low MAP and high IOP demonstrated a drastic increase in <math> <mover><mrow><mi>R</mi></mrow> <mi>‾</mi></mover> </math> in the venules accompanied with a dramatic decrease in <math> <mover><mrow><mi>P</mi></mrow> <mi>‾</mi></mover> </math> in the central retinal vein (CRV). Clinical data indicated that venules in POAG eyes had significantly higher <math> <mover><mrow><mi>R</mi></mrow> <mi>‾</mi></mover> </math> than healthy eyes (p < 0.01), along with decreased <math> <mover><mrow><mi>P</mi></mrow> <mi>‾</mi></mover> </math> in the CRV of POAG eyes compared to healthy eyes (p = 0.01). The study highlights the increased susceptibility to venous collapse in POAG eyes and the importance of considering the venous side of retinal circulation in the combined impact of risk factors in POAG.","PeriodicalId":74051,"journal":{"name":"La matematica","volume":"4 1","pages":"66-83"},"PeriodicalIF":0.0,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12263117/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144651414","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Parity Property of Hexagonal Sliding Puzzles. 六边形滑动谜题的宇称性。

La matematica Pub Date : 2025-01-01 Epub Date: 2025-05-07 DOI: 10.1007/s44007-025-00160-2

Manuel Estévez, Ray Karpman, Érika Roldán

{"title":"Parity Property of Hexagonal Sliding Puzzles.","authors":"Manuel Estévez, Ray Karpman, Érika Roldán","doi":"10.1007/s44007-025-00160-2","DOIUrl":"https://doi.org/10.1007/s44007-025-00160-2","url":null,"abstract":"We study the puzzle graphs of hexagonal sliding puzzles of various shapes, and with various numbers of holes. The puzzle graph is a combinatorial model which captures the solvability and the complexity of sequential mechanical puzzles. Questions relating to the puzzle graph have been previously studied and resolved for the 15 Puzzle, which is the most famous-and unsolvable-square sliding puzzle of all time. It is known that for square puzzles such as the 15 Puzzle, solvability depends on a parity property that splits the puzzle graph into two components. In the case of hexagonal sliding puzzles, we get more interesting parity properties that depend on the shape of the boards and on the missing tiles or holes on the board. We show that for large-enough hexagonal, triangular, or parallelogram-shaped boards with hexagonal tiles, all puzzles with three or more holes are solvable. For puzzles with two or more holes, we give a solvability criterion involving both a parity property, and the placement of tiles in tight corners of the board. The puzzle graph is a discrete model for the configuration space of hard tiles (hexagons or squares) moving on different tessellation-based domains. Understanding the combinatorics of the puzzle graph could lead to understanding some aspects of the topology of these configuration spaces.","PeriodicalId":74051,"journal":{"name":"La matematica","volume":"4 2","pages":"433-458"},"PeriodicalIF":0.0,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12152070/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144287497","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Analysis of Waveform Parameters in the Retinal Vasculature via Mathematical Modeling and Data Analytics Methods. 基于数学建模和数据分析方法的视网膜血管波形参数分析。

La matematica Pub Date : 2024-12-01 Epub Date: 2024-09-11 DOI: 10.1007/s44007-024-00137-7

Lorenzo Sala, Kendall Lyons, Giovanna Guidoboni, Alon Harris, Marcela Szopos, Sergey Lapin

{"title":"Analysis of Waveform Parameters in the Retinal Vasculature via Mathematical Modeling and Data Analytics Methods.","authors":"Lorenzo Sala, Kendall Lyons, Giovanna Guidoboni, Alon Harris, Marcela Szopos, Sergey Lapin","doi":"10.1007/s44007-024-00137-7","DOIUrl":"10.1007/s44007-024-00137-7","url":null,"abstract":"Patient-specific mathematical modeling combined with data analytics methods presents a promising approach for analyzing retinal hemodynamics. In this study, we build upon previous developments in retinal blood flow modeling, integrating clinical measurements and physiological insights to reconstruct parameters such as the central retinal artery velocity (CRA) Doppler profile and pressure wave. By leveraging personalized input data, including CRA velocity profile, systemic blood pressure, heart rate, and intraocular pressure, we evaluate the performance of our in silico approach. Our investigation highlights the significance of methodological considerations in combining automatic image processing and mathematical modeling, particularly concerning the selection of appropriate strategies and the inclusion of personalized supplementary data. Through extensive validation and comparison with prior works, we demonstrate the impact of different assessment methods on clinically meaningful quantities, particularly biomarkers related to blood flow. Furthermore, our study introduces a novel metric based on the Wasserstein distance for monitoring temporal changes in retinal blood flow dynamics, providing valuable insights into the evolution of vascular function. Overall, our findings underscore the importance of patient-specific input data, automatic image processing, and personalized mathematical modeling to ensure robust and clinically relevant outcomes in retinal vasculature analysis.","PeriodicalId":74051,"journal":{"name":"La matematica","volume":"3 4","pages":"1297-1319"},"PeriodicalIF":0.0,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12250142/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144627960","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Anisotropic Fractional Sobolev Space Restricted on a Bounded Domain 限制在有界域上的各向异性分形索波列夫空间

La matematica Pub Date : 2024-07-23 DOI: 10.1007/s44007-024-00127-9

Shaoxiong Hou, Liqing Li, Jing Liu