Pub Date : 2019-04-17DOI: 10.1101/2020.04.08.20057497
B. Emmanuel
We have advanced a point-process based framework for the regulation of heart beats by the autonomous nervous system and analyzed the model with and without feedback. The model without feedback was found amenable to several analytical results that help develop an intuition about the way the heart interacts with the nervous system. However, in reality, feedback, baroreflex and chemoreflex controls are important to model healthy and unhealthy scenarios for the heart. Based on the Hurst exponent as an index of health of the heart we show how the state of the nervous system may tune it in health and disease. Monte Carlo simulation is used to generate RR interval series of the Electrocardiogram (ECG) for different sympathetic and parasympathetic nerve excitations. Key words: Heart, Autonomous Nervous System, ECG, RR intervals, Hurst Exponents, Point-Process Theory, Monte Carlo Simulation
{"title":"Regulation of Heart Beats by the Autonomous Nervous System in Health and Disease: Point-Process-Theory based Models and Simulation","authors":"B. Emmanuel","doi":"10.1101/2020.04.08.20057497","DOIUrl":"https://doi.org/10.1101/2020.04.08.20057497","url":null,"abstract":"We have advanced a point-process based framework for the regulation of heart beats by the autonomous nervous system and analyzed the model with and without feedback. The model without feedback was found amenable to several analytical results that help develop an intuition about the way the heart interacts with the nervous system. However, in reality, feedback, baroreflex and chemoreflex controls are important to model healthy and unhealthy scenarios for the heart. Based on the Hurst exponent as an index of health of the heart we show how the state of the nervous system may tune it in health and disease. Monte Carlo simulation is used to generate RR interval series of the Electrocardiogram (ECG) for different sympathetic and parasympathetic nerve excitations. Key words: Heart, Autonomous Nervous System, ECG, RR intervals, Hurst Exponents, Point-Process Theory, Monte Carlo Simulation","PeriodicalId":119149,"journal":{"name":"arXiv: Quantitative Methods","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126421406","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-01-11DOI: 10.13140/rg.2.2.17832.01284
Samira Masoudi, C. Wright, N. Rahnavard, J. Gatlin, J. Oakey
Microtubules are inherently dynamic sub-cellular filamentuous polymers that are spatially organized within the cell by motor proteins which cross-link and move microtubules. In-vitro microtubule motility assays, in which motors attached to a surface move microtubules along it, have been used traditionally to study motor function. However, the way in which microtubule-microtubule interactions affect microtubule movement remains largely unexplored. To address this question, time-lapse image series of in-vitro microtubule motility assays were obtained using total internal reflection fluorescence (TIRF) microscopy. Categorized as a general problem of multiple object tracking (MOT), particular challenges arising in this project include low feature diversity, dynamic instability, sudden changes in microtubules motility patterns, as well as their instantaneous appearance/disappearance. This work describes a new application of piecewise-stationary multiple motion model Kalman smoother (PMMS) for modeling individual microtubules motility trends. To both evaluate the capability of this procedure and optimize its hyper-parameters, a large dataset simulating the series of time-lapse images was used first. Next, we applied it to the sequence of frames from the real data. Results of our analyses provide a quantitative description of microtubule velocity which, in turn, enumerates the occurrence of microtubule-microtubule interactions per frame.
{"title":"Multiple Microtubule Tracking in Microscopy Time-Lapse Images Using Piecewise-stationary Multiple Motion Model Kalman Smoother","authors":"Samira Masoudi, C. Wright, N. Rahnavard, J. Gatlin, J. Oakey","doi":"10.13140/rg.2.2.17832.01284","DOIUrl":"https://doi.org/10.13140/rg.2.2.17832.01284","url":null,"abstract":"Microtubules are inherently dynamic sub-cellular filamentuous polymers that are spatially organized within the cell by motor proteins which cross-link and move microtubules. In-vitro microtubule motility assays, in which motors attached to a surface move microtubules along it, have been used traditionally to study motor function. However, the way in which microtubule-microtubule interactions affect microtubule movement remains largely unexplored. To address this question, time-lapse image series of in-vitro microtubule motility assays were obtained using total internal reflection fluorescence (TIRF) microscopy. Categorized as a general problem of multiple object tracking (MOT), particular challenges arising in this project include low feature diversity, dynamic instability, sudden changes in microtubules motility patterns, as well as their instantaneous appearance/disappearance. This work describes a new application of piecewise-stationary multiple motion model Kalman smoother (PMMS) for modeling individual microtubules motility trends. To both evaluate the capability of this procedure and optimize its hyper-parameters, a large dataset simulating the series of time-lapse images was used first. Next, we applied it to the sequence of frames from the real data. Results of our analyses provide a quantitative description of microtubule velocity which, in turn, enumerates the occurrence of microtubule-microtubule interactions per frame.","PeriodicalId":119149,"journal":{"name":"arXiv: Quantitative Methods","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122727629","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
D. Ostwald, Sebastian C. Schneider, R. Bruckner, Lilla Horvath
P-values and null-hypothesis significance testing are popular data-analytical tools in functional neuroimaging. Sparked by the analysis of resting-state fMRI data, there has recently been a resurgence of interest in the validity of some of the p-values evaluated with the widely used software SPM. The default parametric p-values reported in SPM are based on the application of results from random field theory to statistical parametric maps, a framework we refer to as RFP. While RFP was established almost two decades ago and has since been applied in a plethora of fMRI studies, there does not exist a unified documentation of the mathematical and computational underpinnings of RFP as implemented in current versions of SPM. Here, we provide such a documentation with the aim of contributing to contemporary efforts towards higher levels of computational transparency in functional neuroimaging.
{"title":"Random field theory-based p-values: a review of the SPM implementation","authors":"D. Ostwald, Sebastian C. Schneider, R. Bruckner, Lilla Horvath","doi":"10.17605/OSF.IO/3DX9W","DOIUrl":"https://doi.org/10.17605/OSF.IO/3DX9W","url":null,"abstract":"P-values and null-hypothesis significance testing are popular data-analytical tools in functional neuroimaging. Sparked by the analysis of resting-state fMRI data, there has recently been a resurgence of interest in the validity of some of the p-values evaluated with the widely used software SPM. The default parametric p-values reported in SPM are based on the application of results from random field theory to statistical parametric maps, a framework we refer to as RFP. While RFP was established almost two decades ago and has since been applied in a plethora of fMRI studies, there does not exist a unified documentation of the mathematical and computational underpinnings of RFP as implemented in current versions of SPM. Here, we provide such a documentation with the aim of contributing to contemporary efforts towards higher levels of computational transparency in functional neuroimaging.","PeriodicalId":119149,"journal":{"name":"arXiv: Quantitative Methods","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129886411","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A major contribution to the onset and development of autoimmune disease is known to come from infections. An important practical problem is identifying the precise mechanism by which the breakdown of immune tolerance as a result of immune response to infection leads to autoimmunity. In this paper, we develop a mathematical model of immune response to a viral infection, which includes T cells with different activation thresholds, regulatory T cells (Tregs), and a cytokine mediating immune dynamics. Particular emphasis is made on the role of time delays associated with the processes of infection and mounting the immune response. Stability analysis of various steady states of the model allows us to identify parameter regions associated with different types of immune behaviour, such as, normal clearance of infection, chronic infection, and autoimmune dynamics. Numerical simulations are used to illustrate different dynamical regimes, and to identify basins of attraction of different dynamical states. An important result of the analysis is that not only the parameters of the system, but also the initial level of infection and the initial state of the immune system determine the progress and outcome of the dynamics.
{"title":"Effects of Viral and Cytokine Delays on Dynamics of Autoimmunity","authors":"F. F. Chenar, Y. Kyrychko, K. Blyuss","doi":"10.3390/math6050066","DOIUrl":"https://doi.org/10.3390/math6050066","url":null,"abstract":"A major contribution to the onset and development of autoimmune disease is known to come from infections. An important practical problem is identifying the precise mechanism by which the breakdown of immune tolerance as a result of immune response to infection leads to autoimmunity. In this paper, we develop a mathematical model of immune response to a viral infection, which includes T cells with different activation thresholds, regulatory T cells (Tregs), and a cytokine mediating immune dynamics. Particular emphasis is made on the role of time delays associated with the processes of infection and mounting the immune response. Stability analysis of various steady states of the model allows us to identify parameter regions associated with different types of immune behaviour, such as, normal clearance of infection, chronic infection, and autoimmune dynamics. Numerical simulations are used to illustrate different dynamical regimes, and to identify basins of attraction of different dynamical states. An important result of the analysis is that not only the parameters of the system, but also the initial level of infection and the initial state of the immune system determine the progress and outcome of the dynamics.","PeriodicalId":119149,"journal":{"name":"arXiv: Quantitative Methods","volume":"267 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115683714","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-02-15DOI: 10.5433/1679-0375.2017v38n2p50
N. Romeiro, Fernanda Bezerra Mangili, R. Costanzi, E. Cirilo, Paulo Laerte Natti
The concentration of biochemical oxygen demand, BOD5, was studied in order to evaluate the water quality of the Igap'o I Lake, in Londrina, Paran'a State, Brazil. The simulation was conducted by means of the discretization in curvilinear coordinates of the geometry of Igap'o I Lake, together with finite difference and finite element methods. The evaluation of the proposed numerical model for water quality was performed by comparing the experimental values of BOD5 with the numerical results. The evaluation of the model showed quantitative results compatible with the actual behavior of Igap'o I Lake in relation to the simulated parameter. The qualitative analysis of the numerical simulations provided a better understanding of the dynamics of the BOD5 concentration at Igap'o I Lake, showing that such concentrations in the central regions of the lake have values above those allowed by Brazilian law. The results can help to guide choices by public officials, as: (i) improve the identification mechanisms of pollutant emitters on Lake Igap'o I, (ii) contribute to the optimal treatment of the recovery of the polluted environment and (iii) provide a better quality of life for the regulars of the lake as well as for the residents living on the lakeside.
为评价巴西帕兰纳州隆德里纳Igap o I湖的水质，对其生化需氧量BOD5浓度进行了研究。采用几何曲线坐标的离散化方法，结合有限差分法和有限元法进行仿真。通过将BOD5的实验值与数值结果进行比较，对所建立的水质数值模型进行了评价。对模型的评价表明，定量结果与模拟参数的实际行为相一致。数值模拟的定性分析提供了对Igap 'o I湖BOD5浓度动态的更好理解，表明该湖中心地区的BOD5浓度高于巴西法律允许的值。研究结果有助于指导政府官员的选择，因为:(i)完善伊格普湖污染物排放者的识别机制;(ii)有助于对污染环境的恢复进行优化处理;(iii)为湖泊的居民和居住在湖边的居民提供更好的生活质量。
{"title":"Numerical simulation of BOD5 dynamics in Igap'o I lake, Londrina, Paran'a, Brazil: Experimental measurement and mathematical modeling","authors":"N. Romeiro, Fernanda Bezerra Mangili, R. Costanzi, E. Cirilo, Paulo Laerte Natti","doi":"10.5433/1679-0375.2017v38n2p50","DOIUrl":"https://doi.org/10.5433/1679-0375.2017v38n2p50","url":null,"abstract":"The concentration of biochemical oxygen demand, BOD5, was studied in order to evaluate the water quality of the Igap'o I Lake, in Londrina, Paran'a State, Brazil. The simulation was conducted by means of the discretization in curvilinear coordinates of the geometry of Igap'o I Lake, together with finite difference and finite element methods. The evaluation of the proposed numerical model for water quality was performed by comparing the experimental values of BOD5 with the numerical results. The evaluation of the model showed quantitative results compatible with the actual behavior of Igap'o I Lake in relation to the simulated parameter. The qualitative analysis of the numerical simulations provided a better understanding of the dynamics of the BOD5 concentration at Igap'o I Lake, showing that such concentrations in the central regions of the lake have values above those allowed by Brazilian law. The results can help to guide choices by public officials, as: (i) improve the identification mechanisms of pollutant emitters on Lake Igap'o I, (ii) contribute to the optimal treatment of the recovery of the polluted environment and (iii) provide a better quality of life for the regulars of the lake as well as for the residents living on the lakeside.","PeriodicalId":119149,"journal":{"name":"arXiv: Quantitative Methods","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125200242","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-10-01DOI: 10.3929/ethz-b-000197274
L. D. Wittwer, M. Peters, S. Aland, D. Iber
During organogenesis tissue grows and deforms. The growth processes are controlled by diffusible proteins, so-called morphogens. Many different patterning mechanisms have been proposed. The stereotypic branching program during lung development can be recapitulated by a receptor-ligand based Turing model. Our group has previously used the Arbitrary Lagrangian-Eulerian (ALE) framework for solving the receptor-ligand Turing model on growing lung domains. However, complex mesh deformations which occur during lung growth severely limit the number of branch generations that can be simulated. A new Phase-Field implementation avoids mesh deformations by considering the surface of the modelling domains as interfaces between phases, and by coupling the reaction-diffusion framework to these surfaces. In this paper, we present a rigorous comparison between the Phase-Field approach and the ALE-based simulation.
{"title":"Simulating Organogenesis in COMSOL: Comparison Of Methods For Simulating Branching Morphogenesis","authors":"L. D. Wittwer, M. Peters, S. Aland, D. Iber","doi":"10.3929/ethz-b-000197274","DOIUrl":"https://doi.org/10.3929/ethz-b-000197274","url":null,"abstract":"During organogenesis tissue grows and deforms. The growth processes are controlled by diffusible proteins, so-called morphogens. Many different patterning mechanisms have been proposed. The stereotypic branching program during lung development can be recapitulated by a receptor-ligand based Turing model. Our group has previously used the Arbitrary Lagrangian-Eulerian (ALE) framework for solving the receptor-ligand Turing model on growing lung domains. However, complex mesh deformations which occur during lung growth severely limit the number of branch generations that can be simulated. A new Phase-Field implementation avoids mesh deformations by considering the surface of the modelling domains as interfaces between phases, and by coupling the reaction-diffusion framework to these surfaces. In this paper, we present a rigorous comparison between the Phase-Field approach and the ALE-based simulation.","PeriodicalId":119149,"journal":{"name":"arXiv: Quantitative Methods","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115202330","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-09-15DOI: 10.11145/texts.2017.11.197
Nicholas A. Battista, J. Samson, S. Khatri, L. Miller
While many organisms filter feed and exchange heat or nutrients in flow, few benthic organisms also actively pulse to enhance feeding and exchange. One example is the pulsing soft coral (Heteroxenia fuscescens). Pulsing corals live in colonies, where each polyp actively pulses through contraction and relaxation of their tentacles. The pulses are typically out of phase and without a clear pattern. These corals live in lagoons and bays found in the Red Sea and Indian Ocean where they at times experience strong ambient flows. In this paper, $3D$ fluid-structure interaction simulations are used to quantify the effects of ambient flow on the exchange currents produced by the active contraction of pulsing corals. We find a complex interaction between the flows produced by the coral and the background flow. The dynamics can either enhance or reduce the upward jet generated in a quiescent medium. The pulsing behavior also slows the average horizontal flow near the polyp when there is a strong background flow. The dynamics of these flows have implications for particle capture and nutrient exchange.
{"title":"Under the sea: Pulsing corals in ambient flow","authors":"Nicholas A. Battista, J. Samson, S. Khatri, L. Miller","doi":"10.11145/texts.2017.11.197","DOIUrl":"https://doi.org/10.11145/texts.2017.11.197","url":null,"abstract":"While many organisms filter feed and exchange heat or nutrients in flow, few benthic organisms also actively pulse to enhance feeding and exchange. One example is the pulsing soft coral (Heteroxenia fuscescens). Pulsing corals live in colonies, where each polyp actively pulses through contraction and relaxation of their tentacles. The pulses are typically out of phase and without a clear pattern. These corals live in lagoons and bays found in the Red Sea and Indian Ocean where they at times experience strong ambient flows. In this paper, $3D$ fluid-structure interaction simulations are used to quantify the effects of ambient flow on the exchange currents produced by the active contraction of pulsing corals. We find a complex interaction between the flows produced by the coral and the background flow. The dynamics can either enhance or reduce the upward jet generated in a quiescent medium. The pulsing behavior also slows the average horizontal flow near the polyp when there is a strong background flow. The dynamics of these flows have implications for particle capture and nutrient exchange.","PeriodicalId":119149,"journal":{"name":"arXiv: Quantitative Methods","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117066867","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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