Mathematical medicine and biology : a journal of the IMA最新文献

Effects of reduced temperature on oxygen transport from capillaries to brain tissue.

Mathematical medicine and biology : a journal of the IMA Pub Date : 2025-03-27 DOI: 10.1093/imammb/dqaf002

Samikshaa Natarajan, Timothy W Secomb

{"title":"Effects of reduced temperature on oxygen transport from capillaries to brain tissue.","authors":"Samikshaa Natarajan, Timothy W Secomb","doi":"10.1093/imammb/dqaf002","DOIUrl":"https://doi.org/10.1093/imammb/dqaf002","url":null,"abstract":"The normal function of the brain depends on adequate oxygen supply. Oxygen deprivation (hypoxia) can result in irreversible damage to neurons within minutes. Cooling (hypothermia) of brain tissue can reduce the rate of damage, and is used in surgeries where blood flow to the brain is interrupted, such as aortic arch reconstruction. Hypothermia affects several factors that influence tissue oxygen levels, including oxygen consumption rate, diffusivity and solubility. The goal of the present work is to predict the effects of hypothermia on the partial pressure of oxygen in brain tissue. The dependence on temperature of parameters governing oxygen transport is estimated from literature data. A theoretical model based on the Krogh cylinder configuration is used to predict the effects of hypothermia on the distribution of oxygen partial pressure in the cylindrical tissue region surrounding a capillary. For a given blood flow rate and inflowing oxygen level, tissue oxygen levels are shown to increase with decreasing temperature. Although oxygen diffusivity in tissue declines with hypothermia, the reduction in oxygen consumption leads to a net increase in predicted oxygen levels. Tissue hypoxia resulting from reductions in blood flow rate can be ameliorated by reductions in temperature. For example, if blood flow is reduced to 36% of normal, temperature reduction by 2.3°C can increase tissue oxygen levels above the hypoxic range. The results support the use of hypothermia to reduce brain damage under conditions of reduced blood flow.","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2025-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143733663","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}

引用次数: 0

A network-level transport model of tau progression in the Alzheimer's brain.

Mathematical medicine and biology : a journal of the IMA Pub Date : 2025-03-13 DOI: 10.1093/imammb/dqaf003

Veronica Tora, Justin Torok, Michiel Bertsch, Ashish Raj

{"title":"A network-level transport model of tau progression in the Alzheimer's brain.","authors":"Veronica Tora, Justin Torok, Michiel Bertsch, Ashish Raj","doi":"10.1093/imammb/dqaf003","DOIUrl":"https://doi.org/10.1093/imammb/dqaf003","url":null,"abstract":"One of the hallmarks of Alzheimer's disease (AD) is the accumulation and spread of toxic aggregates of tau protein. The progression of AD tau pathology is thought to be highly stereotyped, which is in part due to the fact that tau can spread between regions via the white matter tracts that connect them. Mathematically, this phenomenon has been described using models of \"network diffusion,\" where the rate of spread of tau between brain regions is proportional to its concentration gradient and the amount of white matter between them. Although these models can robustly predict the progression of pathology in a wide variety of neurodegenerative diseases, including AD, an underexplored aspect of tau spreading is that it is governed not simply by diffusion but also active transport along axonal microtubules. Spread can therefore take on a directional bias, resulting in distinct patterns of deposition, but current models struggle to capture this phenomenon. Recently, we have developed a mathematical model of the axonal transport of toxic tau proteins that takes into account the effects tau exerts on the molecular motors. Here we describe and implement a macroscopic version of this model, which we call the Network Transport Model (NTM). A key feature of this model is that, while it predicts tau dynamics at a regional level, it is parameterized in terms of only microscopic processes such as aggregation and transport rates; that is, differences in brain-wide tau progression can be explained by its microscopic properties. We provide numerical evidence that, as with the two-neuron model that the NTM extends, there are distinct and rich dynamics with respect to the overall rate of spread and the staging of pathology when we simulated the NTM on the hippocampal subnetwork. The theoretical insights provided by the NTM have broad implications for understanding AD pathophysiology more generally.","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2025-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143627310","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}

引用次数: 0

Mathematical modeling and analysis of emission and mitigation of methane from the integrated rice-livestock farming system. 水稻-牲畜综合养殖系统甲烷排放与减排的数学建模与分析。

Mathematical medicine and biology : a journal of the IMA Pub Date : 2025-02-12 DOI: 10.1093/imammb/dqaf001

Maitri Verma, Alok Kumar Verma

{"title":"Mathematical modeling and analysis of emission and mitigation of methane from the integrated rice-livestock farming system.","authors":"Maitri Verma, Alok Kumar Verma","doi":"10.1093/imammb/dqaf001","DOIUrl":"https://doi.org/10.1093/imammb/dqaf001","url":null,"abstract":"Controlling the elevated levels of methane (CH4) in the atmosphere is crucial to tackling the problem of climate change. Both rice paddies and livestock farming are substantial contributors to this elevated methane. The integrated rice-livestock farming system is an agricultural practice designed to optimize the use of agricultural waste, while concurrently boosting rice and livestock productivity. Achieving the dual objectives of food security and mitigating climate change demands formulation and implementation of strategies that are aimed at managing the methane emissions from the rice-livestock farming system. This study introduces a nonlinear mathematical model of the emission and mitigation of methane in the integrated rice-livestock farming system. Through qualitative analysis, the model's dynamic behavior is thoroughly explored, identifying conditions for reduction and stabilization of atmospheric methane concentrations. Model parameters are estimated using secondary data on atmospheric methane concentration, rice yield, and livestock population. A sensitivity analysis is presented to evaluate the influence of variations in crucial parameters on the system's behavior. Numerical simulations are conducted to confirm the validity of the theoretical results.","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143400941","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}

引用次数: 0

Effect of diffusivity of amyloid beta monomers on the formation of senile plaques. 淀粉样 beta 单体的扩散性对老年斑形成的影响

Mathematical medicine and biology : a journal of the IMA Pub Date : 2024-12-16 DOI: 10.1093/imammb/dqae019

Andrey V Kuznetsov

{"title":"Effect of diffusivity of amyloid beta monomers on the formation of senile plaques.","authors":"Andrey V Kuznetsov","doi":"10.1093/imammb/dqae019","DOIUrl":"10.1093/imammb/dqae019","url":null,"abstract":"Alzheimer's disease (AD) presents a perplexing question: why does its development span decades, even though individual amyloid beta (Aβ) deposits (senile plaques) can form rapidly in as little as 24 hours, as recent publications suggest? This study investigated whether the formation of senile plaques can be limited by factors other than polymerization kinetics alone. Instead, their formation may be limited by the diffusion-driven supply of Aβ monomers, along with the rate at which the monomers are produced from amyloid precursor protein and the rate at which Aβ monomers undergo degradation. A mathematical model incorporating the nucleation and autocatalytic process (via the Finke-Watzky model), as well as Aβ monomer diffusion, was proposed. The obtained system of partial differential equations was solved numerically, and a simplified version was investigated analytically. The computational results predicted that it takes approximately 7 years for Aβ aggregates to reach a neurotoxic concentration of 50 μM. Additionally, a sensitivity analysis was performed to examine how the diffusivity of Aβ monomers and their production rate impact the concentration of Aβ aggregates.","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":" ","pages":"346-362"},"PeriodicalIF":0.0,"publicationDate":"2024-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142484531","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}

引用次数: 0

Genesis of intimal thickening due to hemodynamical shear stresses. 血流动力学剪切应力导致内膜增厚的成因

Mathematical medicine and biology : a journal of the IMA Pub Date : 2024-12-16 DOI: 10.1093/imammb/dqae018

Avishek Mukherjee, Navid Mohammad Mirzaei, Pak-Wing Fok

{"title":"Genesis of intimal thickening due to hemodynamical shear stresses.","authors":"Avishek Mukherjee, Navid Mohammad Mirzaei, Pak-Wing Fok","doi":"10.1093/imammb/dqae018","DOIUrl":"10.1093/imammb/dqae018","url":null,"abstract":"This paper investigates intimal growth in arteries, induced by hemodynamical shear stress, through finite element simulation using the FEniCS computational environment. In our model, the growth of the intima depends on cross-section geometry and shear stress. In this work, the arterial wall is modeled as three distinct layers: the intima, the media and the adventitia, each with different mechanical properties. We assume that the cross-section of the vessel does not change in the axial direction. We further assume that the blood flow is steady, non-turbulent and unidirectional. Blood flow induces shear stress on the endothelium and stimulates the release of platelet derived growth factor (PDGF) which drives the growth. We simulate intimal growth for three distinct arterial cross section geometries. We show that the qualitative nature of intimal thickening varies depending on arterial geometry. For cross section geometries that are annular, the growth of the intima is uniform in the angular direction, and the endothelium stays circular as the intima grows. For non-annular cross section geometries, the intima grows more quickly where it is thicker, and shear stress and intimal thickening are negatively correlated with the distance from the flow center, where the flow velocity is maximal. Over time, the maxima and minima of the curvature increase and decrease, respectively, the PDGF concentration increases and the lumen becomes more polygonal. The model provides a framework for coupling hemodynamics simulations to mathematical descriptions of atherosclerosis, both of which have been modeled separately in great detail.","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":" ","pages":"363-381"},"PeriodicalIF":0.0,"publicationDate":"2024-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142484532","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}

引用次数: 0

Modelling the influence of vitamin D and probiotic supplementation on the microbiome and immune response. 模拟维生素 D 和益生菌补充剂对微生物组和免疫反应的影响。

Mathematical medicine and biology : a journal of the IMA Pub Date : 2024-12-16 DOI: 10.1093/imammb/dqae017

S J Franks, J L Dunster, S R Carding, J M Lord, M Hewison, P C Calder, J R King

{"title":"Modelling the influence of vitamin D and probiotic supplementation on the microbiome and immune response.","authors":"S J Franks, J L Dunster, S R Carding, J M Lord, M Hewison, P C Calder, J R King","doi":"10.1093/imammb/dqae017","DOIUrl":"10.1093/imammb/dqae017","url":null,"abstract":"The intestinal microbiota play a critical role in human health and disease, maintaining metabolic and immune/inflammatory health, synthesizing essential vitamins and amino acids and maintaining intestinal barrier integrity. The aim of this paper is to develop a mathematical model to describe the complex interactions between the microbiota, vitamin D/vitamin D receptor (VDR) pathway, epithelial barrier and immune response in order to understand better the effects of supplementation with probiotics and vitamin D. This is motivated by emerging data indicating the beneficial effects of vitamin D and probiotics individually and when combined. We propose a system of ordinary differential equations determining the time evolution of intestinal bacterial populations, concentration of the VDR:1,25(OH)$_{2}$D complex in epithelial and immune cells, the epithelial barrier and the immune response. The model shows that administration of probiotics and/or vitamin D upregulates the VDR complex, which enhances barrier function and protects against intestinal inflammation. The model also suggests co-supplementation to be superior to individual supplements. We explore the effects of inflammation on the populations of commensal and pathogenic bacteria and the vitamin D/VDR pathway and discuss the value of gathering additional experimental data motivated by the modelling insights.","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":" ","pages":"304-345"},"PeriodicalIF":0.0,"publicationDate":"2024-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142368080","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}

引用次数: 0

Polymer-interface-tissue model to estimate leachable release from medical devices. 估算医疗器械可渗漏释放的聚合物-界面-组织模型。

Mathematical medicine and biology : a journal of the IMA Pub Date : 2024-12-16 DOI: 10.1093/imammb/dqae020

Martin L Tanaka, David M Saylor, Robert M Elder

{"title":"Polymer-interface-tissue model to estimate leachable release from medical devices.","authors":"Martin L Tanaka, David M Saylor, Robert M Elder","doi":"10.1093/imammb/dqae020","DOIUrl":"10.1093/imammb/dqae020","url":null,"abstract":"The ability to predict clinically relevant exposure to potentially hazardous compounds that can leach from polymeric components can help reduce testing needed to evaluate the biocompatibility of medical devices. In this manuscript, we compare two physics-based exposure models: 1) a simple, one-component model that assumes the only barrier to leaching is the migration of the compound through the polymer matrix and 2) a more clinically relevant, two-component model that also considers partitioning across the polymer-tissue interface and migration in the tissue away from the interface. Using data from the literature, the variation of the model parameters with key material properties were established, enabling the models to be applied to a wide range of combinations of leachable compound, polymer matrix and tissue type. Exposure predictions based on the models suggest that the models are indistinguishable over much of the range of clinically relevant scenarios. However, for systems with low partitioning and/or slow tissue diffusion, the two-component model predicted up to three orders of magnitude less mass release over the same time period. Thus, despite the added complexity, in some scenarios it can be beneficial to use the two-component model to provide more clinically relevant estimates of exposure to leachable substances from implanted devices.","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":" ","pages":"382-403"},"PeriodicalIF":0.0,"publicationDate":"2024-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142484533","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}

引用次数: 0

Correction to: Inference on an interacting diffusion system with application to in vitro glioblastoma migration (publication template). 更正：关于相互作用扩散系统在胶质母细胞瘤体外迁移中的应用的推论（出版物模板）。

Mathematical medicine and biology : a journal of the IMA Pub Date : 2024-11-28 DOI: 10.1093/imammb/dqae023

引用次数: 0

HeMiTo-dynamics: a characterisation of mammalian prion toxicity using non-dimensionalisation, linear stability and perturbation analyses. 半微动力学：哺乳动物朊病毒毒性的特征使用无量纲化，线性稳定性和摄动分析。

Mathematical medicine and biology : a journal of the IMA Pub Date : 2024-11-28 DOI: 10.1093/imammb/dqae024

Johannes G Borgqvist, Christoffer Gretarsson Alexandersen

{"title":"HeMiTo-dynamics: a characterisation of mammalian prion toxicity using non-dimensionalisation, linear stability and perturbation analyses.","authors":"Johannes G Borgqvist, Christoffer Gretarsson Alexandersen","doi":"10.1093/imammb/dqae024","DOIUrl":"https://doi.org/10.1093/imammb/dqae024","url":null,"abstract":"Prion-like proteins play crucial parts in biological processes in organisms ranging from yeast to humans. For instance, many neurodegenerative diseases are believed to be caused by the production of prion-like proteins in neural tissue. As such, understanding the dynamics of prion-like protein production is a vital step toward treating neurodegenerative disease. Mathematical models of prion-like protein dynamics show great promise as a tool for predicting disease trajectories and devising better treatment strategies for prion-related diseases. Herein, we investigate a generic model for prion-like dynamics consisting of a class of non-linear ordinary differential equations (ODEs), establishing constraints through a linear stability analysis that enforce the expected properties of mammalian prion-like toxicity. Furthermore, we identify that prion toxicity evolves through three distinct phases for which we provide analytical descriptions using perturbation analyses. Specifically, prion-toxicity is initially characterised by the healthy phase, where the dynamics are dominated by the healthy form of prions, thereafter the system enters the mixed phase, where both healthy and toxic prions interact, and lastly, the system enters the toxic phase, where toxic prions dominate, and we refer to these phases as HeMiTo-dynamics. These findings hold the potential to aid researchers in developing precise mathematical models for prion-like dynamics, enabling them to better understand underlying mechanisms and devise effective treatments for prion-related diseases.","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142752730","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}

引用次数: 0

Beyond SIRD models: a novel dynamic model for epidemics, relating infected with entries to health care units and application for identification and restraining policy. 超越 SIRD 模型：一种新型的流行病动态模型，将感染者与进入医疗单位的人员联系起来，并应用于识别和限制政策。

Mathematical medicine and biology : a journal of the IMA Pub Date : 2024-09-16 DOI: 10.1093/imammb/dqae008

Christos Tsiliyannis

{"title":"Beyond SIRD models: a novel dynamic model for epidemics, relating infected with entries to health care units and application for identification and restraining policy.","authors":"Christos Tsiliyannis","doi":"10.1093/imammb/dqae008","DOIUrl":"10.1093/imammb/dqae008","url":null,"abstract":"Epidemic models of susceptibles, exposed, infected, recovered and deceased (SΕIRD) presume homogeneity, constant rates and fixed, bilinear structure. They produce short-range, single-peak responses, hardly attained under restrictive measures. Tuned via uncertain I,R,D data, they cannot faithfully represent long-range evolution. A robust epidemic model is presented that relates infected with the entry rate to health care units (HCUs) via population averages. Model uncertainty is circumvented by not presuming any specific model structure, or constant rates. The model is tuned via data of low uncertainty, by direct monitoring: (a) of entries to HCUs (accurately known, in contrast to delayed and non-reliable I,R,D data) and (b) of scaled model parameters, representing population averages. The model encompasses random propagation of infections, delayed, randomly distributed entries to HCUs and varying exodus of non-hospitalized, as disease severity subdues. It closely follows multi-pattern growth of epidemics with possible recurrency, viral strains and mutations, varying environmental conditions, immunity levels, control measures and efficacy thereof, including vaccination. The results enable real-time identification of infected and infection rate. They allow design of resilient, cost-effective policy in real time, targeting directly the key variable to be controlled (entries to HCUs) below current HCU capacity. As demonstrated in ex post case studies, the policy can lead to lower overall cost of epidemics, by balancing the trade-off between the social cost of infected and the economic contraction associated with social distancing and mobility restriction measures.","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":" ","pages":"192-224"},"PeriodicalIF":0.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142001625","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}

引用次数: 0