Mathematical Medicine and Biology-A Journal of the Ima最新文献_第2页

Exploring the constituent mechanisms of hepatitis: a dynamical systems approach. 探索肝炎的组成机制:动力系统方法。

IF 1.1 4区数学

Mathematical Medicine and Biology-A Journal of the Ima Pub Date : 2023-03-13 DOI: 10.1093/imammb/dqac013

Joanne L Dunster, Jonathan M Gibbins, Martin R Nelson

引用次数: 1

Computer simulation of surgical interventions for the treatment of refractory pulmonary hypertension. 难治性肺动脉高压手术干预的计算机模拟。

IF 1.1 4区数学

Mathematical Medicine and Biology-A Journal of the Ima Pub Date : 2023-03-13 DOI: 10.1093/imammb/dqac011

Seong Woo Han, Charles Puelz, Craig G Rusin, Daniel J Penny, Ryan Coleman, Charles S Peskin

{"title":"Computer simulation of surgical interventions for the treatment of refractory pulmonary hypertension.","authors":"Seong Woo Han, Charles Puelz, Craig G Rusin, Daniel J Penny, Ryan Coleman, Charles S Peskin","doi":"10.1093/imammb/dqac011","DOIUrl":"https://doi.org/10.1093/imammb/dqac011","url":null,"abstract":"This paper describes computer models of three interventions used for treating refractory pulmonary hypertension (RPH). These procedures create either an atrial septal defect, a ventricular septal defect or, in the case of a Potts shunt, a patent ductus arteriosus. The aim in all three cases is to generate a right-to-left shunt, allowing for either pressure or volume unloading of the right side of the heart in the setting of right ventricular failure, while maintaining cardiac output. These shunts are created, however, at the expense of introducing de-oxygenated blood into the systemic circulation, thereby lowering the systemic arterial oxygen saturation. The models developed in this paper are based on compartmental descriptions of human hemodynamics and oxygen transport. An important parameter included in our models is the cross-sectional area of the surgically created defect. Numerical simulations are performed to compare different interventions and various shunt sizes and to assess their impact on hemodynamic variables and oxygen saturations. We also create a model for exercise and use it to study exercise tolerance in simulated pre-intervention and post-intervention RPH patients.","PeriodicalId":49863,"journal":{"name":"Mathematical Medicine and Biology-A Journal of the Ima","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2023-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9504650","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Predicting elimination of evolving virus variants. 预测消除不断进化的病毒变体。

IF 1.1 4区数学

Mathematical Medicine and Biology-A Journal of the Ima Pub Date : 2022-12-02 DOI: 10.1093/imammb/dqac012

Elliott Hughes, Rachelle Binny, Shaun Hendy, Alex James

引用次数: 0

Estimating decay curves of neutralizing antibodies to SARS-CoV-2 infection. 估计SARS-CoV-2感染中和抗体的衰减曲线。

IF 1.1 4区数学

Mathematical Medicine and Biology-A Journal of the Ima Pub Date : 2022-12-02 DOI: 10.1093/imammb/dqac008

Elliot Poehler, Liam Gibson, Audrey Lustig, Nicole J Moreland, Reuben McGregor, Alex James

引用次数: 4

How quickly does a wound heal? Bayesian calibration of a mathematical model of venous leg ulcer healing. 伤口愈合得多快?贝叶斯校正腿部静脉溃疡愈合的数学模型。

IF 1.1 4区数学

Mathematical Medicine and Biology-A Journal of the Ima Pub Date : 2022-12-02 DOI: 10.1093/imammb/dqac007

Adriana Zanca, James M Osborne, Sophie G Zaloumis, Carolina D Weller, Jennifer A Flegg

{"title":"How quickly does a wound heal? Bayesian calibration of a mathematical model of venous leg ulcer healing.","authors":"Adriana Zanca, James M Osborne, Sophie G Zaloumis, Carolina D Weller, Jennifer A Flegg","doi":"10.1093/imammb/dqac007","DOIUrl":"https://doi.org/10.1093/imammb/dqac007","url":null,"abstract":"Chronic wounds, such as venous leg ulcers, are difficult to treat and can reduce the quality of life for patients. Clinical trials have been conducted to identify the most effective venous leg ulcer treatments and the clinical factors that may indicate whether a wound will successfully heal. More recently, mathematical modelling has been used to gain insight into biological factors that may affect treatment success but are difficult to measure clinically, such as the rate of oxygen flow into wounded tissue. In this work, we calibrate an existing mathematical model using a Bayesian approach with clinical data for individual patients to explore which clinical factors may impact the rate of wound healing for individuals. Although the model describes group-level behaviour well, it is not able to capture individual-level responses in all cases. From the individual-level analysis, we propose distributions for coefficients of clinical factors in a linear regression model, but ultimately find that it is difficult to draw conclusions about which factors lead to faster wound healing based on the existing model and data. This work highlights the challenges of using Bayesian methods to calibrate partial differential equation models to individual patient clinical data. However, the methods used in this work may be modified and extended to calibrate spatiotemporal mathematical models to multiple data sets, such as clinical trials with several patients, to extract additional information from the model and answer outstanding biological questions.","PeriodicalId":49863,"journal":{"name":"Mathematical Medicine and Biology-A Journal of the Ima","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"10452695","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Multi-scale modelling of nanoparticle delivery and heat transport in vascularised tumours. 血管化肿瘤中纳米颗粒传递和热传递的多尺度建模。

IF 1.1 4区数学

Mathematical Medicine and Biology-A Journal of the Ima Pub Date : 2022-12-02 DOI: 10.1093/imammb/dqac009

Tahani Al Sariri, Raimondo Penta

{"title":"Multi-scale modelling of nanoparticle delivery and heat transport in vascularised tumours.","authors":"Tahani Al Sariri, Raimondo Penta","doi":"10.1093/imammb/dqac009","DOIUrl":"https://doi.org/10.1093/imammb/dqac009","url":null,"abstract":"We focus on modelling of cancer hyperthermia driven by the application of the magnetic field to iron oxide nanoparticles. We assume that the particles are interacting with the tumour environment by extravasating from the vessels into the interstitial space. We start from Darcy's and Stokes' problems in the interstitial and fluid vessels compartments. Advection-diffusion of nanoparticles takes place in both compartments (as well as uptake in the tumour interstitium), and a heat source proportional to the concentration of nanoparticles drives heat diffusion and convection in the system. The system under consideration is intrinsically multi-scale. The distance between adjacent vessels (the micro-scale) is much smaller than the average tumour size (the macro-scale). We then apply the asymptotic homogenisation technique to retain the influence of the micro-structure on the tissue scale distribution of heat and particles. We derive a new system of homogenised partial differential equations (PDEs) describing blood transport, delivery of nanoparticles and heat transport. The new model comprises a double Darcy's law, coupled with two double advection-diffusion-reaction systems of PDEs describing fluid, particles and heat transport and mass, drug and heat exchange. The role of the micro-structure is encoded in the coefficients of the model, which are to be computed solving appropriate periodic problems. We show that the heat distribution is impaired by increasing vessels' tortuosity and that regularization of the micro-vessels can produce a significant increase (1-2 degrees) in the maximum temperature. We quantify the impact of modifying the properties of the magnetic field depending on the vessels' tortuosity.","PeriodicalId":49863,"journal":{"name":"Mathematical Medicine and Biology-A Journal of the Ima","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"10477222","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 3

On a tumor growth model with brain lactate kinetics. 基于脑乳酸动力学的肿瘤生长模型。

IF 1.1 4区数学

Mathematical Medicine and Biology-A Journal of the Ima Pub Date : 2022-12-02 DOI: 10.1093/imammb/dqac010

Laurence Cherfils, Stefania Gatti, Carole Guillevin, Alain Miranville, Rémy Guillevin

引用次数: 1

Non-vanishing sharp-fronted travelling wave solutions of the Fisher-Kolmogorov model. Fisher-Kolmogorov模型的非消失锐前行波解。

IF 1.1 4区数学

Mathematical Medicine and Biology-A Journal of the Ima Pub Date : 2022-09-08 DOI: 10.1093/imammb/dqac004

Maud El-Hachem, Scott W McCue, Matthew J Simpson

{"title":"Non-vanishing sharp-fronted travelling wave solutions of the Fisher-Kolmogorov model.","authors":"Maud El-Hachem, Scott W McCue, Matthew J Simpson","doi":"10.1093/imammb/dqac004","DOIUrl":"https://doi.org/10.1093/imammb/dqac004","url":null,"abstract":"The Fisher-Kolmogorov-Petrovsky-Piskunov (KPP) model, and generalizations thereof, involves simple reaction-diffusion equations for biological invasion that assume individuals in the population undergo linear diffusion with diffusivity $D$, and logistic proliferation with rate $lambda $. For the Fisher-KPP model, biologically relevant initial conditions lead to long-time travelling wave solutions that move with speed $c=2sqrt {lambda D}$. Despite these attractive features, there are several biological limitations of travelling wave solutions of the Fisher-KPP model. First, these travelling wave solutions do not predict a well-defined invasion front. Second, biologically relevant initial conditions lead to travelling waves that move with speed $c=2sqrt {lambda D}> 0$. This means that, for biologically relevant initial data, the Fisher-KPP model cannot be used to study invasion with $c ne 2sqrt {lambda D}$, or retreating travelling waves with $c < 0$. Here, we reformulate the Fisher-KPP model as a moving boundary problem and show that this reformulated model alleviates the key limitations of the Fisher-KPP model. Travelling wave solutions of the moving boundary problem predict a well-defined front that can propagate with any wave speed, $-infty < c < infty $. Here, we establish these results using a combination of high-accuracy numerical simulations of the time-dependent partial differential equation, phase plane analysis and perturbation methods. All software required to replicate this work is available on GitHub.","PeriodicalId":49863,"journal":{"name":"Mathematical Medicine and Biology-A Journal of the Ima","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"40513741","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2

Modelling the spreading of the SARS-CoV-2 in presence of the lockdown and quarantine measures by a kinetic-type reactions approach. 通过动力学型反应方法模拟在封锁和隔离措施下SARS-CoV-2的传播。

IF 1.1 4区数学

Mathematical Medicine and Biology-A Journal of the Ima Pub Date : 2022-06-11 DOI: 10.1093/imammb/dqab017

Giorgio Sonnino, Philippe Peeters, Pasquale Nardone

{"title":"Modelling the spreading of the SARS-CoV-2 in presence of the lockdown and quarantine measures by a kinetic-type reactions approach.","authors":"Giorgio Sonnino, Philippe Peeters, Pasquale Nardone","doi":"10.1093/imammb/dqab017","DOIUrl":"10.1093/imammb/dqab017","url":null,"abstract":"We propose a realistic model for the evolution of the COVID-19 pandemic subject to the lockdown and quarantine measures, which takes into account the timedelay for recovery or death processes. The dynamic equations for the entire process are derived by adopting a kinetic-type reactions approach. More specifically, the lockdown and the quarantine measures are modelled by some kind of inhibitor reactions where susceptible and infected individuals can be trapped into inactive states. The dynamics for the recovered people is obtained by accounting people who are only traced back to hospitalized infected people. To get the evolution equation we take inspiration from the Michaelis Menten's enzyme-substrate reaction model (the so-called MM reaction) where the enzyme is associated to the available hospital beds, the substrate to the infected people, and the product to the recovered people, respectively. In other words, everything happens as if the hospitals beds act as a catalyzer in the hospital recovery process. Of course, in our case, the reverse MM reaction has no sense in our case and, consequently, the kinetic constant is equal to zero. Finally, the ordinary differential equations (ODEs) for people tested positive to COVID-19 is simply modelled by the following kinetic scheme $S+IRightarrow 2I$ with $IRightarrow R$ or $IRightarrow D$, with $S$, $I$, $R$ and $D$ denoting the compartments susceptible, infected, recovered and deceased people, respectively. The resulting kinetic-type equations provide the ODEs, for elementary reaction steps, describing the number of the infected people, the total number of the recovered people previously hospitalized, subject to the lockdown and the quarantine measure and the total number of deaths. The model foresees also the second wave of infection by coronavirus. The tests carried out on real data for Belgium, France and Germany confirmed the correctness of our model.","PeriodicalId":49863,"journal":{"name":"Mathematical Medicine and Biology-A Journal of the Ima","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8689708/pdf/dqab017.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"39699688","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 4

Modelling articular cartilage: the relative motion of two adjacent poroviscoelastic layers. 关节软骨的建模:两个相邻的孔粘弹性层的相对运动。

IF 1.1 4区数学

Mathematical Medicine and Biology-A Journal of the Ima Pub Date : 2022-06-09 DOI: 10.1093/imammb/dqac005

J. Whiteley, Cameron P. Brown, E. Gaffney

{"title":"Modelling articular cartilage: the relative motion of two adjacent poroviscoelastic layers.","authors":"J. Whiteley, Cameron P. Brown, E. Gaffney","doi":"10.1093/imammb/dqac005","DOIUrl":"https://doi.org/10.1093/imammb/dqac005","url":null,"abstract":"In skeletal joints two layers of adjacent cartilage are often in relative motion. The individual cartilage layers are often modelled as a poroviscoelastic material. To model the relative motion, noting the separation of scales between the pore level and the macroscale, a homogenization based on multiple scale asymptotic analysis has been used in this study to derive a macroscale model for the relative translation of two poroviscoelastic layers separated by a very thin layer of fluid. In particular the fluid layer thickness is essentially zero at the macroscale so that the two poroviscoelastic layers are effectively in contact and their interaction is captured in the derived model via a set of interfacial conditions, including a generalization of the Beavers-Joseph condition at the interface between a viscous fluid and a porous medium. In the simplifying context of a uniform geometry, constant fixed charge density, a Newtonian interstitial fluid and a viscoelastic scaffold, modelled via finite deformation theory, we present preliminary simulations that may be used to highlight predictions for how oscillatory relative movement of cartilage under load influences the peak force the cartilage experiences and the extent of the associated deformations. In addition to highlighting such cartilage mechanics, the systematic derivation of the macroscale models will enable the study of how nanoscale cartilage physics, such as the swelling pressure induced by fixed charges, manifests in cartilage mechanics at much higher lengthscales.","PeriodicalId":49863,"journal":{"name":"Mathematical Medicine and Biology-A Journal of the Ima","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83113969","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0