Mathematical medicine and biology : a journal of the IMA最新文献_第5页

Calculating prescription rates and addiction probabilities for the four most commonly prescribed opioids and evaluating their impact on addiction using compartment modelling 计算四种最常用的阿片类药物的处方率和成瘾概率，并使用隔室模型评估其对成瘾的影响

Mathematical medicine and biology : a journal of the IMA Pub Date : 2021-01-01 DOI: 10.1093/imammb/dqab001

Samantha R Rivas;Alex C Tessner;Eli E Goldwyn

{"title":"Calculating prescription rates and addiction probabilities for the four most commonly prescribed opioids and evaluating their impact on addiction using compartment modelling","authors":"Samantha R Rivas;Alex C Tessner;Eli E Goldwyn","doi":"10.1093/imammb/dqab001","DOIUrl":"10.1093/imammb/dqab001","url":null,"abstract":"In 2016, more than 11 million Americans abused prescription opioids. The National Institute on Drug Abuse considers the opioid crisis a national addiction epidemic, as an increasing number of people are affected each year. Using the framework developed in mathematical modelling of infectious diseases, we create and analyse a compartmental opioid-abuse model consisting of a system of ordinary differential equations. Since \u0000<tex>$40%$</tex>\u0000 of opioid overdoses are caused by prescription opioids, our model includes prescription compartments for the four most commonly prescribed opioids, as well as for the susceptible, addicted and recovered populations. While existing research has focused on drug abuse models in general and opioid models with one prescription compartment, no previous work has been done comparing the roles that the most commonly prescribed opioids have had on the crisis. By combining data from the Substance Abuse and Mental Health Services Administration (which tracked the proportion of people who used or misused one of the four individual opioids) with data from the Centers of Disease Control and Prevention (which counted the total number of prescriptions), we estimate prescription rates and probabilities of addiction for the four most commonly prescribed opioids. Additionally, we perform a sensitivity analysis and reallocate prescriptions to determine which opioid has the largest impact on the epidemic. Our results indicate that oxycodone prescriptions are both the most likely to lead to addiction and have the largest impact on the size of the epidemic, while hydrocodone prescriptions had the smallest impact.","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":"38 2","pages":"202-217"},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imammb/dqab001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"25369726","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: 4

Existence of solutions and numerical approximation of a non-local tumor growth model 非局部肿瘤生长模型解的存在性及数值逼近

Mathematical medicine and biology : a journal of the IMA Pub Date : 2020-02-01 DOI: 10.1093/imammb/dqz005

Lucia Maddalena;Stefania Ragni

引用次数: 3

A hybrid discrete–continuum approach for modelling microcirculatory blood flow 模拟微循环血流的一种混合离散-连续方法

Mathematical medicine and biology : a journal of the IMA Pub Date : 2020-02-01 DOI: 10.1093/imammb/dqz006

Rebecca J Shipley;Amy F Smith;Paul W Sweeney;Axel R Pries;Timothy W Secomb

{"title":"A hybrid discrete–continuum approach for modelling microcirculatory blood flow","authors":"Rebecca J Shipley;Amy F Smith;Paul W Sweeney;Axel R Pries;Timothy W Secomb","doi":"10.1093/imammb/dqz006","DOIUrl":"10.1093/imammb/dqz006","url":null,"abstract":"In recent years, biological imaging techniques have advanced significantly and it is now possible to digitally reconstruct microvascular network structures in detail, identifying the smallest capillaries at sub-micron resolution and generating large 3D structural data sets of size >10\u0000<sup>6</sup>\u0000 vessel segments. However, this relies on ex vivo imaging; corresponding in vivo measures of microvascular structure and flow are limited to larger branching vessels and are not achievable in three dimensions for the smallest vessels. This suggests the use of computational modelling to combine in vivo measures of branching vessel architecture and flows with ex vivo data on complete microvascular structures to predict effective flow and pressures distributions. In this paper, a hybrid discrete–continuum model to predict microcirculatory blood flow based on structural information is developed and compared with existing models for flow and pressure in individual vessels. A continuum-based Darcy model for transport in the capillary bed is coupled via point sources of flux to flows in individual arteriolar vessels, which are described explicitly using Poiseuille's law. The venular drainage is represented as a spatially uniform flow sink. The resulting discrete–continuum framework is parameterized using structural data from the capillary network and compared with a fully discrete flow and pressure solution in three networks derived from observations of the rat mesentery. The discrete–continuum approach is feasible and effective, providing a promising tool for extracting functional transport properties in situations where vascular branching structures are well defined.","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":"37 1","pages":"40-57"},"PeriodicalIF":0.0,"publicationDate":"2020-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imammb/dqz006","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37249690","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: 24

A Markov decision process approach to optimizing cancer therapy using multiple modalities 利用马尔可夫决策过程方法优化多种方式的癌症治疗

Mathematical medicine and biology : a journal of the IMA Pub Date : 2020-02-01 DOI: 10.1093/imammb/dqz004

Kelsey Maass;Minsun Kim

{"title":"A Markov decision process approach to optimizing cancer therapy using multiple modalities","authors":"Kelsey Maass;Minsun Kim","doi":"10.1093/imammb/dqz004","DOIUrl":"10.1093/imammb/dqz004","url":null,"abstract":"There are several different modalities, e.g. surgery, chemotherapy and radiotherapy, that are currently used to treat cancer. It is common practice to use a combination of these modalities to maximize clinical outcomes, which are often measured by a balance between maximizing tumor damage and minimizing normal tissue side effects due to treatment. However, multi-modality treatment policies are mostly empirical in current practice and are therefore subject to individual clinicians' experiences and intuition. We present a novel formulation of optimal multi-modality cancer management using a finite-horizon Markov decision process approach. Specifically, at each decision epoch, the clinician chooses an optimal treatment modality based on the patient's observed state, which we define as a combination of tumor progression and normal tissue side effect. Treatment modalities are categorized as (1) type 1, which has a high risk and high reward, but is restricted in the frequency of administration during a treatment course; (2) type 2, which has a lower risk and lower reward than type 1, but may be repeated without restriction; and (3) type 3, no treatment (surveillance), which has the possibility of reducing normal tissue side effect at the risk of worsening tumor progression. Numerical simulations using various intuitive, concave reward functions show the structural insights of optimal policies and demonstrate the potential applications of using a rigorous approach to optimizing multi-modality cancer management.","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":"37 1","pages":"22-39"},"PeriodicalIF":0.0,"publicationDate":"2020-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imammb/dqz004","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37049811","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: 7

A mathematical model of viral oncology as an immuno-oncology instigator 病毒肿瘤学作为免疫肿瘤学教唆者的数学模型

Mathematical medicine and biology : a journal of the IMA Pub Date : 2020-02-01 DOI: 10.1093/imammb/dqz008

Tyler Cassidy;Antony R Humphries

引用次数: 13

A model of strongly biased chemotaxis reveals the trade-offs of different bacterial migration strategies 一个强烈偏向趋化的模型揭示了不同细菌迁移策略的权衡

Mathematical medicine and biology : a journal of the IMA Pub Date : 2020-02-01 DOI: 10.1093/imammb/dqz007

R N Bearon;W M Durham

{"title":"A model of strongly biased chemotaxis reveals the trade-offs of different bacterial migration strategies","authors":"R N Bearon;W M Durham","doi":"10.1093/imammb/dqz007","DOIUrl":"10.1093/imammb/dqz007","url":null,"abstract":"Many bacteria actively bias their motility towards more favourable nutrient environments. In liquid, cells rotate their corkscrew-shaped flagella to swim, but in surface attached biofilms cells instead use grappling hook-like appendages called pili to pull themselves along. In both forms of motility, cells selectively alternate between relatively straight 'runs' and sharp reorientations to generate biased random walks up chemoattractant gradients. However, recent experiments suggest that swimming and biofilm cells employ fundamentally different strategies to generate chemotaxis: swimming cells typically suppress reorientations when moving up a chemoattractant gradient, whereas biofilm cells increase reorientations when moving down a chemoattractant gradient. The reason for this difference remains unknown. Here we develop a mathematical framework to understand how these different chemotactic strategies affect the distribution of cells at the population level. Current continuum models typically assume a weak bias in the reorientation rate and are not able to distinguish between these two strategies, so we derive a model for strong chemotaxis that resolves how both the drift and diffusive components depend on the underlying chemotactic strategy. We then test predictions from our continuum model against individual-based simulations and identify further refinements that allow our continuum model to resolve boundary effects. Our analyses reveal that the strategy employed by swimming cells yields a larger chemotactic drift, but the strategy used by biofilm cells allows them to more tightly aggregate where the chemoattractant is most abundant. This new modelling framework provides new quantitative insights into how the different chemical landscapes experienced by swimming and biofilm cells might select for divergent ways of generating chemotaxis.","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":"37 1","pages":"83-116"},"PeriodicalIF":0.0,"publicationDate":"2020-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imammb/dqz007","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37122334","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: 3

Optimal control with MANF treatment of photoreceptor degeneration MANF处理光感受器退化的最优控制

Mathematical medicine and biology : a journal of the IMA Pub Date : 2020-02-01 DOI: 10.1093/imammb/dqz003

Erika T Camacho;Suzanne Lenhart;Luis A Melara;M Cristina Villalobos;Stephen Wirkus

{"title":"Optimal control with MANF treatment of photoreceptor degeneration","authors":"Erika T Camacho;Suzanne Lenhart;Luis A Melara;M Cristina Villalobos;Stephen Wirkus","doi":"10.1093/imammb/dqz003","DOIUrl":"10.1093/imammb/dqz003","url":null,"abstract":"People afflicted with diseases such as retinitis pigmentosa and age-related macular degeneration experience a decline in vision due to photoreceptor degeneration, which is currently unstoppable and irreversible. Currently there is no cure for diseases linked to photoreceptor degeneration. Recent experimental work showed that mesencephalic astrocyte-derived neurotrophic factor (MANF) can reduce neuron death and, in particular, photoreceptor death by reducing the number of cells that undergo apoptosis. In this work, we build on an existing system of ordinary differential equations that represent photoreceptor interactions and incorporate MANF treatment for three experimental mouse models having undergone varying degrees of photoreceptor degeneration. Using MANF treatment levels as controls, we investigate optimal control results in the three mouse models. In addition, our numerical solutions match the experimentally observed surviving percentage of photoreceptors and our uncertainty and sensitivity analysis identifies significant parameters in the math model both with and without MANF treatment.","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":"37 1","pages":"1-21"},"PeriodicalIF":0.0,"publicationDate":"2020-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imammb/dqz003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37003196","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: 7

Mass drug administration: the importance of synchrony 大规模药物管理：同步性的重要性。

Mathematical medicine and biology : a journal of the IMA Pub Date : 2017-06-01 DOI: 10.1093/imammb/dqw005

Daozhou Gao;Thomas M. Lietman;Chao-Ping Dong;Travis C. Porco

{"title":"Mass drug administration: the importance of synchrony","authors":"Daozhou Gao;Thomas M. Lietman;Chao-Ping Dong;Travis C. Porco","doi":"10.1093/imammb/dqw005","DOIUrl":"10.1093/imammb/dqw005","url":null,"abstract":"Mass drug administration, a strategy in which all individuals in a population are subject to treatment without individual diagnosis, has been recommended by the World Health Organization for controlling and eliminating several neglected tropical diseases, including trachoma and soil-transmitted helminths. In this article, we derive effective reproduction numbers and average post-treatment disease prevalences of a simple susceptible–infectious–susceptible epidemic model with constant, impulsive synchronized and non-synchronized drug administration strategies. In the non-synchronized model, the individuals in the population are treated at most once per period and their treatment times are uniformly distributed. Mathematically, the set of pulses for the non-synchronized model has the cardinality of the continuum. We show that synchronized and constant strategies are, respectively, the most and least effective treatments in disease control. Elimination through synchronized treatment is always possible when adequate drug efficacy and coverage are fulfilled and sustained. For a strategy with multiple rounds of synchronized treatment per period, the average post-treatment prevalence is irrelevant what the time differences between treatments are, as long as there are the same number of treatments per period.","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":"34 2","pages":"241-260"},"PeriodicalIF":0.0,"publicationDate":"2017-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imammb/dqw005","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"34337172","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: 9

A model of the effects of cancer cell motility and cellular adhesion properties on tumour-immune dynamics 癌细胞运动和细胞粘附特性对肿瘤免疫动力学影响的模型

Mathematical medicine and biology : a journal of the IMA Pub Date : 2017-06-01 DOI: 10.1093/imammb/dqw004

Federico Frascoli;Emelie Flood;Peter S. Kim

{"title":"A model of the effects of cancer cell motility and cellular adhesion properties on tumour-immune dynamics","authors":"Federico Frascoli;Emelie Flood;Peter S. Kim","doi":"10.1093/imammb/dqw004","DOIUrl":"10.1093/imammb/dqw004","url":null,"abstract":"We present a three-dimensional model simulating the dynamics of an anti-cancer T-cell response against a small, avascular, early-stage tumour. Interactions at the tumour site are accounted for using an agent-based model (ABM), while immune cell dynamics in the lymph node are modelled as a system of delay differential equations (DDEs). We combine these separate approaches into a two-compartment hybrid ABM-DDE system to capture the T-cell response against the tumour. In the ABM at the tumour site, movement of tumour cells is modelled using effective physical forces with a specific focus on cell-to-cell adhesion properties and varying levels of tumour cell motility, thus taking into account the ability of cancer cells to spread and form clusters. We consider the effectiveness of the immune response over a range of parameters pertaining to tumour cell motility, cell-to-cell adhesion strength and growth rate. We also investigate the dependence of outcomes on the distribution of tumour cells. Low tumour cell motility is generally a good indicator for successful tumour eradication before relapse, while high motility leads, almost invariably, to relapse and tumour escape. In general, the effect of cell-to-cell adhesion on prognosis is dependent on the level of tumour cell motility, with an often unpredictable cross influence between adhesion and motility, which can lead to counterintuitive effects. In terms of overall tumour shape and structure, the spatial distribution of cancer cells in clusters of various sizes has shown to be strongly related to the likelihood of extinction.","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":"34 2","pages":"215-240"},"PeriodicalIF":0.0,"publicationDate":"2017-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imammb/dqw004","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"34416274","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: 10

Mathematical modelling of cardiovascular response to the Valsalva manoeuvre 瓦尔萨尔瓦演习心血管反应的数学模型

Mathematical medicine and biology : a journal of the IMA Pub Date : 2017-06-01 DOI: 10.1093/imammb/dqw008

Leszek Pstras;Karl Thomaseth;Jacek Waniewski;Italo Balzani;Federico Bellavere

{"title":"Mathematical modelling of cardiovascular response to the Valsalva manoeuvre","authors":"Leszek Pstras;Karl Thomaseth;Jacek Waniewski;Italo Balzani;Federico Bellavere","doi":"10.1093/imammb/dqw008","DOIUrl":"10.1093/imammb/dqw008","url":null,"abstract":"The Valsalva manoeuvre (VM) used for clinical autonomic testing results in a complex cardiovascular response with a concomitant action of several regulatory mechanisms whose nonlinear interactions are difficult to analyse without the aid of a mathematical model. The article presents a new non-pulsatile compartmental model of the human cardiovascular system with a variable intrathoracic pressure enabling the simulation of the haemodynamic response to the VM. The model is based on physiological data and includes three baroreflex mechanisms acting on heart rate, systemic resistance and venous unstressed volume. New nonlinear functions have been proposed to model cardiac output dependence on preload and afterload. Following the individual fitting of some parameters with a clear physiological meaning, the model is able to fit clinical data from patients with both typical and abnormal haemodynamic response to the VM. The sensitivity analysis showed that the model is most sensitive to the parameters describing the vascular pressure–volume relationships (the maximal volume of systemic veins and the relative level of vascular compliance). The use of nonlinear pressure–volume relationships for systemic veins proved crucial for the accurate modelling of the VM. On the contrary, the introduction of aroreflex time delays did not change significantly the haemodynamic response to the manoeuvre. The model can be a useful tool for aiding the interpretation of patient's response to the VM and provides a framework for analysing the interactions between the cardiovascular system and autonomic regulatory mechanisms.","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":"34 2","pages":"261-292"},"PeriodicalIF":0.0,"publicationDate":"2017-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imammb/dqw008","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"34510929","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: 15