D. C. Trost, E. Overman, J. Ostroff, W. Xiong, Peter March
{"title":"A Model for Liver Homeostasis Using Modified Mean-Reverting Ornstein-Uhlenbeck Process","authors":"D. C. Trost, E. Overman, J. Ostroff, W. Xiong, Peter March","doi":"10.1080/17486700802653925","DOIUrl":"https://doi.org/10.1080/17486700802653925","url":null,"abstract":"Short of a liver biopsy, hepatic disease and drug-induced liver injury are diagnosed and classified from clinical findings, especially laboratory results. It was hypothesized that a healthy hepatic dynamic equilibrium might be modelled by an Ornstein–Uhlenbeck (OU) stochastic process, which might lead to more sensitive and specific diagnostic criteria. Using pooled data from healthy volunteers in pharmaceutical clinical trials, this model was applied using maximum likelihood (ML) methods. It was found that the exponent of the autocorrelation function was proportional to the square root of time rather than time itself, as predicted by the OU model. This finding suggests a stronger autocorrelation than expected and may have important implications regarding the use of laboratory testing in clinical diagnosis, in clinical trial design, and in monitoring drug safety. Besides rejecting the OU hypothesis for liver test homeostasis, this paper presents ML estimates for the multivariate Gaussian distribution for healthy adult males. This work forms the basis for a new approach to mathematical modelling to improve both the sensitivity and specificity of clinical measurements over time.","PeriodicalId":182719,"journal":{"name":"Comput. Math. Methods Medicine","volume":"2010 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129570565","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}
{"title":"A Hypothetical-Mathematical Model of Acute Myeloid Leukaemia Pathogenesis","authors":"A. Cucuianu, R. Precup","doi":"10.1080/17486700902973751","DOIUrl":"https://doi.org/10.1080/17486700902973751","url":null,"abstract":"Acute myeloid leukaemia is defined by the expansion of a mutated haematopoietic stem cell clone, with the inhibition of surrounding normal clones. Haematopoiesis can be seen as an evolutionary tree, starting with one cell that undergoes several divisions during the expansion phase, afterwards losing functional cells during the aging-related contraction phase. During divisions, offspring cells acquire ‘variations’, which can be either normal or abnormal. If an abnormal variation is present in more than 25% of the final cells, a monoclonal, leukemic pattern occurs. Such a pattern develops if: (A1) The abnormal variation occurs early, during the first or second divisions; (A2) The variation confers exceptional proliferative capacity; (B) A sizable proportion of the normal clones are destroyed and a previously non-significant abnormal clone gains relative dominance over a depleted environment; (C) The abnormal variation confers relative ‘immortality’, rendering it significant during the contraction phase. Combinations of these pathways further enhance the leukemic risk of the system. A simple mathematical model is used in order to characterize normal and leukemic states and to explain the above cellular processes generating monoclonal leukemic patterns.","PeriodicalId":182719,"journal":{"name":"Comput. Math. Methods Medicine","volume":"57 10","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120968811","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}
{"title":"Stability and Hopf Bifurcation Analysis of a Vector-Borne Disease Model with Two Delays and Reinfection","authors":"Yanxia Zhang, Long Li, Junjian Huang, Yanjun Liu","doi":"10.1155/2021/6648959","DOIUrl":"https://doi.org/10.1155/2021/6648959","url":null,"abstract":"In this paper, a vector-borne disease model with two delays and reinfection is established and considered. First of all, the existence of the equilibrium of the system, under different cases of two delays, is discussed through analyzing the corresponding characteristic equation of the linear system. Some conditions that the system undergoes Hopf bifurcation at the endemic equilibrium are obtained. Furthermore, by employing the normal form method and the center manifold theorem for delay differential equations, some explicit formulas used to describe the properties of bifurcating periodic solutions are derived. Finally, the numerical examples and simulations are presented to verify our theoretical conclusions. Meanwhile, the influences of the degree of partial protection for recovered people acquired by a primary infection on the endemic equilibrium and the critical values of the two delays are analyzed.","PeriodicalId":182719,"journal":{"name":"Comput. Math. Methods Medicine","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117043975","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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