Two mathematical models for generation of crowned tooth surface.
Ontology highlight
ABSTRACT:
SUBMITTER: Kelemen L
PROVIDER: S-EPMC3918377 | biostudies-other | 2014
REPOSITORIES: biostudies-other
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Project description:Muscle fatigue models (MFM) have broad potential application if they can accurately predict muscle capacity and/or endurance time during the execution of diverse tasks. As an initial step toward facilitating improved MFMs, we assessed the sensitivity of selected existing models to their inherent parameters, specifically that model the fatigue and recovery processes, and the accuracy of model predictions. These evaluations were completed for both prolonged and intermittent isometric contractions, and were based on model predictions of endurance times. Based on a recent review of the literature, four MFMs were initially chosen, from which a preliminary assessment led to two of these being considered for more comprehensive evaluation. Both models had a higher sensitivity to their fatigue parameter. Predictions of both models were also more sensitive to the alteration of their parameters in conditions involving lower to moderate levels of effort, though such conditions may be of most practical, contemporary interest or relevance. Although both models yielded accurate predictions of endurance times during prolonged contractions, their predictive ability was inferior for more complex (intermittent) conditions. When optimizing model parameters for different loading conditions, the recovery parameter showed considerably larger variability, which might be related to the inability of these MFMs in simulating the recovery process under different loading conditions. It is argued that such models may benefit in future work from improving their representation of recovery process, particularly how this process differs across loading conditions.
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Project description:Neuromuscular physiology is a vibrant research field that has recently seen exciting advances. Previous publications have focused on thorough analyses of particular aspects of neuromuscular physiology, yet an integration of the various novel findings into a single, comprehensive model is missing. In this article, we provide a unified description of a comprehensive mathematical model of surface electromyographic (EMG) measurements and the corresponding force signal in skeletal muscles, both consolidating and extending the results of previous studies regarding various components of the neuromuscular system. The model comprises motor unit (MU) pool organization, recruitment and rate coding, intracellular action potential generation and the resulting EMG measurements, as well as the generated muscular force during voluntary isometric contractions. Mathematically, it consists of a large number of linear PDEs, ODEs, and various stochastic nonlinear relationships, some of which are solved analytically, others numerically. A parameterization of the electrical and mechanical components of the model is proposed that ensures a physiologically meaningful EMG-force relation in the simulated signals, in particular taking the continuous, size-dependent distribution of MU parameters into account. Moreover, a novel nonlinear transformation of the common drive model input is proposed, which ensures that the model force output equals the desired target force. On a physiological level, this corresponds to adjusting the rate coding model to the force generating capabilities of the simulated muscle, while from a control theoretic point of view, this step is equivalent to an exact linearizing transformation of the controlled neuromuscular system. Finally, an alternative analytical formulation of the EMG model is proposed, which renders the physiological meaning of the model more clear and facilitates a mathematical proof that muscle fibers in this model at no point in time represent a net current source or sink. A consistent description of a complete physiological model as presented here, including thorough justification of model component choices, will facilitate the use of these advanced models in future research. Results of a numerical simulation highlight the model's capability to reproduce many physiological effects observed in experimental measurements, and to produce realistic synthetic data that are useful for the validation of signal processing algorithms.
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Project description:The aim of this study is to identify biomarkers of disease recurrence and prognosis to optimize patient selection for treatment with cytoreductive surgery (CRS) with hyperthermic intraperitoneal chemotherapy (HIPEC), and through animal models to explore different treatment strategies for peritoneal surface malignancies (PSM).
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Project description:Dorsal closure is a model cell sheet movement that occurs midway through Drosophila embryogenesis. A dorsal hole, filled with amnioserosa, closes through the dorsalward elongation of lateral epidermal cell sheets. Closure requires contributions from 5 distinct tissues and well over 140 genes (see Mortensen et al., 2018, reviewed in Kiehart et al., 2017 and Hayes and Solon, 2017). In spite of this biological complexity, the movements (kinematics) of closure are geometrically simple at tissue, and in certain cases, at cellular scales. This simplicity has made closure the target of a number of mathematical models that seek to explain and quantify the processes that underlie closure's kinematics. The first (purely kinematic) modeling approach recapitulated well the time-evolving geometry of closure even though the underlying physical principles were not known. Almost all subsequent models delve into the forces of closure (i.e. the dynamics of closure). Models assign elastic, contractile and viscous forces which impact tissue and/or cell mechanics. They write rate equations which relate the forces to one another and to other variables, including those which represent geometric, kinematic, and or signaling characteristics. The time evolution of the variables is obtained by computing the solution of the model's system of equations, with optimized model parameters. The basis of the equations range from the phenomenological to biophysical first principles. We review various models and present their contribution to our understanding of the molecular mechanisms and biophysics of closure. Models of closure will contribute to our understanding of similar movements that characterize vertebrate morphogenesis.
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Project description:The tug-of-war model was developed in a series of papers of McFarland and co-authors to account for existence of mutually counteracting rare advantageous driver mutations and more frequent slightly deleterious passenger mutations in cancer. In its original version, it was a state-dependent branching process. Because of its formulation, the tug-of-war model is of importance for tackling the problem as to whether evolution of cancerous tumors is "Darwinian" or "non-Darwinian." We define two Time-Continuous Markov Chain versions of the model, including identical mutation processes but adopting different drift and selection components. In Model A, drift and selection process preserves expected fitness whereas in Model B it leads to non-decreasing expected fitness. We investigate these properties using mathematical analysis and extensive simulations, which detect the effect of the so-called drift barrier in Model B but not in Model A. These effects are reflected in different structure of clone genealogies in the two models. Our work is related to the past theoretical work in the field of evolutionary genetics, concerning the interplay among mutation, drift and selection, in absence of recombination (asexual reproduction), where epistasis plays a major role. Finally, we use the statistics of mutation frequencies known as the Site Frequency Spectra (SFS), to compare the variant frequencies in DNA of sequenced HER2+ breast cancers, to those based on Model A and B simulations. The tumor-based SFS are better reproduced by Model A, pointing out a possible selection pattern of HER2+ tumor evolution. To put our models in context, we carried out an exploratory study of how publicly accessible data from breast, prostate, skin and ovarian cancers fit a range of models found in the literature.
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Project description:Early afterdepolarizations (EADs), which are abnormal oscillations of the membrane potential at the plateau phase of an action potential, are implicated in the development of cardiac arrhythmias like Torsade de Pointes. We carry out extensive numerical simulations of the TP06 and ORd mathematical models for human ventricular cells with EADs. We investigate the different regimes in both these models, namely, the parameter regimes where they exhibit (1) a normal action potential (AP) with no EADs, (2) an AP with EADs, and (3) an AP with EADs that does not go back to the resting potential. We also study the dependence of EADs on the rate of at which we pace a cell, with the specific goal of elucidating EADs that are induced by slow or fast rate pacing. In our simulations in two- and three-dimensional domains, in the presence of EADs, we find the following wave types: (A) waves driven by the fast sodium current and the L-type calcium current (Na-Ca-mediated waves); (B) waves driven only by the L-type calcium current (Ca-mediated waves); (C) phase waves, which are pseudo-travelling waves. Furthermore, we compare the wave patterns of the various wave-types (Na-Ca-mediated, Ca-mediated, and phase waves) in both these models. We find that the two models produce qualitatively similar results in terms of exhibiting Na-Ca-mediated wave patterns that are more chaotic than those for the Ca-mediated and phase waves. However, there are quantitative differences in the wave patterns of each wave type. The Na-Ca-mediated waves in the ORd model show short-lived spirals but the TP06 model does not. The TP06 model supports more Ca-mediated spirals than those in the ORd model, and the TP06 model exhibits more phase-wave patterns than does the ORd model.
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Project description:With plasmid-mediated antibiotic resistance thriving and threatening to become a serious public health problem, it is paramount to increase our understanding of the forces that enable the spread and maintenance of drug resistance genes encoded in mobile genetic elements. The relevance of plasmids as vehicles for the dissemination of antibiotic resistance genes, in addition to the extensive use of plasmid-derived vectors for biotechnological and industrial purposes, has promoted the in-depth study of the molecular mechanisms controlling multiple aspects of a plasmids' life cycle. This body of experimental work has been paralleled by the development of a wealth of mathematical models aimed at understanding the interplay between transmission, replication, and segregation, as well as their consequences in the ecological and evolutionary dynamics of plasmid-bearing bacterial populations. In this review, we discuss theoretical models of plasmid dynamics that span from the molecular mechanisms of plasmid partition and copy-number control occurring at a cellular level, to their consequences in the population dynamics of complex microbial communities. We conclude by discussing future directions for this exciting research topic.
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Project description:Mathematical models have been used to provide an explicit framework for understanding malaria transmission dynamics in human population for over 100 years. With the disease still thriving and threatening to be a major source of death and disability due to changed environmental and socio-economic conditions, it is necessary to make a critical assessment of the existing models, and study their evolution and efficacy in describing the host-parasite biology. In this article, starting from the basic Ross model, the key mathematical models and their underlying features, based on their specific contributions in the understanding of spread and transmission of malaria have been discussed. The first aim of this article is to develop, starting from the basic models, a hierarchical structure of a range of deterministic models of different levels of complexity. The second objective is to elaborate, using some of the representative mathematical models, the evolution of modelling strategies to describe malaria incidence by including the critical features of host-vector-parasite interactions. Emphasis is more on the evolution of the deterministic differential equation based epidemiological compartment models with a brief discussion on data based statistical models. In this comprehensive survey, the approach has been to summarize the modelling activity in this area so that it helps reach a wider range of researchers working on epidemiology, transmission, and other aspects of malaria. This may facilitate the mathematicians to further develop suitable models in this direction relevant to the present scenario, and help the biologists and public health personnel to adopt better understanding of the modelling strategies to control the disease.
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Project description:BackgroundArtificial intelligence (AI) shows great potential to streamline the treatment planning process. However, its clinical adoption is slow due to the limited number of clinical evaluation studies and because often, the translation of the predicted dose distribution to a deliverable plan is lacking. This study evaluates two different, deliverable AI plans in terms of their clinical acceptability based on quantitative parameters and qualitative evaluation by four radiation oncologists.MethodsFor 20 left-sided node-negative breast cancer patients, treated with a prescribed dose of 40.05 Gy, using tangential beam intensity modulated radiotherapy, two model-based treatment plans were evaluated against the corresponding manual plan. The two models used were an in-house developed U-net model and a vendor-developed contextual atlas regression forest model (cARF). Radiation oncologists evaluated the clinical acceptability of each blinded plan and ranked plans according to preference. Furthermore, a comparison with the manual plan was made based on dose volume histogram parameters, clinical evaluation criteria and preparation time.ResultsThe U-net model resulted in a higher average and maximum dose to the PTV (median difference 0.37 Gy and 0.47 Gy respectively) and a slightly higher mean heart dose (MHD) (0.01 Gy). The cARF model led to higher average and maximum doses to the PTV (0.30 and 0.39 Gy respectively) and a slightly higher MHD (0.02 Gy) and mean lung dose (MLD, 0.04 Gy). The maximum MHD/MLD difference was ≤ 0.5 Gy for both AI plans. Regardless of these dose differences, 90-95% of the AI plans were considered clinically acceptable versus 90% of the manual plans. Preferences varied between the radiation oncologists. Plan preparation time was comparable between the U-net model and the manual plan (287 s vs 253 s) while the cARF model took longer (471 s). When only considering user interaction, plan generation time was 121 s for the cARF model and 137 s for the U-net model.ConclusionsTwo AI models were used to generate deliverable plans for breast cancer patients, in a time-efficient manner, requiring minimal user interaction. Although the AI plans resulted in slightly higher doses overall, radiation oncologists considered 90-95% of the AI plans clinically acceptable.
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Project description:An important aspect of multi-scale modelling is the ability to represent mathematical models in forms that can be exchanged between modellers and tools. While the development of languages like CellML and SBML have provided standardised declarative exchange formats for mathematical models, independent of the algorithm to be applied to the model, to date these standards have not provided a clear mechanism for describing parameter uncertainty. Parameter uncertainty is an inherent feature of many real systems. This uncertainty can result from a number of situations, such as: when measurements include inherent error; when parameters have unknown values and so are replaced by a probability distribution by the modeller; when a model is of an individual from a population, and parameters have unknown values for the individual, but the distribution for the population is known. We present and demonstrate an approach by which uncertainty can be described declaratively in CellML models, by utilising the extension mechanisms provided in CellML. Parameter uncertainty can be described declaratively in terms of either a univariate continuous probability density function or multiple realisations of one variable or several (typically non-independent) variables. We additionally present an extension to SED-ML (the Simulation Experiment Description Markup Language) to describe sampling sensitivity analysis simulation experiments. We demonstrate the usability of the approach by encoding a sample model in the uncertainty markup language, and by developing a software implementation of the uncertainty specification (including the SED-ML extension for sampling sensitivty analyses) in an existing CellML software library, the CellML API implementation. We used the software implementation to run sampling sensitivity analyses over the model to demonstrate that it is possible to run useful simulations on models with uncertainty encoded in this form.
| S-EPMC3389025 | biostudies-literature