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Theoretical biology medical modelling [journal]
- Stochastic Model for Tumor Control Probability: Effects of Cell Cycle and (A)symmetric Proliferation. [JOURNAL ARTICLE]
- Theor Biol Med Model 2014 Nov 22; 11(1):49.
is called the tumor control probability (TCP), and is often used to comparevarious treatment strategies used in radiation therapy.In this paper, we aim to investigate the effects of including cell-cycle phase on the TCP by analyzing astochastic model of a tumor comprised of actively dividing cells and quiescent cells with differentradiation sensitivities. Moreover, we use a novel numerical approach based on the method ofcharacteristics for partial differential equations, validated by the Gillespie algorithm, to compute theTCP as a function of time.We derive an exact phase-diagram for the steady-state TCP of the model and show that at high,clinically-relevant doses of radiation, the distinction between active and quiescent tumor cells (i.e.accounting for cell-cycle effects) becomes of negligible importance in terms of its effect on the TCPcurve. However, for very low doses of radiation, these proportions become significant determinantsof the TCP.We also present the results of TCP as a function of time for different values of asymmetricdivision factor.We observe that our results differ from the results in the literature using similar existing models, eventhough similar parameters values are used, and the reasons for this are discussed.
- Correction: improvement of design of a surgical interface using an eye tracking device. [Journal Article]
- Theor Biol Med Model 2014; 11(1):48.
- Animal evolution and atmospheric pO2: is there a link between gradual animal adaptation to terrain elevation due to Ural orogeny and survival of subsequent hypoxic periods? [Journal Article]
- Theor Biol Med Model 2014; 11(1):47.
Considering evolution of terrestrial animals as something happening only on flat continental plains seems wrong. Many mountains have arisen and disappeared over the geologic time scale, so in all periods some areas of high altitude existed, with reduced oxygen pressure (pO2) and increased aridity. During orogeny, animal species of the raising terrain can slowly adapt to reduced oxygen levels.This review proposes that animal evolution was often driven by atmospheric oxygen availability. Transitions of insect ancestors and amphibians out of water are here interpreted as events forced by the lack of oxygen in shallow and warm water during Devonian. Hyperoxia during early Carboniferous allowed giant insects to be predators of lowlands, forcing small amphibians to move to higher terrains, unsuitable to large insects due to reduced pO2. In arid mountainous habitats, ascended animals evolved in early reptiles with more efficient lungs and improved circulation. Animals with alveolar lungs became the mammalian ancestors, while those with respiratory duct lungs developed in archosaurs. In this interpretation, limb precursors of wings and pneumatised bones might have been adaptations for moving on steep slopes.Ural mountains have risen to an estimated height of 3000 m between 318 and 251 Mya. The earliest archosaurs have been found on the European Ural side, estimated 275 Myr old. It is proposed that Ural orogeny slowly elevated several highland habitats within the modern Ural region to heights above 2500 m. Since this process took near 60 Myr, animals in these habitats fully to adapted to hypoxia.The protracted P-Tr hypoxic extinction event killed many aquatic and terrestrial animals. Devastated lowland areas were repopulated by mammaliaformes that came down from mountainous areas. Archosaurs were better adapted to very low pO2, so they were forced to descend to the sea level later when the lack of oxygen became severe. During the Triassic period, when the relative content of O2 reduced to near 12%, archosaurs prevailed as only animals that could cope with profound hypoxia at the sea level. Their diverse descendants has become dominant terrestrial animals, until the K-Pg extinction due to meteor impact.
- A second-generation computational modeling of cardiac electrophysiology: response of action potential to ionic concentration changes and metabolic inhibition. [Journal Article]
- Theor Biol Med Model 2014; 11(1):46.
Cardiac arrhythmias are becoming one of the major health care problem in the world, causing numerous serious disease conditions including stroke and sudden cardiac death. Furthermore, cardiac arrhythmias are intimately related to the signaling ability of cardiac cells, and are caused by signaling defects. Consequently, modeling the electrical activity of the heart, and the complex signaling models that subtend dangerous arrhythmias such as tachycardia and fibrillation, necessitates a quantitative model of action potential (AP) propagation. Yet, many electrophysiological models, which accurately reproduce dynamical characteristic of the action potential in cells, have been introduced. However, these models are very complex and are very time consuming computationally. Consequently, a large amount of research is consecrated to design models with less computational complexity.This paper is presenting a new model for analyzing the propagation of ionic concentrations and electrical potential in space and time. In this model, the transport of ions is governed by Nernst-Planck flux equation (NP), and the electrical interaction of the species is described by a new cable equation. These set of equations form a system of coupled partial nonlinear differential equations that is solved numerically. In the first we describe the mathematical model. To realize the numerical simulation of our model, we proceed by a finite element discretization and then we choose an appropriate resolution algorithm.We give numerical simulations obtained for different input scenarios in the case of suicide substrate reaction which were compared to those obtained in literature. These input scenarios have been chosen so as to provide an intuitive understanding of dynamics of the model. By accessing time and space domains, it is shown that interpreting the electrical potential of cell membrane at steady state is incorrect. This model is general and applies to ions of any charge in space and time domains. The results obtained show a complete agreement with literature findings and also with the physical interpretation of the phenomenon. Furthermore, various numerical experiments are presented to confirm the accuracy, efficiency and stability of the proposed method. In particular, we show that the scheme is second-order accurate in space.
- A mathematical model of dysfunction of the thalamo-cortical loop in schizophrenia. [Journal Article]
- Theor Biol Med Model 2014; 11(1):45.
Recent experimental results suggest that impairment of auditory information processing in the thalamo-cortical loop is crucially related to schizophrenia. Large differences between schizophrenia patients and healthy controls were found in the cortical EEG signals.We derive a phenomenological mathematical model, based on coupled phase oscillators with continuously distributed frequencies to describe the neural activity of the thalamo-cortical loop. We examine the influence of the bidirectional coupling strengths between the thalamic and the cortical area with regard to the phase-locking effects observed in the experiments. We extend this approach to a model consisting of a thalamic area coupled to two cortical areas, each comprising a set of nonidentical phase oscillators. In the investigations of our model, we applied the Ott-Antonsen theory and the Pikovsky-Rosenblum reduction methods to the original system.The results derived from our mathematical model satisfactorily reproduce the experimental data obtained by EEG measurements. Furthermore, they show that modifying the coupling strength from the thalamic region to a cortical region affects the duration of phase synchronization, while a change in the feedback to the thalamus affects the strength of synchronization in the cortex. In addition, our model provides an explanation in terms of nonlinear dynamics as to why brain waves desynchronize after a given phase reset.Our model can explain functional differences seen between EEG records of healthy subjects and schizophrenia patients on a system theoretic basis. Because of this and its predictive character, the model may be considered to pave the way towards an early and reliable clinical detection of schizophrenia that is dependent on the interconnections between the thalamic and cortical regions. In particular, the model parameter that describes the strength of this connection can be used for a diagnostic classification of schizophrenia patients.
- Growth impairment after TBI of leukemia survivors children: a model- based investigation. [Journal Article]
- Theor Biol Med Model 2014; 11(1):44.
Children receiving Total Body Irradiation (TBI) in preparation for Hematopoietic Stem Cell Transplantation (HSCT) are at risk for Growth Hormone Deficiency (GHD), which sometimes severely compromises their Final Height (FH). To better represent the impact of such therapies on growth we apply a mathematical model, which accounts both for the gompertzian-like growth trend and the hormone-related 'spurts', and evaluate how the parameter values estimated on the children undergoing TBI differ from those of the matched normal population.25 patients long-term childhood lymphoblastic and myeloid acute leukaemia survivors followed at Pediatric Onco-Hematology, Stem Cell Transplantation and Cellular Therapy Division, Regina Margherita Children's Hospital (Turin, Italy) were retrospectively analysed for assessing the influence of TBI on their longitudinal growth and for validating a new method to estimate the GH therapy effects. Six were treated with GH therapy after a GHD diagnosis.We show that when TBI was performed before puberty overall growth and pubertal duration were significantly impaired, but such growth limitations were completely reverted in the small sample (6 over 25) of children who underwent GH replacement therapies.Since in principle the model could account for any additional growth 'spurt' induced by therapy, it may become a useful 'simulation' tool for paediatricians for comparing the predicted therapy effectiveness depending on its timing and dosage.
- Dynamical crises, multistability and the influence of the duration of immunity in a seasonally-forced model of disease transmission. [JOURNAL ARTICLE]
- Theor Biol Med Model 2014 Oct 4; 11(1):43.
Highly successful strategies to make populations more resilient to infectious diseases, such as childhood vaccinations programs, may nonetheless lead to unpredictable outcomes due to the interplay between seasonal variations in transmission and a population's immune status.Motivated by the study of diseases such as pertussis we introduce a seasonally-forced susceptibleinfectious- recovered model of disease transmission with waning and boosting of immunity. We study the system's dynamical properties using a combination of numerical simulations and bifurcation techniques, paying particular attention to the properties of the initial condition space.We find that highly unpredictable behaviour can be triggered by changes in biologically relevant model parameters such as the duration of immunity. In the particular system we analyse-previously used in the literature to study pertussis dynamics - we identify the presence of an initial-condition landscape containing three coexisting attractors. The system's response to interventions which perturb population immunity (e.g. vaccination "catch-up" campaigns) is therefore difficult to predict.Given the increasing use of models to inform policy decisions regarding vaccine introduction and scheduling and infectious diseases intervention policy more generally, our findings highlight the importance of thoroughly investigating the dynamical properties of those models to identify key areas of uncertainty. Our findings suggest that the often stated tension between capturing biological complexity and utilising mathematically simple models is perhaps more nuanced than generally suggested. Simple dynamical models, particularly those which include forcing terms, can give rise to incredibly complex behaviour.
- Potential new therapeutic modality revealed through agent-based modeling of the neuromuscular junction and acetylcholinesterase inhibition. [JOURNAL ARTICLE]
- Theor Biol Med Model 2014 Oct 2; 11(1):42.
One of the leading causes of death and illness within the agriculture industry is through unintentionally ingesting or inhaling organophosphate pesticides. OP intoxication directly inhibits acetylcholinesterase, resulting in an excitatory signaling cascade leading to fasciculation, loss of control of bodily fluids, and seizures.Our model was developed using a discrete, rules-based modeling approach in NetLogo. This model includes acetylcholinesterase, the nicotinic acetylcholine receptor responsible for signal transduction, a single release of acetylcholine, organophosphate inhibitors, and a theoretical novel medical countermeasure. We have parameterized the system considering the molecular reaction rate constants in an agent-based approach, as opposed to apparent macroscopic rates used in differential equation models.Our model demonstrates how the cholinergic crisis can be mitigated by therapeutic intervention with an acetylcholinesterase activator. Our model predicts signal rise rates and half-lives consistent with in vitro and in vivo data in the absence and presence of inhibitors. It also predicts the efficacy of theoretical countermeasures acting through three mechanisms: increasing catalytic turnover of acetylcholine, increasing acetylcholine binding affinity to the enzyme, and decreasing binding rates of inhibitors.We present a model of the neuromuscular junction confirming observed acetylcholine signaling data and suggesting that developing a countermeasure capable of reducing inhibitor binding, and not activator concentration, is the most important parameter for reducing organophosphate (OP) intoxication.
- Mathematical modeling of multi-drugs therapy: a challenge for determining the optimal combinations of antiviral drugs. [JOURNAL ARTICLE]
- Theor Biol Med Model 2014 Sep 25; 11(1):41.
In the current era of antiviral drug therapy, combining multiple drugs is a primary approach for improving antiviral effects, reducing the doses of individual drugs, relieving the side effects of strong antiviral drugs, and preventing the emergence of drug-resistant viruses. Although a variety of new drugs have been developed for HIV, HCV and influenza virus, the optimal combinations of multiple drugs are incompletely understood. To optimize the benefits of multi-drugs combinations, we must investigate the interactions between the combined drugs and their target viruses. Mathematical models of viral infection dynamics provide an ideal tool for this purpose. Additionally, whether drug combinations computed by these models are synergistic can be assessed by two prominent drug combination theories, Loewe additivity and Bliss independence. By combining the mathematical modeling of virus dynamics with drug combination theories, we could show the principles by which drug combinations yield a synergistic effect. Here, we describe the theoretical aspects of multi-drugs therapy and discuss their application to antiviral research.
- A model to explain specific cellular communications and cellular harmony:- a hypothesis of coupled cells and interactive coupling molecules. [JOURNAL ARTICLE]
- Theor Biol Med Model 2014 Sep 14; 11(1):40.
The various cell types and their relative numbers in multicellular organisms are controlled by growth factors and related extracellular molecules which affect genetic expression pathways. However, these substances may have both/either inhibitory and/or stimulatory effects on cell division and cell differentiation depending on the cellular environment. It is not known how cells respond to these substances in such an ambiguous way. Many cellular effects have been investigated and reported using cell culture from cancer cell lines in an effort to define normal cellular behaviour using these abnormal cells.A model is offered to explain the harmony of cellular life in multicellular organisms involving interacting extracellular substances.A basic model was proposed based on asymmetric cell division and evidence to support the hypothetical model was accumulated from the literature. In particular, relevant evidence was selected for the Insulin-Like Growth Factor system from the published data, especially from certain cell lines, to support the model. The evidence has been selective in an attempt to provide a picture of normal cellular responses, derived from the cell lines.The formation of a pair of coupled cells by asymmetric cell division is an integral part of the model as is the interaction of couplet molecules derived from these cells. Each couplet cell will have a receptor to measure the amount of the couplet molecule produced by the other cell; each cell will be receptor-positive or receptor-negative for the respective receptors. The couplet molecules will form a binary complex whose level is also measured by the cell. The hypothesis is heavily supported by selective collection of circumstantial evidence and by some direct evidence. The basic model can be expanded to other cellular interactions.These couplet cells and interacting couplet molecules can be viewed as a mechanism that provides a controlled and balanced division-of-labour between the two progeny cells, and, in turn, their progeny. The presence or absence of a particular receptor for a couplet molecule will define a cell type and the presence or absence of many such receptors will define the cell types of the progeny within cell lineages.