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Register a new userMathematical Modelling of Heart Rate Changes in the Mouse
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The CVS is composed of numerous interacting and dynamically regulated physiological subsystems which each generate measurable periodic components such that the CVS can itself be presented as a system of weakly coupled oscillators. The interactions between these oscillators generate a chaotic blood pressure waveform signal, where periods of apparent rhythmicity are punctuated by asynchronous behaviour. It is this variability which seems to characterise the normal state. We used a standard experimental data set for the purposes of analysis and modelling. Arterial blood pressure waveform data was collected from conscious mice instrumented with radiotelemetry devices over $24$ hours, at a $100$ Hz and $1$ kHz time base. During a $24$ hour period, these mice display diurnal variation leading to changes in the cardiovascular waveform. We undertook preliminary analysis of our data using Fourier transforms and subsequently applied a series of both linear and nonlinear mathematical approaches in parallel. We provide a minimalistic linear and nonlinear coupled oscillator model and employed spectral and Hilbert analysis as well as a phase plane analysis. This provides a route to a three way synergistic investigation of the original blood pressure data by a combination of physiological experiments, data analysis viz. Fourier and Hilbert transforms and attractor reconstructions, and numerical solutions of linear and nonlinear coupled oscillator models. We believe that a minimal model of coupled oscillator models that quantitatively describes the complex physiological data could be developed via such a method. Further investigations of each of these techniques will be explored in separate publications.
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How do you use imaging to analyse the development of the heart, which not only changes shape but also undergoes constant, high-speed, quasi-periodic changes? We have integrated ideas from prospective and retrospective optical gating to capture long-term, phase-locked developmental time-lapse videos. In this paper we demonstrate the success of this approach over a key developmental time period: heart looping, where large changes in heart shape prevent previous prospective gating approaches from capturing phase-locked videos. We use the comparison with other approaches to in vivo heart imaging to highlight the importance of collecting the most appropriate data for the biological question.
We demonstrate the robust scale-invariance in the probability density function (PDF) of detrended healthy human heart rate increments, which is preserved not only in a quiescent condition, but also in a dynamic state where the mean level of heart rate is dramatically changing. This scale-independent and fractal structure is markedly different from the scale-dependent PDF evolution observed in a turbulent-like, cascade heart rate model. These results strongly support the view that healthy human heart rate is controlled to converge continually to a critical state.
Mathematical modeling in cancer has been growing in popularity and impact since its inception in 1932. The first theoretical mathematical modeling in cancer research was focused on understanding tumor growth laws and has grown to include the competition between healthy and normal tissue, carcinogenesis, therapy and metastasis. It is the latter topic, metastasis, on which we will focus this short review, specifically discussing various computational and mathematical models of different portions of the metastatic process, including: the emergence of the metastatic phenotype, the timing and size distribution of metastases, the factors that influence the dormancy of micrometastases and patterns of spread from a given primary tumor.
In this article, we review the mathematical modeling for the vascular system.
The concept of internal anatomical asymmetry is familiar; usually in humans the heart is on the left and the liver is on the right, however how does the developing embryo know to produce this consistent laterality? Symmetry breaking initiates with left-right asymmetric cilia-driven fluid mechanics in a small fluid-filled structure called the ventral node in mice. However the question of what converts this flow into left-right asymmetric development remains unanswered. A leading hypotheses is that flow transports morphogen containing vesicles within the node, the absorption of which results in asymmetrical gene expression. To investigate how vesicle transport might result in the situs patterns observed in wildtype and mutant experiments, we extend the open source Stokes flow package, NEAREST, to consider the hydrodynamic and Brownian motion of particles in a mouse model with flow driven by one, two, and 112 beating cilia. Three models for morphogen-containing particle released are simulated to assess their compatibility with observed results in oligociliated and wildtype mouse embryos: uniformly random release, localised cilium stress induced release, and localised release from motile cilia themselves. Only the uniformly random release model appears consistent with the data, with neither localised-release model resulting in significant transport in the oligociliated embryo.
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