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Register a new userModelling afferent nerve responses to bladder filling
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A sensation of fullness in the bladder is a regular experience, yet the mechanisms that act to generate this sensation remain poorly understood. This is an important issue because of the clinical problems that can result when this system does not function properly. The aim of the study group activity was to develop mathematical models that describe the mechanics of bladder filling, and how stretch modulates the firing rate of afferent nerves. Several models were developed, which were qualitatively consistent with experimental data obtained from a mouse model.
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We apply three optical coherence tomography (OCT) image analysis techniques to extract morphometric information from OCT images obtained on peripheral nerves of rat. The accuracy of each technique is evaluated against histological measurements accurate to +/-1 um. The three OCT techniques are: 1) average depth resolved profile (ADRP); 2) autoregressive spectral estimation (AR-SE); and, 3) correlation of the derivative spectral estimation (CoD-SE). We introduce a scanning window to the ADRP technique which provides transverse resolution, and improves epineurium thickness estimates - with the number of analysed images showing agreement with histology increasing from 2/10 to 5/10 (Kruskal-Wallis test, {alpha} = 0.05). A new method of estimating epineurium thickness, using the AR-SE technique, showed agreement with histology in 6/10 analysed images (Kruskal-Wallis test, {alpha} = 0.05). Using a tissue sample in which histology identified two fascicles with an estimated difference in mean fibre diameter of 4 um, the AR-SE and CoD-SE techniques both correctly identified the fascicle with larger fibre diameter distribution but incorrectly estimated the magnitude of this difference as 0.5um. The ability of OCT signal analysis techniques to extract accurate morphometric details from peripheral nerve is promising but restricted in depth by scattering in adipose and neural tissues.
A simplified mathematical model of oral hydrocortisone delivery in adrenal insufficiency is described; the model is based on three components (gastric hydrocortisone, free serum cortisol and bound serum cortisol) and is formulated in terms of linear kinetics, taking into account the dynamics of glucocorticoid-protein binding. Motivated by the need to optimise cortisol replacement in the situations of COVID-19 infection, the model is fitted to recently-published data on 50 mg dosing and earlier data on 10 mg dosing. The fitted model is used to predict typical responses to standard dosing regimes, which involve a larger dose in the morning and 1 or 2 smaller doses later in the day, and the same regimes with doses doubled. In all cases there is a circadian-like response, with early morning nadir. The model is also used to consider an alternative dosing strategy based on four equal and equally-spaced doses of 10, 20 or 30 mg per 24 h, resulting in a more even response resembling a response to sustained inflammatory stress.
Maintenance of epidermal thickness is critical to the barrier function of the skin. Decreased tissue thickness, specifically in the stratum corneum (the outermost layer of the tissue), causes discomfort and inflammation, and is related to several severe diseases of the tissue. In order to maintain both stratum corneum thickness and overall tissue thickness it is necessary for the system to balance cell proliferation and cell loss. Cell proliferation in the epidermis occurs in the basal layer and causes constant upwards movement in the tissue. Cell loss occurs when dead cells at the top of the tissue are lost to the environment through a process called desquamation. Desquamation is thought to occur through a gradual reduction in adhesion between cells, due to the cleaving of adhesion proteins by enzymes, in the stratum corneum. In this paper we will investigate combining a (mass action) subcellular model of desquamation with a three dimensional (cell centre based) multicellular model of the interfollicular epidermis to better understand maintenance of epidermal thickness. These investigations show that hypothesised biological models for the degradation of cell-cell adhesion from the literature are able to provide a consistent rate of cell loss in the multicellular model. This loss balances proliferation, and hence maintains a homeostatic tissue thickness. Moreover, we find that multiple proliferative cell populations in the basal layer can be represented by a single proliferative cell population, simplifying investigations with this model. The model is used to investigate a disorder (Netherton Syndrome) which disrupts desquamation. The model shows how biochemical changes can cause disruptions to the tissue, resulting in a reduced tissue thickness and consequently diminishing the protective role of the tissue. A hypothetical treatment result is also investigated. [ABR]
We present a mathematical study of the emergence of phenotypic heterogeneity in vascularised tumours. Our study is based on formal asymptotic analysis and numerical simulations of a system of non-local parabolic equations that describes the phenotypic evolution of tumour cells and their nonlinear dynamic interactions with the oxygen, which is released from the intratumoural vascular network. Numerical simulations are carried out both in the case of arbitrary distributions of intratumour blood vessels and in the case where the intratumoural vascular network is reconstructed from clinical images obtained using dynamic optical coherence tomography. The results obtained support a more in-depth theoretical understanding of the eco-evolutionary process which underpins the emergence of phenotypic heterogeneity in vascularised tumours. In particular, our results offer a theoretical basis for empirical evidence indicating that the phenotypic properties of cancer cells in vascularised tumours vary with the distance from the blood vessels, and establish a relation between the degree of tumour tissue vascularisation and the level of intratumour phenotypic heterogeneity.
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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