Modelling the effect of gap junctions on tissue-level cardiac electrophysiology

When modelling tissue-level cardiac electrophysiology, continuum approximations to the discrete cell-level equations are used to maintain computational tractability. One of the most commonly used models is represented by the bidomain equations, the derivation of which relies on a homogenisation technique to construct a suitable approximation to the discrete model. This derivation does not explicitly account for the presence of gap junctions connecting one cell to another. It has been seen experimentally [Rohr, Cardiovasc. Res. 2004] that these gap junctions have a marked effect on the propagation of the action potential, specifically as the upstroke of the wave passes through the gap junction. In this paper we explicitly include gap junctions in a both a 2D discrete model of cardiac electrophysiology, and the corresponding continuum model, on a simplified cell geometry. Using these models we compare the results of simulations using both continuum and discrete systems. We see that the form of the action potential as it passes through gap junctions cannot be replicated using a continuum model, and that the underlying propagation speed of the action potential ceases to match up between models when gap junctions are introduced. In addition, the results of the discrete simulations match the characteristics of those shown in Rohr 2004. From this, we suggest that a hybrid model -- a discrete system following the upstroke of the action potential, and a continuum system elsewhere -- may give a more accurate description of cardiac electrophysiology.Comment: In Proceedings HSB 2012, arXiv:1208.315

Predictive mathematical models for the spread and treatment of hyperoxia-induced photoreceptor degeneration in retinitis pigmentosa

Purpose: To determine whether the oxygen toxicity hypothesis can explain the distinctive spatio-temporal patterns of retinal degeneration associated with human retinitis pigmentosa (RP) and to predict the effects of antioxidant and trophic factor treatments under this hypothesis. Methods: Three mathematical models were derived to describe the evolution of the retinal oxygen concentration and photoreceptor density over time. The first model considers only hyperoxia-induced degeneration, while the second and third models include mutation-induced rod and cone loss respectively. The models were formulated as systems of partial differential equations, defined on a two-dimensional domain spanning the region between the foveal center and the ora serrata, and were solved numerically using the finite element method. Results: The mathematical models recapitulate patterns of retinal degeneration which involve preferential loss of photoreceptors in the parafoveal/perifoveal and far-peripheral retina, while those which involve a preferential loss of midperipheral photoreceptors cannot be reproduced. Treatment with antioxidants or trophic factors is predicted to delay, halt, or partially reverse retinal degeneration, depending upon the strength and timing of treatment and disease severity. Conclusions: The model simulations indicate that while the oxygen toxicity hypothesis is sufficient to explain some of the patterns of retinal degeneration observed in human RP, additional mechanisms are necessary to explain the full range of behaviors. The models further suggest that antioxidant and trophic factor treatments have the potential to reduce hyperoxia-induced disease severity and that, where possible, these treatments should be targeted at retinal regions with low photoreceptor density to maximize their efficacy

Representation of multiple cellular phenotypes within tissue-level simulations of cardiac electrophysiology

Distinct electrophysiological phenotypes are exhibited 1 by biological cells that have differentiated into particular cell types. The usual approach when simulating the cardiac electrophysiology of tissue that includes different cell types is to model the different cell types as occupying spatially distinct yet coupled regions. Instead, we model the electrophysiology of well-mixed cells by using homogenisation to derive an extension to the commonly used monodomain or bidomain equations. These new equations permit spatial variations in the distribution of the different subtypes of cells and will reduce the computational demands of solving the governing equations. We validate the homogenisation computationally, and then use the new model to explain some experimental observations from stem cell-derived cardiomyocyte monolayers

Representation of multiple cellular phenotypes within tissue-level simulations of cardiac electrophysiology

Distinct electrophysiological phenotypes are exhibited 1 by biological cells that have differentiated into particular cell types. The usual approach when simulating the cardiac electrophysiology of tissue that includes different cell types is to model the different cell types as occupying spatially distinct yet coupled regions. Instead, we model the electrophysiology of well-mixed cells by using homogenisation to derive an extension to the commonly used monodomain or bidomain equations. These new equations permit spatial variations in the distribution of the different subtypes of cells and will reduce the computational demands of solving the governing equations. We validate the homogenisation computationally, and then use the new model to explain some experimental observations from stem cell-derived cardiomyocyte monolayers

Mathematical modelling of cell layer growth in a hollow fibre bioreactor.

Generating autologous tissue grafts of a clinically useful volume requires efficient and controlled expansion of cell populations harvested from patients. Hollow fibre bioreactors show promise as cell expansion devices, owing to their potential for scale-up. However, further research is required to establish how to specify appropriate hollow fibre bioreactor operating conditions for expanding different cell types. In this study we develop a simple model for the growth of a cell layer seeded on the outer surface of a single fibre in a perfused hollow fibre bioreactor. Nutrient-rich culture medium is pumped through the fibre lumen and leaves the bioreactor via the lumen outlet or passes through the porous fibre walls and cell layer, and out via ports on the outer wall of the extra-capillary space. Stokes and Darcy equations for fluid flow in the fibre lumen, fibre wall, cell layer and extra-capillary space are coupled to reaction-advection-diffusion equations for oxygen and lactate transport through the bioreactor, and to a simple growth law for the evolution of the free boundary of the cell layer. Cells at the free boundary are assumed to proliferate at a rate that increases with the local oxygen concentration, and to die and detach from the layer if the local fluid shear stress or lactate concentration exceed critical thresholds. We use the model to predict operating conditions that maximise the cell layer growth for different cell types. In particular, we predict the optimal flow rate of culture medium into the fibre lumen and fluid pressure imposed at the lumen outlet for cell types with different oxygen demands and fluid shear stress tolerances, and compare the growth of the cell layer when the exit ports on the outside of the bioreactor are open with that when they are closed. Model simulations reveal that increasing the inlet flow rate and outlet fluid pressure increases oxygen delivery to the cell layer and, therefore, the growth rate of cells that are tolerant to high shear stresses, but may be detrimental for shear-sensitive cells. The cell layer growth rate is predicted to increase, and be less sensitive to the lactate tolerance of the cells, when the exit ports are opened, as the radial flow through the bioreactor is enhanced and the lactate produced by the cells cleared more rapidly from the cell layer

Homogenization via formal multiscale asymptotics and volume averaging: How do the two techniques compare?

A wide variety of techniques have been developed to homogenize transport equations in multiscale and multiphase systems. This has yielded a rich and diverse field, but has also resulted in the emergence of isolated scientific communities and disconnected bodies of literature. Here, our goal is to bridge the gap between formal multiscale asymptotics and the volume averaging theory. We illustrate the methodologies via a simple example application describing a parabolic transport problem and, in so doing, compare their respective advantages/disadvantages from a practical point of view. This paper is also intended as a pedagogical guide and may be viewed as a tutorial for graduate students as we provide historical context, detail subtle points with great care, and reference many fundamental works

Effects of antiplatelet therapy on stroke risk by brain imaging features of intracerebral haemorrhage and cerebral small vessel diseases: subgroup analyses of the RESTART randomised, open-label trial

Background Findings from the RESTART trial suggest that starting antiplatelet therapy might reduce the risk of recurrent symptomatic intracerebral haemorrhage compared with avoiding antiplatelet therapy. Brain imaging features of intracerebral haemorrhage and cerebral small vessel diseases (such as cerebral microbleeds) are associated with greater risks of recurrent intracerebral haemorrhage. We did subgroup analyses of the RESTART trial to explore whether these brain imaging features modify the effects of antiplatelet therapy

Homogenization via formal multiscale asymptotics and volume averaging: How do the two techniques compare?

A wide variety of techniques have been developed to homogenize transport equations in multiscale and multiphase systems. This has yielded a rich and diverse field, but has also resulted in the emergence of isolated scientific communities and disconnected bodies of literature. Here, our goal is to bridge the gap between formal multiscale asymptotics and the volume averaging theory. We illustrate the methodologies via a simple example application describing a parabolic transport problem and, in so doing, compare their respective advantages/disadvantages from a practical point of view. This paper is also intended as a pedagogical guide and may be viewed as a tutorial for graduate students as we provide historical context, detail subtle points with great care, and reference many fundamental works

Automated quantitative MRI volumetry reports support diagnostic interpretation in dementia: a multi-rater, clinical accuracy study

Objectives: We examined whether providing a quantitative report (QReport) of regional brain volumes improves radiologists’ accuracy and confidence in detecting volume loss, and in differentiating Alzheimer’s disease (AD) and frontotemporal dementia (FTD), compared with visual assessment alone. Methods: Our forced-choice multi-rater clinical accuracy study used MRI from 16 AD patients, 14 FTD patients, and 15 healthy controls; age range 52–81. Our QReport was presented to raters with regional grey matter volumes plotted as percentiles against data from a normative population (n = 461). Nine raters with varying radiological experience (3 each: consultants, registrars, ‘non-clinical image analysts’) assessed each case twice (with and without the QReport). Raters were blinded to clinical and demographic information; they classified scans as ‘normal’ or ‘abnormal’ and if ‘abnormal’ as ‘AD’ or ‘FTD’. Results: The QReport improved sensitivity for detecting volume loss and AD across all raters combined (p = 0.015* and p = 0.002*, respectively). Only the consultant group’s accuracy increased significantly when using the QReport (p = 0.02*). Overall, raters’ agreement (Cohen’s κ) with the ‘gold standard’ was not significantly affected by the QReport; only the consultant group improved significantly (κs 0.41➔0.55, p = 0.04*). Cronbach’s alpha for interrater agreement improved from 0.886 to 0.925, corresponding to an improvement from ‘good’ to ‘excellent’. Conclusion: Our QReport referencing single-subject results to normative data alongside visual assessment improved sensitivity, accuracy, and interrater agreement for detecting volume loss. The QReport was most effective in the consultants, suggesting that experience is needed to fully benefit from the additional information provided by quantitative analyses. Key Points: • The use of quantitative report alongside routine visual MRI assessment improves sensitivity and accuracy for detecting volume loss and AD vs visual assessment alone. • Consultant neuroradiologists’ assessment accuracy and agreement (kappa scores) significantly improved with the use of quantitative atrophy reports. • First multi-rater radiological clinical evaluation of visual quantitative MRI atrophy report for use as a diagnostic aid in dementia