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  1. Ismail Z, Fitt AD, Please CP
    Math Med Biol, 2013 Dec;30(4):339-55.
    PMID: 23054933 DOI: 10.1093/imammb/dqs028
    Descemet membrane detachment (DMD) is a rare but potentially serious surgical complication that arises most often during cataract surgery. A recent study (Couch, S. M. & Baratz, K. H. (2009) Cornea, 28, 1160-1163) cited the case of a patient with DMDs in both eyes, noting that though one detachment was surgically repaired, the other spontaneously reattached and needed no further treatment. A fluid mechanical model of buoyancy-driven aqueous humour flow in the anterior chamber around a DMD is developed to explain this phenomenon. The analytical model is based on the lubrication theory limit of the Navier-Stokes equations. The flow is determined for a fixed geometry and the possible motion of the DMD is then analysed. Numerical calculations are also carried out (using COMSOL© Multiphysics) to confirm the lubrication theory results. The analytical and numerical results both show that, under the correct conditions, either spontaneous reattachment or worsening of the tear may occur. We conclude that it is possible that clinical outcomes for DMDs may be controlled by adjusting the temperature difference across the eye and/or the orientation of the patient.
  2. Simitev RD, Al Dawoud A, Aziz MHN, Myles R, Smith GL
    Math Med Biol, 2023 Jun 14;40(2):175-198.
    PMID: 36689769 DOI: 10.1093/imammb/dqad001
    Current understanding of arrhythmia mechanisms and design of anti-arrhythmic drug therapies hinges on the assumption that myocytes from the same region of a single heart have similar, if not identical, action potential waveforms and drug responses. On the contrary, recent experiments reveal significant heterogeneity in uncoupled healthy myocytes both from different hearts as well as from identical regions within a single heart. In this work, a methodology is developed for quantifying the individual electrophysiological properties of large numbers of uncoupled cardiomyocytes under ion channel block in terms of the parameters values of a conceptual fast-slow model of electrical excitability. The approach is applied to a population of nearly 500 rabbit ventricular myocytes for which action potential duration (APD) before and after the application of the drug nifedipine was experimentally measured (Lachaud et al., 2022, Cardiovasc. Res.). To this end, drug action is represented by a multiplicative factor to an effective ion conductance, a closed form asymptotic expression for APD is derived and inverted to determine model parameters as functions of APD and $\varDelta $APD (drug-induced change in APD) for each myocyte. Two free protocol-related quantities are calibrated to experiment using an adaptive-domain procedure based on an original assumption of optimal excitability. The explicit APD expression and the resulting set of model parameter values allow (a) direct evaluation of conditions necessary to maintain fixed APD or $\varDelta $APD, (b) predictions of the proportion of cells remaining excitable after drug application, (c) predictions of stimulus period dependency and (d) predictions of dose-response curves, the latter being in agreement with additional experimental data.
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