ORCID Profile
0000-0002-8643-3901
Current Organisation
Griffith University
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Publisher: Elsevier BV
Date: 03-2011
DOI: 10.1016/J.JELECTROCARD.2010.11.015
Abstract: Simulation studies of ST depression arising from subendocardial ischemia show a marked difference in the resulting epicardial potential distributions depending on which of the 3 common experimentally determined bidomain conductivity data sets is chosen. Here, the governing equation is rendered nondimensional by iding by the difference in normal and ischemic transmembrane potentials during the ST segment and by the sum of the intracellular and extracellular conductivities in the transverse direction, yielding the ratio of the sum of the intracellular and extracellular longitudinal conductivities ided by the sum of the intracellular and extracellular transverse conductivities as a dimensionless group. Averaging this ratio over the 3 sets of experimentally determined data gives the value of 3.21 ± 0.08. The effect of this narrow range means that the left-hand side of the governing equation can be considered, as a good approximation, to be the same for all these sets of conductivity data. Hence, the right hand of the nondimensional differential equation contains all the necessary information to compare the effect different conductivity data sets have on the epicardial potential distribution. As an ex le, an explanation is given as to why values from one data set give rise to epicardial distributions that are markedly different from those obtained from the other 2 data sets.
Publisher: American Physical Society (APS)
Date: 02-10-2008
Publisher: IOP Publishing
Date: 10-04-2007
DOI: 10.1088/0031-9155/52/9/013
Abstract: This study looks at blood flow in four different human right coronary arteries (RCAs), which have been reconstructed from bi-plane angiograms. A generalized power-law model of blood viscosity is used to study the blood flow at a particular point in the cardiac cycle. Large differences are found in the wall shear stress magnitude (WSS) distributions in the four arteries, leading to the conclusion that it is not possible to make generalizations based on the study of a single artery. The pattern of WSS is found to be related to the geometry of a particular artery, that is, lumen diameter and arterial curvature as well as a combination of these two factors. There is a strong correlation between WSS and reciprocal radius and a weaker correlation between high curvature and extremes of WSS, with high WSS on the 'inside' of a bend and low WSS on the 'outside' of a bend. This is in contrast to the situation for a simple curved tube with constant radius where the inverse is observed. For each artery, a region proximal to the acute margin is identified where low WSS is found and where WSS is lower on the 'inner' wall of the RCA than on the 'outer' wall. This region is one where several studies have found that the human RCA preferentially exhibits atherogenesis.
Publisher: Elsevier BV
Date: 04-2018
DOI: 10.1016/J.COMPBIOMED.2018.02.003
Abstract: There is considerable interest in simulating ischaemia in the ventricle and its effect on the electrocardiogram, because a better understanding of the connection between the two may lead to improvements in diagnosis of myocardial ischaemia. In this work we studied subendocardial ischaemia, in a simplified half-ellipsoidal bidomain model of a ventricle, and its effect on ST segment epicardial potential distributions (EPDs). We found that the EPD changed as the ischaemic depth increased, from a single minimum (min1) over the ischaemic region to a maximum (max) there, with min1 over the border of the region. Lastly, a second minimum (min2) developed on the opposite side of the ischaemic region, in addition to min1 and max. We replicated these results in a realistic ventricular model and showed that the min1 only case could be found for ischaemic depths of up to around 35% of the ventricular wall. In addition, we systematically examined the sensitivity of EPD parameters, such as the potentials and positions of min1, max and min2, to various inputs to the half-ellipsoidal model, such as fibre rotation angle, ischaemic depth and conductivities. We found that the EPD parameters were not sensitive to the blood or transverse bidomain conductivities and were most sensitive to either ischaemic depth and/or fibre rotation angle. This allowed us to conclude that the asynchronous development of the two minima might provide a way of distinguishing between low and high thickness subendocardial ischaemia, and that this method may well be valid despite variability in the population.
Publisher: Wiley
Date: 2003
DOI: 10.1002/NME.589
Publisher: Elsevier BV
Date: 11-2018
DOI: 10.1016/J.COMPBIOMED.2018.09.016
Abstract: Solving the inverse problem of electrocardiology via the Method of Fundamental Solutions has been proposed previously. The advantage of this approach is that it is a meshless method, so it is far easier to implement numerically than many other approaches. However, determining the heart surface potential distribution is still an ill-posed problem and thus requires some form of Tikhonov regularisation to obtain the required distributions. In this study, several methods for determining an "optimal" regularisation parameter are compared in the context of solving the inverse problem of electrocardiology via the Method of Fundamental Solutions. It is found that the Robust Generalised Cross-Validation method most often yields epicardial potential distributions with the least relative error when compared to the input distribution. The study also compares the inverse solutions obtained with the Method of Fundamental Solutions with those obtained in a previous study using the boundary element method. It is found that choosing the best solution methodology and regularisation parameter determination method depends on the particular scenario being considered.
Publisher: Elsevier BV
Date: 2004
Publisher: Springer Science and Business Media LLC
Date: 05-05-2006
DOI: 10.1007/S10439-006-9098-4
Abstract: : This paper describes a multi-electrode grid, which could be used to determine cardiac tissue parameters by direct measurement. A two pass process is used, where potential measurements are made, during the plateau phase of the action potential, on a subset of these electrodes and these measurements are used to determine the bidomain conductivities. In the first pass, the potential measurements are made on a set of 'closely-spaced' electrodes and the parameters are fitted to the potential measurements in an iterative process using a bidomain model and a solver based on a modified Shor's r-algorithm. This first pass yields the extracellular conductivities. The second pass is similar except that a 'widely-spaced' electrode set is used and this time the intracellular conductivities are recovered. In addition, it is possible to determine the fibre rotation throughout the tissue, since the bidomain model used here is able to include the effects of fibre rotation. In the simulation studies presented here, the model is solved with known conductivities, on each of the two subsets of electrodes, to generate two sets of 'measured potentials.' Conductivities are then recovered by solving an inverse problem based on the measured potentials, to which various levels of noise are added. For ex le, simulations in the first pass are performed using an electrode spacing of 500 mum, for a situation where the longitudinal and transverse space constants are 769 and 308 mum, respectively. These give very accurate average percentage relative errors for the longitudinal and transverse extracellular conductivities, over five simulations with 1% noise added, of 0.3 and 0.2%. Twenty-five second pass simulations, on a 1 mm grid, yield average percentage relative errors of 3.8, 2.6 and 1.4% for the corresponding intracellular values and the fibre rotation angle, respectively.
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 25-07-2019
DOI: 10.21914/ANZIAMJ.V59I0.12654
Abstract: The ability to accurately predict the course of an epidemic is extremely important. This article looks at an influenza outbreak that spread through a small boarding school. Predictions are made on multiple days throughout the epidemic using the stochastic Galerkin method to consider a range of plausible values for the parameters. These predictions are then compared to known data points. Predictions made before the peak of the epidemic had much larger variances compared to predictions made after the peak of the epidemic. References B. M. Chen-Charpentier, J. C. Cortes, J. V. Romero, and M. D. Rosello. Some recommendations for applying gPC (generalized polynomial chaos) to modeling: An analysis through the Airy random differential equation. Applied Mathematics and Computation, 219(9):4208 4218, 2013. doi:10.1016/j.amc.2012.11.007 B. M. Chen-Charpentier and D. Stanescu. Epidemic models with random coefficients. Mathematical and Computer Modelling, 52:1004 1010, 2010. doi:10.1016/j.mcm.2010.01.014 D. B. Harman and P. R. Johnston. Applying the stochastic galerkin method to epidemic models with in idualised parameter distributions. In Proceedings of the 12th Biennial Engineering Mathematics and Applications Conference, EMAC-2015, volume 57 of ANZIAM J., pages C160C176, August 2016. doi:10.21914/anziamj.v57i0.10394 D. B. Harman and P. R. Johnston. Applying the stochastic galerkin method to epidemic models with uncertainty in the parameters. Mathematical Biosciences, 277:25 37, 2016. doi:10.1016/j.mbs.2016.03.012 D. B. Harman and P. R. Johnston. Boarding house: find border. 2019. doi:10.6084/m9.figshare.7699844.v1 D. B. Harman and P. R. Johnston. SIR uniform equations. 2 2019. doi:10.6084/m9.figshare.7692392.v1 H. W. Hethcote. The mathematics of infectious diseases. SIAM Review, 42(4):599653, 2000. doi:10.1137/S0036144500371907 R.I. Hickson and M.G. Roberts. How population heterogeneity in susceptibility and infectivity influences epidemic dynamics. Journal of Theoretical Biology, 350(0):70 80, 2014. doi:10.1016/j.jtbi.2014.01.014 W. O. Kermack and A. G. McKendrick. A contribution to the mathematical theory of epidemics. Proceedings of the Royal Society of London. Series A, 115(772):700721, August 1927. doi:10.1098/rspa.1927.0118 M. G. Roberts. A two-strain epidemic model with uncertainty in the interaction. The ANZIAM Journal, 54:108115, 10 2012. doi:10.1017/S1446181112000326 M. G. Roberts. Epidemic models with uncertainty in the reproduction number. Journal of Mathematical Biology, 66(7):14631474, 2013. doi:10.1007/s00285-012-0540-y F. Santonja and B. Chen-Charpentier. Uncertainty quantification in simulations of epidemics using polynomial chaos. Computational and Mathematical Methods in Medicine, 2012:742086, 2012. doi:10.1155/2012/742086 Communicable Disease Surveillance Centre (Public Health Laboratory Service) and Communicable Diseases (Scotland) Unit. Influenza in a boarding school. BMJ, 1(6112):587, 1978. doi:10.1136/bmj.1.6112.586 G. Strang. Linear Algebra and Its Applications. Thomson, Brooks/Cole, 2006. D. Xiu. Numerical Methods for Stochastic Computations: A Spectral Method Approach. Princeton University Press, 2010.
Publisher: Elsevier BV
Date: 11-2005
DOI: 10.1016/J.MBS.2005.06.002
Abstract: In this study various electrical conductivity approximations used in bidomain models of cardiac tissue are considered. Comparisons are based on epicardial surface potential distributions arising from regions of subendocardial ischaemia situated within the cardiac tissue. Approximations studied are a single conductivity bidomain model, an isotropic bidomain model and equal and reciprocal anisotropy ratios both with and without fibre rotation. It is demonstrated both analytically and numerically that the approximations involving a single conductivity bidomain, an isotropic bidomain or equal anisotropy ratios (ignoring fibre rotation) results in identical epicardial potential distributions for all degrees of subendocardial ischaemia. This result is contrary to experimental observations. It is further shown that by assuming reciprocal anisotropy ratios, epicardial potential distributions vary with the degree of subendocardial ischaemia. However, it is concluded that unequal anisotropy ratios must be used to obtain the true character of experimental observations.
Publisher: Informa UK Limited
Date: 04-2010
DOI: 10.1080/10255840903067072
Abstract: This paper presents an implementation of the finite volume method with the aim of studying subendocardial ischaemia during the ST segment. In this implementation, based on hexahedral finite volumes, each quadrilateral sub-face is split into two triangles to improve the accuracy of the numerical integration in complex geometries and when fibre rotation is included. The numerical method is validated against previously published solutions obtained from slab and cylindrical models of the left ventricle with subendocardial ischaemia and no fibre rotation. Epicardial potential distributions are then obtained for a half-ellipsoid model of the left ventricle. In this case it is shown that for isotropic cardiac tissue the degree of subendocardial ischaemia does not affect the epicardial potential distribution, which is consistent with previous findings from analytical studies in simpler geometries. The paper also considers the behaviour of various preconditioners for solving numerically the resulting system of algebraic equations resulting from the implementation of the finite volume method. It is observed that each geometry considered has its own optimal preconditioner.
Publisher: Elsevier BV
Date: 02-2016
DOI: 10.1016/J.COMPBIOMED.2015.12.011
Abstract: Robust Generalised Cross-Validation was proposed recently as a method for determining near optimal regularisation parameters in inverse problems. It was introduced to overcome a problem with the regular Generalised Cross-Validation method in which the function that is minimised to obtain the regularisation parameter often has a broad, flat minimum, resulting in a poor estimate for the parameter. The robust method defines a new function to be minimised which has a narrower minimum, but at the expense of introducing a new parameter called the robustness parameter. In this study, the Robust Generalised Cross-Validation method is applied to the inverse problem of electrocardiology. It is demonstrated that, for realistic situations, the robustness parameter can be set to zero. With this choice of robustness parameter, it is shown that the robust method is able to obtain estimates of the regularisation parameter in the inverse problem of electrocardiology that are comparable to, or better than, many of the standard methods that are applied to this inverse problem.
Publisher: Elsevier BV
Date: 11-2018
DOI: 10.1016/J.COMPBIOMED.2018.06.005
Abstract: Although computational studies are increasingly used to gain insight into diseases such as myocardial ischaemia, there is still considerable uncertainty about the values for many of the parameters in these studies. This is particularly true for the bidomain conductivity values that are used in normal tissue and, even more so, in ischaemic tissue, when modelling ischaemia. In this work, we extended a previous study that used a half-ellipsoidal model and a realistic model to study subendocardial ischaemia during the ST segment, so that we could simulate both early and late stage ischaemia. We found that, for both stages of ischaemia, there was still the same connection between the degree of ischaemia and the development of features such as minima and maxima in the epicardial potential distribution (EPD), although the magnitudes of the potentials were very often less, which may be significant in terms of detecting them experimentally. Using uncertainty quantification associated with the ischaemic region conductivities, we also determined that the EPD features were sensitive to the ischaemic region extracellular normal and longitudinal conductivities during early stage ischaemia, whereas, during late stage ischaemia, the intracellular longitudinal conductivity was the most significant. However, since we again found that these effects were minor compared with the effects of fibre rotation angle and ischaemic depth, this might suggest that it is not necessary to use different conductivity values inside and outside the ischaemic region when modelling ST segment subendocardial ischaemia, unless the magnitudes of the potentials are an important part of the study.
Publisher: Elsevier BV
Date: 08-2021
Publisher: Elsevier BV
Date: 2006
Publisher: Elsevier BV
Date: 2008
Publisher: Informa UK Limited
Date: 26-10-2017
DOI: 10.1080/10255842.2017.1382483
Abstract: Coarctation of the Aorta is a congenital narrowing of the aorta. Two commonly used treatments are resection and end-to-end anastomosis, and stent placements. We simulate blood flow through one-dimensional models of aortas. Different artery stiffnesses, due to treatments, are included in our model, and used to compare blood flow properties in the treated aortas. We expand our previously published model to include the natural tapering of aortas. We look at change in aorta wall radius, blood pressure and blood flow velocity, and find that, of the two treatments, the resection and end-to-end anastomosis treatment more closely matches healthy aortas.
Publisher: Elsevier BV
Date: 12-2019
DOI: 10.1016/J.MBS.2019.108273
Abstract: Mathematical modelling is a useful technique to help elucidate the connection between non-transmural ischaemia and ST elevation and depression of the ECG. Generally, models represent non-transmural ischaemia using an ischaemic zone that extends from the endocardium partway to the epicardium. However, recent experimental work has suggested that ischaemia typically arises within the heart wall. This work examines the effect of modelling cardiac ischaemia in the left ventricle using two different models: subendocardial ischaemia and partial thickness ischaemia, representing the first and second scenarios, respectively. We found that it is possible, only in the model of subendocardial ischaemia, to see a single minimum on the epicardial surface above the ischaemic region, and this only occurs for low ischaemic thicknesses. This may help to explain the rarity of ST depression that is located over the ischaemic region. It was also found that, in both models, the epicardial potential distribution is most sensitive to the proximity of the ischaemic region to the epicardium, rather than to the thickness of the ischaemic region. Since proximity does not indicate the thickness of the ischaemic region, this suggests a reason why it may be difficult to determine the degree of ischaemia using the ST segment of the ECG.
Publisher: Elsevier BV
Date: 06-2013
Publisher: Elsevier BV
Date: 04-2013
Publisher: Wiley
Date: 2005
DOI: 10.1002/NME.1208
Publisher: Wiley
Date: 30-09-2002
DOI: 10.1002/CNM.542
Publisher: Wiley
Date: 31-07-2007
DOI: 10.1002/NME.1816
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
Date: 02-2003
Publisher: Informa UK Limited
Date: 06-2008
DOI: 10.1080/10255840701747594
Abstract: A recently presented solution method for the bidomain model (Johnston et al. 2006), which involves the application of direct current for studying electrical potential in a slab of cardiac tissue, is extended here to allow the use of an applied alternating current. The advantage of using AC current, in a four-electrode method for determining cardiac conductivities, is that instead of using 'close' and 'wide' electrode spacings to make potential measurements, increasing the frequency of the AC current redirects a fraction of the current from the extracellular space into the intracellular space. The model is based on the work of Le Guyader et al. (2001), but is able to include the effects of the fibre rotation between the epicardium and the endocardium on the potentials. Also, rather than using a full numerical technique, the solution method uses Fourier series and a simple one dimensional finite difference scheme, which has the advantage of allowing the potentials to be calculated only at points, such as the measuring electrodes, where they are required. The new alternating current model, which includes intracellular capacitance, is used with a particular four-electrode configuration, to show that the potential measured is affected by changes in fibre rotation. This is significant because it indicates that it is necessary to include fibre rotation in models, which are to be used in conjunction with measuring arrays that are more complex than those involving simply surface probes or a single vertical probe.
Publisher: Informa UK Limited
Date: 09-2013
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2008
DOI: 10.1137/07070200X
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 12-08-2022
DOI: 10.21914/ANZIAMJ.V63.17148
Abstract: Accurate values for the six cardiac conductivities of the bidomain model are crucial for meaningful electrophysiological simulations of cardiac tissue and are yet to be achieved. A two-stage optimisation process is used to retrieve the cardiac conductivities from cardiac potentials measured on a multi-electrode array—the first stage simultaneously fits all six conductivities, and the second stage fits a subset of the conductivities (intracellular conductivities), while holding the remainder of the conductivities (extracellular conductivities) constant. Previous studies have shown that the intracellular conductivities are retrieved to a lesser degree of accuracy than extracellular conductivities. This study tests the proposition that there exists a relationship between the extracellular and intracellular conductivities during the second stage of the optimisation that affects the accuracy of the retrieved intracellular conductivities. A measure to quantify this relationship is developed using polynomial chaos. The results show that a significant relationship does exist, and thus any errors in the extracellular conductivities are magnified in the retrieved intracellular conductivities. Thus, it is suggested that future protocols for retrieving conductivities incorporate the uncertainty in the extracellular conductivities. References R. C. Aster, B. Borchers, and C. H. Thurber. Parameter Estimation and Inverse Problems. Elsevier, 2018. doi: 10.1016/C2015-0-02458-3 W. Huberts, W. P. Donders, T. Delhaas, and F. N. van de Vosse. Applicability of the polynomial chaos expansion method for personalization of a cardiovascular pulse wave propagation model. Int. J. Numer. Meth. Biomed. Eng. 30.12 (2014), pp. 1679–1704. doi: 10.1002/cnm.2695 B. M. Johnston, S. Coveney, E. T. Y. Chang, P. R. Johnston, and R. H. Clayton. Quantifying the effect of uncertainty in input parameters in a simplified bidomain model of partial thickness ischaemia. Med. Bio. Eng. Comput. 56.5 (2018), pp. 761–780. doi: 10.1007/s11517-017-1714-y B. M. Johnston and P. R. Johnston. Approaches for determining cardiac bidomain conductivity values: Progress and challenges. Med. Bio. Eng. Comput. 58 (2020), pp. 2919–2935. doi: 10.1007/s11517-020-02272-z B. M. Johnston and P. R. Johnston. Determining six cardiac conductivities from realistically large datasets. Math. Biosci. 266 (2015), pp. 15–22. doi: 10.1016/j.mbs.2015.05.008 B. M. Johnston, P. R. Johnston, and D. Kilpatrick. A new approach to the determination of cardiac potential distributions: Application to the analysis of electrode configurations. Math. Biosci. 202.2 (2006), pp. 288–309. doi: 10.1016/j.mbs.2006.04.004 A. Kamalakkannan, P. R Johnston, and B. M. Johnston. A modified approach to determine the six cardiac bidomain conductivities. In: Comput. Bio. Med. 135, 104549 (2021). doi: 10.1016/j.compbiomed.2021.104549 I. J. Legrice, P. J. Hunter, and B. H. Smaill. Laminar structure of the heart: A mathematical model. Am. J. Physiol. Heart Circ. Physiol. 272.5 (1997), H2466–H2476. doi: 10.1152/ajpheart.1997.272.5.H2466 References C166 R. Plonsey and R. Barr. The four-electrode resistivity technique as applied to cardiac muscle. IEEE Trans. Bio-med. Eng. 29.7 (1982), pp. 541–546. doi: 10.1109/tbme.1982.324927 D. D. Streeter Jr, H. M. Spotnitz, D. P. Patel, J. Ross Jr, and E. H. Sonnenblick. Fiber orientation in the canine left ventricle during diastole and systole. Circ. Res. 24.3 (1969), pp. 339–347. doi: 10.1161/01.res.24.3.339 M. Sun, N. M. S. de Groot, and R. C. Hendriks. Cardiac tissue conductivity estimation using confirmatory factor analysis. In: Comput. Bio. Med. 135, 104604 (2021). doi: 10.1016/j.compbiomed.2021.104604 L. Tung. A Bi-Domain Model for Describing Ischemic Myocardial D-C Potentials. Thesis. Massachusetts Institute of Technology, 1978. url: 721.1/16177 [13] S. Weidmann. Electrical constants of trabecular muscle from mammalian heart. J. Physiol. 210.4 (1970), pp. 1041–1054. doi: 10.1113/jphysiol.1970.sp009256 N. Wiener. The homogeneous chaos. Am. J. Math. 60.4 (1938), pp. 897–936. doi: 10.2307/2371268 D. Xiu and G. E. Karniadakis. The Wiener–Askey polynomial chaos for stochastic differential equations. SIAM J. Sci. Comput. 24.2 (2002), pp. 619–644. doi: 10.1137/S1064827501387826
Publisher: Wiley
Date: 16-01-2002
DOI: 10.1002/CNM.482
Publisher: Elsevier BV
Date: 08-2006
DOI: 10.1016/J.MBS.2006.04.004
Abstract: This paper presents a mathematical model and new solution technique for studying the electric potential in a slab of cardiac tissue. The model is based on the bidomain representation of cardiac tissue and also allows for the effects of fibre rotation between the epicardium and the endocardium. A detailed solution method, based on Fourier Series and a simple one-dimensional finite difference scheme, for the governing equations for electric potential in the tissue and the blood, is also presented. This method has the advantage that the potential can be calculated only at points where it is required, such as the measuring electrodes. The model is then used to study various electrode configurations which have been proposed to determine cardiac tissue conductivity parameters. Three electrode configurations are analysed in terms of electrode spacing, placement position and the effect of including fibre rotation: the usual surface four-electrode configuration a single vertical analogue of this and a two probe configuration, which has the current electrodes on one probe and the measuring electrodes on the other, a fixed distance away. It is found that including fibre rotation has no effect on the potentials measured in the first two cases however, in the two probe case, non-zero fibre rotation causes a significant drop in the voltage measured. This leads to the conclusion that it is necessary to include the effects of fibre rotation in any model which involves the use of multiple plunge electrodes.
Publisher: Informa UK Limited
Date: 04-02-2019
DOI: 10.1080/10255842.2018.1564821
Abstract: Coarctation of the Aorta is a congenital narrowing of the aorta and diagnosis can be difficult. Treatments result in idiopathic sequelae including hypertension. Untreated patients are known to develop increased arterial stiffness in the upper body, which worsens with time. We present results from simulations with a one-dimensional mathematical model, about the effect of stiffness, stenting, surgery and coarctation severity on blood pressure, Pulsatility and Resistivity Index. One conclusion is that increased stiffness may explain both hypertension in treated patients and why diagnosis can be difficult.
Publisher: Elsevier BV
Date: 12-2019
DOI: 10.1016/J.MEDENGPHY.2019.09.017
Abstract: Increasing impedance during freezing might be a valuable marker for guiding cardiac cryo-ablation. We provide model based insights on how decreasing temperature below the freezing point of tissue relates to the percentage of frozen water. Furthermore, we provide experimental data for comparing this percentage with the increase in impedance. Measurements were performed on a bovine tissue s le at frequencies between 5 and 80 kHz. Slow cooling and heating rates were applied to minimize temperature gradients in the myocardial s le and to allow accurate assessment of the freezing point. Computer simulation was applied to link impedance with temperature dependent conductivities. The osmotic virial equation was used to estimate the percentage of frozen water. Measurements identified the freezing point at -0.6
Publisher: Elsevier BV
Date: 11-2003
DOI: 10.1016/S0025-5564(03)00099-3
Abstract: In this paper a mathematical model of a left ventricle with a cylindrical geometry is presented with the aim of gaining a better understanding of the relationship between subendocardial ischaemia and ST depression. The model is formulated as an infinite cylinder and takes into account the full bidomain nature of cardiac tissue, as well as fibre rotation. A detailed solution method (based on Fourier series, Fourier transforms and a one dimensional finite difference scheme) for the governing equations for electric potential in the tissue and the blood is also presented. The model presented is used to study the effect increasing subendocardial ischaemia has on the epicardial potential distribution as well as the effects of changing the bidomain conductivity values. The epicardial potential distributions obtained with this cylindrical geometry are compared with results obtained using a previously published slab model. Results of the simulations presented show that the morphologies of the epicardial potential distributions are similar between the two geometries, with the main difference being that the cylindrical model predicts slightly higher potentials.
Publisher: Elsevier BV
Date: 06-2007
Publisher: Elsevier BV
Date: 08-2011
DOI: 10.1016/J.MBS.2011.05.004
Abstract: There is a complex interplay between the four conductivity values used in the bidomain equation and the resulting electric potential distribution in cardiac tissue arising from subendocardial ischaemia. Based on the three commonly used experimentally derived conductivity data sets, a non-dimensional formulation of the passive bidomain equation is derived, which gives rise naturally to several dimensionless conductivity ratios. The data sets are then used to define a parameter space of these ratios, which is studied by considering the correlation coefficients between different epicardial potential distributions. From this study, it is shown that the ratio of the intracellular longitudinal conductivity to the intracellular transverse conductivity is the key parameter in explaining the differences between the epicardial potential distributions observed with these three data sets.
Publisher: Elsevier BV
Date: 2006
DOI: 10.1016/J.JBIOMECH.2005.01.034
Abstract: This study looks at pulsatile blood flow through four different right coronary arteries, which have been reconstructed from biplane angiograms. A non-Newtonian blood model (the Generalised Power Law), as well as the usual Newtonian model of blood viscosity, is used to study the wall shear stress in each of these arteries over the entire cardiac cycle. The difference between Newtonian and non-Newtonian blood models is also studied over the whole cardiac cycle using the recently generalised global non-Newtonian importance factor. In addition, the flow is studied by considering paths of massless particles introduced into the flow field. The study shows that, when studying the wall shear stress distribution for transient blood flow in arteries, the use of a Newtonian blood model is a reasonably good approximation. However, to study the flow within the artery in greater detail, a non-Newtonian model is more appropriate.
Publisher: Elsevier BV
Date: 10-2012
DOI: 10.1016/J.MBS.2012.05.009
Abstract: This numerical study uses a simple bidomain model of cardiac tissue to compare the effect of three different ischaemic region geometries (rectangular, cylindrical and semi-ellipsoidal) on the extracellular epicardial potentials during the ST segment. Results are obtained using anisotropic conductivities based on experimentally derived data. The model is then altered, to include heterogeneous conductivities in the ischaemic region and larger border zone widths, in order to better reproduce realistic scenarios. Initial results for the rectangular and cylindrical ischaemic shapes show a central depression over the ischaemic region, for low ischaemic thicknesses, which separates into three depressions as the ischaemic thickness increases. For ischaemic thicknesses above 70% an elevation appears over the ischaemic region and this increases in magnitude as the ischaemia becomes transmural. Results for the semi-ellipsoidal shape, however, differ, with the central depression separating into only two depressions as the thickness increases. Changing the conductivity inside the ischaemic region significantly affects results for each geometry, with depression staying over the ischaemic region for much higher levels of ischaemia (up to 90% thickness). Increasing the intramural border zone thickness did not significantly affect the epicardial potential distributions.
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 07-06-2016
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
Date: 03-2007
Publisher: Elsevier BV
Date: 10-2011
Publisher: Elsevier BV
Date: 05-2004
Publisher: Wiley
Date: 16-11-2008
DOI: 10.1002/NME.2244
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 10-11-2016
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 15-05-2018
Publisher: Elsevier BV
Date: 10-2021
Publisher: Informa UK Limited
Date: 07-09-2021
Start Date: 2020
End Date: 2022
Funder: National Institute of Biomedical Imaging and Bioengineering
View Funded ActivityStart Date: 2008
End Date: 2008
Funder: Australian Research Council
View Funded ActivityStart Date: 2003
End Date: 2004
Funder: Australian Research Council
View Funded ActivityStart Date: 2017
End Date: 2018
Funder: Australian Academy of Technology and Engineering
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