Results 1  10
of
11
Numerical mathematics
, 2000
"... Abstract. In this paper we introduce some basic differential models for the description of blood flow in the circulatory system. We comment on their mathematical properties, their meaningfulness and their limitation to yield realistic and accurate numerical simulations, and their contribution for a ..."
Abstract

Cited by 99 (12 self)
 Add to MetaCart
(Show Context)
Abstract. In this paper we introduce some basic differential models for the description of blood flow in the circulatory system. We comment on their mathematical properties, their meaningfulness and their limitation to yield realistic and accurate numerical simulations, and their contribution for a better understanding of cardiovascular physiopathology. Mathematics Subject Classification (2000). 92C50,96C10,76Z05,74F10,65N30,65M60. Keywords. Cardiovascular mathematics; mathematical modeling; fluid dynamics; Navier– Stokes equations; numerical approximation; finite element method; differential equations. 1.
Minimal haemodynamic system model including ventricular interaction and valve dynamics, Medical Engineering and Physics
, 2004
"... Characterising circulatory dysfunction and choosing a suitable treatment is often difficult and time consuming, and can result in a deterioration in patient condition, or unsuitable therapy choices. A stable minimal model of the human cardiovascular system (CVS) is developed with the ultimate speci ..."
Abstract

Cited by 15 (10 self)
 Add to MetaCart
(Show Context)
Characterising circulatory dysfunction and choosing a suitable treatment is often difficult and time consuming, and can result in a deterioration in patient condition, or unsuitable therapy choices. A stable minimal model of the human cardiovascular system (CVS) is developed with the ultimate specific aim of assisting medical staff for rapid, on site modelling to assist in diagnosis and treatment. Models found in the literature simulate specific areas of the CVS with limited direct usefulness to medical staff. Others model the full CVS as a closed loop system, but models were found to be very complex, difficult to solve, or unstable. This paper develops a model that uses a minimal number of governing equations with the primary goal of accurately capturing trends in the CVS dynamics in a simple, easily solved, robust model. The model is shown to have long term stability and consistency with nonspecific initial conditions as a result. An “open on pressure close on flow ” valve law is created to capture the effects of inertia and the resulting dynamics of blood flow through the cardiac valves. An accurate, stable solution is performed using a method that varies the number of states in the model depending on the specific phase of the cardiac cycle, better matching the real physiological conditions. Examples of results include a 9 % drop in cardiac output when increasing the thoracic pressure from4mmHg to 0mmHg, and an increase in blood pressure from 120/80mmHg to 165/130mmHg when the systemic resistance is doubled. These results show that the model adequately provides appropriate magnitudes and trends that are in agreement with existing data for a variety of physiologically verified test cases simulating human CVS 2 function.
Mathematical Properties of PumpLeak Models of Cell Volume Control and Electrolyte Balance
, 2011
"... Homeostatic control of cell volume and intracellular electrolyte content is a fundamental problem in physiology and is central to the functioning of epithelial systems. These physiological processes are modeled using pumpleak models, a system of differential algebraic equations that describes the b ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
(Show Context)
Homeostatic control of cell volume and intracellular electrolyte content is a fundamental problem in physiology and is central to the functioning of epithelial systems. These physiological processes are modeled using pumpleak models, a system of differential algebraic equations that describes the balance of ions and water flowing across the cell membrane. Despite their widespread use, very little is known about their mathematical properties. Here, we establish analytical results on the existence and stability of steady states for a general class of pumpleak models. We treat two cases. When the ion channel currents have a linear currentvoltage relationship, we show that there is at most one steady state, and that the steady state is globally asymptotically stable. If there are no steady states, the cell volume tends to infinity with time. When minimal assumptions are placed on the properties of ion channel currents, we show that there is an asymptotically stable steady state so long as the pump current is not too large. The key analytical tool is a free energy relation satisfied by a general class of pumpleak models, which can be used as a Lyapunov function to study stability.
Evolution of Analog Circuit Models of Ion Channels
"... Abstract. Analog circuits have long been used to model the electrical properties of biological neurons. For example, the classic HodgkinHuxley model represents ion channels embedded in a neuron’s cell membrane as a capacitor in parallel with batteries and resistors. However, to match the prediction ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
Abstract. Analog circuits have long been used to model the electrical properties of biological neurons. For example, the classic HodgkinHuxley model represents ion channels embedded in a neuron’s cell membrane as a capacitor in parallel with batteries and resistors. However, to match the predictions of the model with their empirical electrophysiological data, Hodgkin and Huxley described the nonlinear resistors using a complex system of coupled differential equations, a celebrated feat that required exceptional creativity and insight. Here, we use evolutionary circuit design to emulate such leaps of human creativity and automatically construct equivalent circuits for neurons. Using only direct electrophysiological observations, the system evolved circuits out of basic electronic components that accurately simulate the behavior of sodium and potassium ion channels. This approach has the potential to serve both as a modeling tool to reverse engineer complex neurophysiological systems and as an assistant in the task of handdesigning neuromorphic circuits. 1
A Multidomain Model for Ionic Electrodiffusion and Osmosis with an Application to Cortical Spreading Depression
, 2014
"... ar ..."
(Show Context)
Systems Biology Approaches to the Computational Modelling of Trypanothione
, 2010
"... A copy can be downloaded for personal noncommercial research or study, without prior permission or charge This thesis cannot be reproduced or quoted extensively from without first obtaining permission in writing from the Author The content must not be changed in any way or sold commercially in any ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
A copy can be downloaded for personal noncommercial research or study, without prior permission or charge This thesis cannot be reproduced or quoted extensively from without first obtaining permission in writing from the Author The content must not be changed in any way or sold commercially in any format or medium without the formal permission of the Author When referring to this work, full bibliographic details including the author, title, awarding institution and date of the thesis must be given.
Algebraic Biology 2005 1 Symbolic Calculation in the Life Sciences — Some Trends and Prospects
"... I discuss the literature and benefits of symbolic calculation in the life sciences; some ways to develop the field; and a way to model sequential processes. ..."
Abstract
 Add to MetaCart
(Show Context)
I discuss the literature and benefits of symbolic calculation in the life sciences; some ways to develop the field; and a way to model sequential processes.
A Model of Electrodiffusion and Osmotic Water Flow and its Energetic Structure
"... We introduce a model for ionic electrodiffusion and osmotic water flow through cells and tissues. The model consists of a system of partial differential equations for ionic concentration and fluid flow with interface conditions at deforming membrane boundaries. The model satisfies a natural energy e ..."
Abstract
 Add to MetaCart
We introduce a model for ionic electrodiffusion and osmotic water flow through cells and tissues. The model consists of a system of partial differential equations for ionic concentration and fluid flow with interface conditions at deforming membrane boundaries. The model satisfies a natural energy equality, in which the sum of the entropic, elastic and electrostatic free energies are dissipated through viscous, electrodiffusive and osmotic flows. We discuss limiting models when certain dimensionless parameters are small. Finally, we develop a numerical scheme for the onedimensional case and present some simple applications of our model to cell volume control. 1.
COMPLIANCE OF THE CARDIOVASCULAR TISSUE: AN INVERSE FLUIDSTRUCTURE INTERACTION PROBLEM
"... Abstract. Estimation of the stiffness of a biological soft tissue is useful for the detection of pathologies such as tumors or atherosclerotic plaques. Elastography is a method based on the comparison between two images before and after a forced deformation of the tissue of interest. An inverse elas ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. Estimation of the stiffness of a biological soft tissue is useful for the detection of pathologies such as tumors or atherosclerotic plaques. Elastography is a method based on the comparison between two images before and after a forced deformation of the tissue of interest. An inverse elasticity problem is then solved for the Young modulus estimation. In the case of arteries, no forced deformation is required, since vessels naturally move under the action of blood. Young modulus can be therefore estimated by solving a coupled inverse fluidstructure interaction problem. In this paper we focus on the mathematical properties of this problem and its numerical solution. We give some well posedness analysis and some preliminary results based on a synthetic dataset, i.e. test cases where the exact Young modulus is known and the displacement dataset is numerically generated by solving a forward fluidstructure interaction problem. We address the problem of the presence of the noise in the measured displacement and of the proper sampling frequency for obtaining reliable estimates. Key words. Fluidstructure Interaction, Inverse Problems, Parameter Estimation 1. Introduction. The
Modelling, analysis and calculation of cerebral hemodynamics
, 2007
"... Mathematical models of cerebral hemodynamics, applicable to humans and rats have been developed and analysed with the purpose of reaching a deeper insight to which degree experimental results on rats can be extrapolated to humans and to clinical management of patients. These models include regulatio ..."
Abstract
 Add to MetaCart
(Show Context)
Mathematical models of cerebral hemodynamics, applicable to humans and rats have been developed and analysed with the purpose of reaching a deeper insight to which degree experimental results on rats can be extrapolated to humans and to clinical management of patients. These models include regulation mechanisms involving the small cerebral arteries and arterioles, flow autoregulation, as well as CO2 and NO reactivity. Bifurcation analysis was conducted on both models. The human model includes Hopfbifurcations, which allow for the existence of periodic solutions with a time scale comparable to Lundberg’s plateau waves in intracranial pressure (Pic). By contrast, the rat model does not manifest Hopfbifurcations and thus does not predict the existence of periodic solutions with critical high Pic. Therefore the model questions the relevance of rodent injury models to predict human physiology following TBI.