Patient-specific modelling of head-up tilt
Short-term cardiovascular responses to head-up tilt (HUT) involve complex cardiovascular regulation in order to maintain blood pressure at homoeostatic levels. This manuscript presents a patient-specific model that uses heart rate as an input to fit the dynamic changes in arterial blood pressure data during HUT. The model contains five compartments representing arteries and veins in the upper and lower body of the systemic circulation, as well as the left ventricle facilitating pumping of the heart. A physiologically based submodel describes gravitational pooling of the blood into the lower extremities during HUT, and a ca...
Source: Mathematical Medicine and Biology - December 10, 2014 Category: Biomedical Science Authors: Williams, N. D., Wind-Willassen, O., Wright, A. A., REU Program, Mehlsen, J., Ottesen, J. T., Olufsen, M. S. Tags: Articles Source Type: research
The time-evolution of DCIS size distributions with applications to breast cancer growth and progression
Ductal carcinoma in situ (DCIS) lesions are non-invasive tumours of the breast that are thought to precede most invasive breast cancers (IBCs). As individual DCIS lesions are initiated, grow and invade (i.e. become IBC), the size distribution of the DCIS lesions present in a given human population will evolve. We derive a differential equation governing this evolution and show, for given assumptions about growth and invasion, that there is a unique distribution which does not vary with time. Further, we show that any initial distribution converges to this stationary distribution exponentially quickly. Therefore, it is reas...
Source: Mathematical Medicine and Biology - December 10, 2014 Category: Biomedical Science Authors: Dowty, J. G., Byrnes, G. B., Gertig, D. M. Tags: Articles Source Type: research
Improved hidden Markov model for nosocomial infections
We propose a novel hidden Markov model (HMM) for parameter estimation in hospital transmission models, and show that commonly made simplifying assumptions can lead to severe model misspecification and poor parameter estimates. A standard HMM that embodies two commonly made simplifying assumptions, namely a fixed patient count and binomially distributed detections is compared with a new alternative HMM that does not require these simplifying assumptions. Using simulated data, we demonstrate how each of the simplifying assumptions used by the standard model leads to model misspecification, whereas the alternative model resul...
Source: Mathematical Medicine and Biology - December 10, 2014 Category: Biomedical Science Authors: Khader, K., Leecaster, M., Greene, T., Samore, M., Thomas, A. Tags: Articles Source Type: research
A mathematical model for the progression of dental caries
A model for the progression of dental caries is derived. The analysis starts at the microscopic reaction and diffusion process. The local equations are averaged to derive a set of macroscopic equations. The global system includes features such as anisotropic diffusion and local changes in the geometry due to the melting of the enamel. The equations are then solved numerically. The simulations highlight the effect of anisotropy. In addition, we draw conclusions on the progression rate of caries, and discuss them in light of a number of experiments. (Source: Mathematical Medicine and Biology)
Source: Mathematical Medicine and Biology - December 10, 2014 Category: Biomedical Science Authors: Fabregas, L. R. I., Rubinstein, J. Tags: Articles Source Type: research
Contents Page
(Source: Mathematical Medicine and Biology)
Source: Mathematical Medicine and Biology - December 10, 2014 Category: Biomedical Science Tags: Cover/Standing Material Source Type: research
Instructions to Authors
(Source: Mathematical Medicine and Biology)
Source: Mathematical Medicine and Biology - December 10, 2014 Category: Biomedical Science Tags: Cover/Standing Material Source Type: research
Editorial Board
(Source: Mathematical Medicine and Biology)
Source: Mathematical Medicine and Biology - December 10, 2014 Category: Biomedical Science Tags: Cover/Standing Material Source Type: research
Cover Page
(Source: Mathematical Medicine and Biology)
Source: Mathematical Medicine and Biology - December 10, 2014 Category: Biomedical Science Tags: Cover/Standing Material Source Type: research
Mathematical modelling of chronic acetaminophen metabolism and liver injury
Acetaminophen (APAP) overdose is the leading cause of acute liver injury in the USA and the UK. Increasingly, liver injury is caused by sustained overuse rather than a single-time overdose. We have recently developed a mathematical model, the Model of APAP-induced Liver Damage (MALD), to predict the outcome of patients with APAP-induced liver damage. The model is based on a single-time overdose and uses measurable markers of liver injury to estimate time since overdose and overdose amount, two variables critical for survival. Here, we extend the model to study liver injury from chronic APAP use. We find that there is a thr...
Source: Mathematical Medicine and Biology - September 9, 2014 Category: Biomedical Science Authors: Remien, C. H., Sussman, N. L., Adler, F. R. Tags: Articles Source Type: research
Impulsive spatial control of invading pests by generalist predators
We model the conditions for pest eradication in a reaction–diffusion system made of a prey and a generalist predator through spatial impulsive control within a bounded domain. The motivating example is the control of the invasive horse chestnut leafminer moth through the yearly destruction of leaves in autumn, in which both the pest and its parasitoids overwinter. The model is made of two integro-partial differential equations, the integral portion describing the within-year immigration from the whole domain. The problem of pest eradication is strongly related to some appropriate eigenvalue problems. Basic properties...
Source: Mathematical Medicine and Biology - September 9, 2014 Category: Biomedical Science Authors: Aniţa, S., Casas, J., Suppo, C. Tags: Articles Source Type: research
Mathematical modelling of active contraction in isolated cardiomyocytes
We investigate the interaction of intracellular calcium spatio-temporal variations with the self-sustained contractions in cardiac myocytes. A consistent mathematical model is presented considering a hyperelastic description of the passive mechanical properties of the cell, combined with an active-strain framework to explain the active shortening of myocytes and its coupling with cytosolic and sarcoplasmic calcium dynamics. A finite element method based on a Taylor-Hood discretization is employed to approximate the nonlinear elasticity equations, whereas the calcium concentration and mechanical activation variables are dis...
Source: Mathematical Medicine and Biology - September 9, 2014 Category: Biomedical Science Authors: Ruiz-Baier, R., Gizzi, A., Rossi, S., Cherubini, C., Laadhari, A., Filippi, S., Quarteroni, A. Tags: Articles Source Type: research
A patient-specific model of the negative-feedback control of the hypothalamus-pituitary-thyroid (HPT) axis in autoimmune (Hashimoto's) thyroiditis
The purpose of modelling the negative-feedback control mechanism of the hypothalamus–pituitary–thyroid (HPT) axis in autoimmune (Hashimoto's) thyroiditis is to describe the clinical course of euthyroidism, subclinical hypothyroidism and overt hypothyroidism for patients. Thyroid hormone thyroxine (T4) and triiodothyronine (T3) levels are controlled by negative-feedback control through thyroid-stimulating hormone (TSH). T4, like other hormones, can be bound or unbound; the unbound T4 (FT4) is used as a marker for hypothyroidism. Autoimmune thyroiditis is a disease in which the thyroid-infiltrating lymphocytes at...
Source: Mathematical Medicine and Biology - September 9, 2014 Category: Biomedical Science Authors: Pandiyan, B., Merrill, S. J., Benvenga, S. Tags: Articles Source Type: research
Bifurcation analysis of an existing mathematical model reveals novel treatment strategies and suggests potential cure for type 1 diabetes
Type 1 diabetes is a disease with serious personal and socioeconomic consequences that has attracted the attention of modellers recently. But as models of this disease tend to be complicated, there has been only limited mathematical analysis to date. Here we address this problem by providing a bifurcation analysis of a previously published mathematical model for the early stages of type 1 diabetes in diabetes-prone NOD mice, which is based on the data available in the literature. We also show positivity and the existence of a family of attracting trapping regions in the positive 5D cone, converging towards a smaller trappi...
Source: Mathematical Medicine and Biology - September 9, 2014 Category: Biomedical Science Authors: Nielsen, K. H. M., Pociot, F. M., Ottesen, J. T. Tags: Articles Source Type: research
Contents Page
(Source: Mathematical Medicine and Biology)
Source: Mathematical Medicine and Biology - September 9, 2014 Category: Biomedical Science Tags: Cover/Standing Material Source Type: research
Instructions to Authors
(Source: Mathematical Medicine and Biology)
Source: Mathematical Medicine and Biology - September 9, 2014 Category: Biomedical Science Tags: Cover/Standing Material Source Type: research
