A Green's function method for simulation of time-dependent solute transport and reaction in realistic microvascular geometries
A novel theoretical method is presented for simulating the spatially resolved convective and diffusive transport of reacting solutes between microvascular networks and the surrounding tissues. The method allows for efficient computational solution of problems involving convection and non-linear binding of solutes in blood flowing through microvascular networks with realistic 3D geometries, coupled with transvascular exchange and diffusion and reaction in the surrounding tissue space. The method is based on a Green's function approach, in which the solute concentration distribution in the tissue is expressed as a sum of fie...
Source: Mathematical Medicine and Biology - December 12, 2016 Category: Biomedical Science Authors: Secomb, T. W. Tags: Articles Source Type: research
Allee effects in tritrophic food chains: some insights in pest biological control
Release of natural enemies to control pest populations is a common strategy in biological control. However, its effectiveness is supposed to be impaired, among other factors, by Allee effects in the biological control agent and by the fact that introduced pest natural enemies interact with some native species of the ecosystem. In this work, we devise a tritrophic food chain model where the assumptions previously raised are proved correct when a hyperpredator attacks the introduced pest natural enemy by a functional response type 2 or 3. Moreover, success of pest control is shown to be related to the release of large amount...
Source: Mathematical Medicine and Biology - December 12, 2016 Category: Biomedical Science Authors: Costa, M. I. d. S., dos Anjos, L. Tags: Articles Source Type: research
Effective equations for anisotropic glioma spread with proliferation: a multiscale approach and comparisons with previous settings
Glioma is a common type of primary brain tumour, with a strongly invasive potential, often exhibiting non-uniform, highly irregular growth. This makes it difficult to assess the degree of extent of the tumour, hence bringing about a supplementary challenge for the treatment. It is therefore necessary to understand the migratory behaviour of glioma in greater detail. In this paper, we propose a multiscale model for glioma growth and migration. Our model couples the microscale dynamics (reduced to the binding of surface receptors to the surrounding tissue) with a kinetic transport equation for the cell density on the mesosco...
Source: Mathematical Medicine and Biology - December 12, 2016 Category: Biomedical Science Authors: Engwer, C., Hunt, A., Surulescu, C. Tags: Articles Source Type: research
On the influence of an equatorial cerclage on closure of posterior retinal detachment
A mechanics-based mathematical model of an eye possessing a posterior retinal detachment is presented for the case where an encircling scleral buckle (a cerclage) is sutured around the equator of the eye. The mechanical behaviour of the retina and the globe, both before and after applying the cerclage, is studied. An energy formulation yields the self-consistent equations of equilibrium and boundary conditions of the ocular system, and analytical solutions are established for the scleral buckle, for the globe and for the detached segment of the retina. Results of numerical simulations based on the solutions unveil characte...
Source: Mathematical Medicine and Biology - December 12, 2016 Category: Biomedical Science Authors: Ge, P., Bottega, W. J., Prenner, J. L., Fine, H. F. Tags: Articles Source Type: research
Uncovering the natural history of cancer from post-mortem cross-sectional diameters of hepatic metastases
We develop a mathematical and statistical methodology for estimation of important unobservable characteristics of the individual natural history of cancer from a sample of cross-sectional diameters of liver metastases measured at autopsy. Estimation of the natural history of cancer is based on a previously proposed stochastic model of cancer progression tailored to this type of observations. The model accounts for primary tumour growth, shedding of metastases, their selection, latency and growth in a given secondary site. The model was applied to the aforementioned data on 428 liver metastases detected in one untreated sma...
Source: Mathematical Medicine and Biology - December 12, 2016 Category: Biomedical Science Authors: Hanin, L., Rose, J. Tags: Articles Source Type: research
A fluid dynamics multidimensional model of biofilm growth: stability, influence of environment and sensitivity
In this article, we study in detail the fluid dynamics system proposed in Clarelli et al. (2013, J. Math. Biol., 66, 1387–1408) to model the formation of cyanobacteria biofilms. After analysing the linear stability of the unique non-trivial equilibrium of the system, we introduce in the model the influence of light and temperature, which are two important factors for the development of a cyanobacteria biofilm. Since the values of the coefficients we use for our simulations are estimated through information found in the literature, some sensitivity and robustness analyses on these parameters are performed. All these e...
Source: Mathematical Medicine and Biology - December 12, 2016 Category: Biomedical Science Authors: Clarelli, F., Di Russo, C., Natalini, R., Ribot, M. Tags: Articles Source Type: research
Paradox of enrichment and system order reduction: bacteriophages dynamics as case study
The paradox of enrichment in a 3D model for bacteriophage dynamics, with a free infection stage of the phage and a bilinear incident rate, is considered. An application of the technique of singular perturbation theory allows us to demonstrate why the paradox arises in this 3D model despite the fact that it has a bilinear incident rate (while in 2D predator–prey models it is usually associated with the concavity of the attack rate). Our analysis demonstrates that the commonly applied approach of the model order reduction using the so-called quasi-steady-state approximation can lead to a loss of important properties of...
Source: Mathematical Medicine and Biology - September 4, 2016 Category: Biomedical Science Authors: Korobeinikov, A., Shchepakina, E., Sobolev, V. Tags: Articles Source Type: research
A coupled non-Fickian model of a cardiovascular drug delivery system
using a biodegradable drug-eluting stent is proposed. The numerical results are obtained using an implicit–explicit finite-element method. The influence of vessel stiffness on the transport of drug eluted from the stent is analysed. The results presented in this paper suggest new perspectives to adapt the drug delivery profile to the needs of the patient. (Source: Mathematical Medicine and Biology)
Source: Mathematical Medicine and Biology - September 4, 2016 Category: Biomedical Science Authors: Ferreira, J. A., Naghipoor, J., Oliveira, P. d. Tags: Articles Source Type: research
Strategy for stochastic dose-rate induced enhanced elimination of malignant tumour without dose escalation
The efficacy of radiation therapy, a primary modality of cancer treatment, depends in general upon the total radiation dose administered to the tumour during the course of therapy. Nevertheless, the delivered radiation also irradiates normal tissues and dose escalation procedure often increases the elimination of normal tissue as well. In this article, we have developed theoretical frameworks under the premise of linear-quadratic-linear (LQL) model using stochastic differential equation and Jensen's inequality for exploring the possibility of attending to the two therapeutic performance objectives in contraposition—i...
Source: Mathematical Medicine and Biology - September 4, 2016 Category: Biomedical Science Authors: Paul, S., Roy, P. K. Tags: Articles Source Type: research
Aggregation and asymptotic analysis of an SI-epidemic model for heterogeneous populations
The paper investigates a version of a simple epidemiological model involving only susceptible and infected individuals, where the heterogeneity of the population with respect to susceptibility/infectiousness is taken into account. A comprehensive analysis of the asymptotic behaviour of the disease is given, based on an explicit aggregation of the model. The results are compared with those of a homogeneous version of the model to highlight the influence of the heterogeneity on the asymptotics. Moreover, the performed analysis reveals in which cases incomplete information about the heterogeneity of the population is sufficie...
Source: Mathematical Medicine and Biology - September 4, 2016 Category: Biomedical Science Authors: Veliov, V. M., Widder, A. Tags: Articles Source Type: research
On the stability of a spherical tumour
The mathematical analysis of the tumour growth attracted a lot of interest in the last two decades. However, as of today no generally accepted model for tumour growth exists. This is due partially to the incomplete understanding of the related pathology as well as the extremely complicated procedure that guides the evolution of a tumour. In the present work, we analyse the stability of a spherical tumour for four continuous models of an avascular tumour. Conditions for the stability are stated and the results are implemented numerically. It is observed that the steady-state radii that secure the stability of the tumour are...
Source: Mathematical Medicine and Biology - September 4, 2016 Category: Biomedical Science Authors: Dassios, G., Christina Panagiotopoulou, V. Tags: Articles Source Type: research
Extreme protraction for low-grade gliomas: theoretical proof of concept of a novel therapeutical strategy
Grade II gliomas are slowly growing primary brain tumours that affect mostly young patients and become fatal after a variable time period. Current clinical handling includes surgery as first-line treatment. Cytotoxic therapies (radiotherapy RT or chemotherapy QT) are used initially only for patients having a bad prognosis. Therapies are administered following the ‘maximum dose in minimum time’ principle, which is the same schedule used for high-grade brain tumours. Using mathematical models describing the growth of these tumours in response to radiotherapy, we find that an extreme protraction therapeutical stra...
Source: Mathematical Medicine and Biology - September 4, 2016 Category: Biomedical Science Authors: Perez-Garcia, V. M., Perez-Romasanta, L. A. Tags: Articles Source Type: research
Optimal fractionation in radiotherapy with multiple normal tissues
We present a formulation of the optimal fractionation problem that includes multiple normal tissues. Our model can tackle any combination of maximum dose, mean dose and dose-volume type constraints for serial and parallel normal tissues as this is characteristic of most treatment protocols. We also allow for a spatially heterogeneous dose distribution within each normal tissue. Furthermore, we do not a priori assume that the doses are invariant across fractions. Finally, our model uses a spatially optimized treatment plan as input and hence can be seamlessly combined with any treatment planning system. Our formulation is a...
Source: Mathematical Medicine and Biology - May 31, 2016 Category: Biomedical Science Authors: Saberian, F., Ghate, A., Kim, M. Tags: Articles Source Type: research
Exploring the benefits of antibody immune response in HIV-1 infection using a discrete model
The role of antibodies in HIV-1 infection is investigated using a discrete-time mathematical model that considers cell-free and cell-associated transmission of the virus. Model analysis shows that the effect of each type of antibody is dependent on the stage of the infection. Neutralizing antibodies are efficient in controlling the viral levels in the early days after seroconversion and antibodies that coat HIV-1-infected cells and recruit effector cells to either kill the HIV-1-infected cells or inhibit viral replication are efficient when the infection becomes established. Model simulations show that antibodies that inhi...
Source: Mathematical Medicine and Biology - May 31, 2016 Category: Biomedical Science Authors: Showa, S. P., Nyabadza, F., Hove-Musekwa, S. D., Magombedze, G. Tags: Articles Source Type: research
Improving Bacillus Calmette-Guerin (BCG) immunotherapy for bladder cancer by adding interleukin 2 (IL-2): a mathematical model
One of the treatments offered to non-invasive bladder cancer patients is BCG instillations, using a well-established, time-honoured protocol. Some of the patients, however, do not respond to this protocol. To examine possible changes in the protocol, we provide a platform for in silico testing of alternative protocols for BCG instillations and combinations with IL-2, to be used by urologists in planning new treatment strategies for subpopulations of bladder cancer patients who may benefit from a personalized protocol. We use a systems biology approach to describe the BCG-tumour-immune interplay and translate it into a set ...
Source: Mathematical Medicine and Biology - May 31, 2016 Category: Biomedical Science Authors: Bunimovich-Mendrazitsky, S., Halachmi, S., Kronik, N. Tags: Articles Source Type: research
