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Mathematical Medicine and Biology: a Journal of the IMA

Angela M Jarrett, Meghan J Bloom, Wesley Godfrey, Anum K Syed, David A Ekrut, Lauren I Ehrlich, Thomas E Yankeelov, Anna G Sorace
The goal of this study is to develop an integrated, mathematical-experimental approach for understanding the interactions between the immune system and the effects of trastuzumab on breast cancer that overexpresses the human epidermal growth factor receptor 2 (HER2+). A system of coupled, ordinary differential equations was constructed to describe the temporal changes in tumour growth, along with intratumoural changes in the immune response, vascularity, necrosis and hypoxia. The mathematical model is calibrated with serially acquired experimental data of tumour volume, vascularity, necrosis and hypoxia obtained from either imaging or histology from a murine model of HER2+ breast cancer...
September 19, 2018: Mathematical Medicine and Biology: a Journal of the IMA
Sevnaz Nourollahi, Archis Ghate, Minsun Kim
The goal in external beam radiotherapy (EBRT) for cancer is to maximize damage to the tumour while limiting toxic effects on the organs-at-risk. EBRT can be delivered via different modalities such as photons, protons and neutrons. The choice of an optimal modality depends on the anatomy of the irradiated area and the relative physical and biological properties of the modalities under consideration. There is no single universally dominant modality. We present the first-ever mathematical formulation of the optimal modality selection problem...
September 6, 2018: Mathematical Medicine and Biology: a Journal of the IMA
Andrew L Krause, Dmitry Beliaev, Robert A Van Gorder, Sarah L Waters
A contemporary procedure to grow artificial tissue is to seed cells onto a porous biomaterial scaffold and culture it within a perfusion bioreactor to facilitate the transport of nutrients to growing cells. Typical models of cell growth for tissue engineering applications make use of spatially homogeneous or spatially continuous equations to model cell growth, flow of culture medium, nutrient transport and their interactions. The network structure of the physical porous scaffold is often incorporated through parameters in these models, either phenomenologically or through techniques like mathematical homogenization...
August 10, 2018: Mathematical Medicine and Biology: a Journal of the IMA
Bruno Buonomo, Rossella Della Marca, Alberto d'Onofrio
Hesitancy and refusal of vaccines preventing childhood diseases are spreading due to 'pseudo-rational' behaviours: parents overweigh real and imaginary side effects of vaccines. Nonetheless, the 'Public Health System' (PHS) may enact public campaigns to favour vaccine uptake. To determine the optimal time profiles for such campaigns, we apply the optimal control theory to an extension of the susceptible-infectious-removed (SIR)-based behavioural vaccination model by d'Onofrio et al. (2012, PLoS ONE, 7, e45653)...
July 27, 2018: Mathematical Medicine and Biology: a Journal of the IMA
Wenjing Zhang, Sophia Jang, Colleen B Jonsson, Linda J S Allen
Inflammatory responses to an infection from a zoonotic pathogen, such as avian influenza viruses, hantaviruses and some coronaviruses, are distinctly different in their natural reservoir versus human host. While not as well studied in the natural reservoirs, the pro-inflammatory response and viral replication appear controlled and show no obvious pathology. In contrast, infection in humans results in an initial high viral load marked by an aggressive pro-inflammatory response known as a cytokine storm. The key difference in the course of the infection between the reservoir and human host is the inflammatory response...
June 29, 2018: Mathematical Medicine and Biology: a Journal of the IMA
Artur C Fassoni, Hyun M Yang
Tumorigenesis has been described as a multistep process, where each step is associated with a genetic alteration, in the direction to progressively transform a normal cell and its descendants into a malignant tumour. Into this work, we propose a mathematical model for cancer onset and development, considering three populations: normal, premalignant and cancer cells. The model takes into account three hallmarks of cancer: self-sufficiency on growth signals, insensibility to anti-growth signals and evading apoptosis...
June 27, 2018: Mathematical Medicine and Biology: a Journal of the IMA
Shi Chen, Suzanne Lenhart, Judy D Day, Chihoon Lee, Michael Dulin, Cristina Lanzas
Queueing theory studies the properties of waiting queues and has been applied to investigate direct host-to-host transmitted disease dynamics, but its potential in modelling environmentally transmitted pathogens has not been fully explored. In this study, we provide a flexible and customizable queueing theory modelling framework with three major subroutines to study the in-hospital contact processes between environments and hosts and potential nosocomial pathogen transfer, where environments are servers and hosts are customers...
September 11, 2018: Mathematical Medicine and Biology: a Journal of the IMA
V S K Manem, A Dhawan
In the past few years, proton therapy has taken the centre stage in treating various tumour types. The primary contribution of this study is to investigate the tumour control probability (TCP), relapse time and the corresponding secondary cancer risks induced by proton beam radiation therapy. We incorporate tumour relapse kinetics into the TCP framework and calculate the associated second cancer risks. To calculate proton therapy-induced secondary cancer induction, we used the well-known biologically motivated mathematical model, initiation-inactivation-proliferation formalism...
September 11, 2018: Mathematical Medicine and Biology: a Journal of the IMA
Atanaska Dobreva, Ralf Paus, N G Cogan
Alopecia areata (AA) is a CD8$^{+}$ T cell-dependent autoimmune disease that disrupts the constantly repeating cyclic transformations of hair follicles (HFs). Among the three main HF cycle stages-growth (anagen), regression (catagen) and relative quiescence (telogen)-only anagen HFs are attacked and thereby forced to prematurely enter into catagen, thus shortening active hair growth substantially. After having previously modelled the dynamics of immune system components critically involved in the disease development (Dobreva et al...
September 11, 2018: Mathematical Medicine and Biology: a Journal of the IMA
Jennifer H Tweedy, Jan O Pralits, Rodolfo Repetto, Paolo Soleri
Flow in the aqueous humour that fills the anterior chamber of the eye occurs in response to the production and drainage of the aqueous humour, and also due to buoyancy effects produced by thermal gradients. Phakic intraocular lenses are manufactured lenses that are surgically inserted in the eyes of patients to correct refractive errors. Their presence has a dramatic effect on the circulation of the aqueous humour, resulting a very different flow in the anterior chamber, the effects of which have not been extensively investigated...
September 11, 2018: Mathematical Medicine and Biology: a Journal of the IMA
J E F Green, J P Whiteley, J M Oliver, H M Byrne, S L Waters
We develop a continuum model for the aggregation of cells cultured in a nutrient-rich medium in a culture well. We consider a 2D geometry, representing a vertical slice through the culture well, and assume that the cell layer depth is small compared with the typical lengthscale of the culture well. We adopt a continuum mechanics approach, treating the cells and culture medium as a two-phase mixture. Specifically, the cells and culture medium are treated as fluids. Additionally, the cell phase can generate forces in response to environmental cues, which include the concentration of a chemoattractant that is produced by the cells within the culture medium...
September 11, 2018: Mathematical Medicine and Biology: a Journal of the IMA
Benjamin Engelhardt, Janine Holze, Christina Elliott, George S Baillie, Maik Kschischo, Holger Fröhlich
The muscarinic M$_{2}$ receptor is a prominent member of the GPCR family and strongly involved in heart diseases. Recently published experimental work explored the cellular response to iperoxo-induced M$_{2}$ receptor stimulation in Chinese hamster ovary (CHO) cells. To better understand these responses, we modelled and analysed the muscarinic M$_{2}$ receptor-dependent signalling pathway combined with relevant secondary messenger molecules using mass action. In our literature-based joint signalling and secondary messenger model, all binding and phosphorylation events are explicitly taken into account in order to enable subsequent stoichiometric matrix analysis...
September 11, 2018: Mathematical Medicine and Biology: a Journal of the IMA
Alfonso Sepúlveda-Gálvez, Jesús Agustín Badillo-Corona, Isaac Chairez
Mathematical modelling applied to biological systems allows for the inferring of changes in the dynamic behaviour of organisms associated with variations in the environment. Models based on ordinary differential equations are most commonly used because of their ability to describe the mechanisms of biological systems such as transcription. The disadvantage of using this approach is that there is a large number of parameters involved and that it is difficult to obtain them experimentally. This study presents an algorithm to obtain a finite-time parameter characterization of the model used to describe changes in the metabolic behaviour of Escherichia coli associated with environmental changes...
September 11, 2018: Mathematical Medicine and Biology: a Journal of the IMA
Miquel Gomez, Francisco Maduell
Kinetic modelling in haemodialysis is usually based upon the resolution of volume-defined compartment models. The interaction among these compartments is described by purely diffusive processes. In this paper we present an alternative kinetic model for uremic toxins in post-dilutional haemodiafiltration treatments by means of a unidimensional diffusion equation. A wide range of solutes such as urea, creatinine, $\beta _{2}$-microglobulin, myoglobin and prolactin were studied by imposing appropriate boundary and initial conditions in a virtual [0,1] domain...
June 15, 2018: Mathematical Medicine and Biology: a Journal of the IMA
Larisse Bolton, Alain H J J Cloot, Schalk W Schoombie, Jacobus P Slabbert
No abstract text is available yet for this article.
June 13, 2018: Mathematical Medicine and Biology: a Journal of the IMA
Todd R Young, Erik M Boczko
As technological improvements continue to infiltrate and impact medical practice, it has become possible to non-invasively collect dense physiological time series data from individual patients in real time. These advances continue to improve physicians' ability to detect and to treat infections early. One important benefit of early detection and treatment of nascent infections is that it leads to earlier resolution. In response to current and anticipated advances in data capture, we introduce the Early Treatment Gain (ETG) as a measure to quantify this benefit...
June 13, 2018: Mathematical Medicine and Biology: a Journal of the IMA
Ryan Nikin-Beers, Stanca M Ciupe
Cross-reactive T cell responses induced by a primary dengue virus infection may contribute to increased disease severity following heterologous infections with a different virus serotype in a phenomenon known as the original antigenic sin. In this study, we developed and analyzed in-host models of T cell responses to primary and secondary dengue virus infections that considered the effect of T cell cross-reactivity in disease enhancement. We fitted the models to published patient data and showed that the overall infected cell killing is similar in dengue heterologous infections, resulting in dengue fever and dengue hemorrhagic fever...
June 13, 2018: Mathematical Medicine and Biology: a Journal of the IMA
Ana Victoria Ponce Bobadilla, Philip K Maini, Helen Byrne
The tumour control probability (TCP) is the probability that a treatment regimen of radiation therapy (RT) eradicates all tumour cells in a given tissue. To decrease the toxic effects on healthy cells, RT is usually delivered over a period of weeks in a series of fractions. This allows tumour cells to repair sublethal damage (RSD) caused by radiation. In this article, we introduce a stochastic model for tumour response to radiotherapy which accounts for the effects of RSD. The tumour is subdivided into two cell types: 'affected' cells which have been damaged by RT and 'unaffected' cells which have not...
June 13, 2018: Mathematical Medicine and Biology: a Journal of the IMA
Jian Du, Aaron L Fogelson
We present a two-phase model of platelet aggregation in coronary-artery-sized blood vessels. The model tracks the number densities of three platelet populations as well as the concentration of a platelet activating chemical. Through the formation of elastic bonds, activated platelets can cohere with one another to form a platelet thrombus. Bound platelets in a thrombus move in a velocity field different from that of the bulk fluid. Stresses produced by the elastic bonds act on the bound platelet material. Movement of the bound platelet material and that of the background fluid are coupled through an interphase drag and an incompressibility constraint...
June 13, 2018: Mathematical Medicine and Biology: a Journal of the IMA
Richard J Braun, Tobin A Driscoll, Carolyn G Begley, P Ewen King-Smith, Javed I Siddique
We report the results of some recent experiments to visualize tear film dynamics. We then study a mathematical model for tear film thinning and tear film breakup (TBU), a term from the ocular surface literature. The thinning is driven by an imposed tear film thinning rate which is input from in vivo measurements. Solutes representing osmolarity and fluorescein are included in the model. Osmolarity causes osmosis from the model ocular surface, and the fluorescein is used to compute the intensity corresponding closely to in vivo observations...
June 13, 2018: Mathematical Medicine and Biology: a Journal of the IMA
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