A mathematical model of tumor-immune interactions

A mathematical model of the interactions between a growing tumor and the immune system is presented. The equations and parameters of the model are based on experimental and clinical results from published studies. The model includes the primary cell populations involved in effector T cell mediated tumor killing: regulatory T cells, helper T cells, and dendritic cells. A key feature is the inclusion of multiple mechanisms of immunosuppression through the main cytokines and growth factors mediating the interactions between the cell populations. Decreased access of effector cells to the tumor interior with increasing tumor size is accounted for. The model is applied to tumors with different growth rates and antigenicities to gauge the relative importance of various immunosuppressive mechanisms. The most important factors leading to tumor escape are TGF-induced immunosuppression, conversion of helper T cells into regulatory T cells, and the limitation of immune cell access to the full tumor at large tumor sizes. The results suggest that for a given tumor growth rate, there is an optimal antigenicity maximizing the response of the immune system. Further increases in antigenicity result in increased immunosuppression, and therefore a decrease in tumor killing rate

In situ synchrotron tomography of granular deformation in semi-solid Al-Cu alloys

Optimising casting routes involving semi-solid deformation such as semi-solid processing and high-pressure die casting requires a fundamental understanding of the globule-scale mechanisms behind the macroscopic rheological behaviour. This thesis uses time-resolved 3D imaging to directly observe and measure semi-solid alloy deformation from a microstructural perspective. Under isothermal conditions and constant strain rates, deformation mechanisms both at the crystal scale and at the specimen scale were identified during deformation in globular Al-Cu alloys at 64-93% solid. Imaging and quantifying these mechanisms has led to the emergence of a refined understanding of semi-solid deformation based on granular material concepts. It is shown that globularised crystals (above fs> 60%) exclusively rearrange as individual grains during parallel plate compression and backward extrusion at low strain rates. Crystal-crystal interactions are identified for the two loading modes and are not accompanied by plastic deformation of the individual crystals during acquisition. The ubiquitous grain rearrangement is coupled with shear-induced dilation of the solid assembly, whereby the crystals push each other apart in order to accommodate the increasing strain. It is also shown that, for specimens lacking a liquid reservoir, shear-induced dilation causes menisci to be pulled into the specimen from the surface and additionally, at high solid fractions, internal pores to grow. The origins of cracking during semi-solid processing are explored in a granular framework and linked to the shear-induced dilation associated with the solid assembly which increases the initial width of the liquid channels between the grains. Finally, the discrete grain analysis is coupled with the bulk mechanical results to explore the shape of the stress-strain curve and relate it to the imaged and quantified behaviours. All solid fractions tend to the same final stress, hinting at the possibility of a critical state analogous to that in soil mechanics, although fully testing this hypothesis requires varying the confining pressure.Open Acces

A Mathematical Model for Cisplatin Cellular Pharmacodynamics

AbstractA simple theoretical model for the cellular pharmacodynamics of cisplatin is presented. The model, which takes into account the kinetics of cisplatin uptake by cells and the intracellular binding of the drug, can be used to predict the dependence of survival (relative to controls) on the time course of extracellular exposure. Cellular pharmacokinetic parameters are derived from uptake data for human ovarian and head and neck cancer cell lines. Survival relative to controls is assumed to depend on the peak concentration of DNA-bound intracellular platinum. Model predictions agree well with published data on cisplatin cytotoxicity for three different cancer cell lines, over a wide range of exposure times. In comparison with previously published mathematical models for anticancer drug pharmacodynamics, the present model provides a better fit to experimental data sets including long exposure times (∼100 hours). The model provides a possible explanation for the fact that cell kill correlates well with area under the extracellular concentration-time curve in some data sets, but not in others. The model may be useful for optimizing delivery schedules and for the dosing of cisplatin for cancer therapy

Two-Mechanism Peak Concentration Model for Cellular Pharmacodynamics of Doxorubicin

AbstractA mathematical model is presented for the cellular uptake and cytotoxicity of the anticancer drug doxorubicin. The model assumes sigmoidal, Hill-type dependence of cell survival on drug-induced damage. Experimental evidence indicates distinct intracellular and extracellular mechanisms of doxorubicin cytotoxicity. Drug-induced damage is therefore expressed as the sum of two terms, representing the peak values over time of concentrations of intracellular and extracellular drugs. Dependence of cell kill on peak values of concentration rather than on an integral over time is consistent with observations that dose-response curves for doxorubicin converge to a single curve as exposure time is increased. Drug uptake by cells is assumed to include both saturable and unsaturable components, consistent with experimental data. Overall, the model provides better fits to in vitro cytotoxicity data than previous models. It shows how saturation of cellular uptake or binding with concentration can result in plateaus in the dose-response curve at high concentrations and short exposure, as observed experimentally in some cases. The model provides a unified framework for analyzing doxorubicin cellular pharmacokinetic and pharmacodynamic data, can be applied in mathematical models for tumor response and treatment optimization

Discriminative and Distinct Phenotyping by Constrained Tensor Factorization

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Multi-element cylindrical electrostatic lens systems for focusing and controlling charged particles

This paper describes theoretical modelling of electrostatic lenses based on 3, 4 and 5 closely spaced cylindrical electrodes, respectively. In each case, modelling is carried out numerically using commercial packages SIMION and LENSYS, and a variety of performance parameters are obtained. These include the magnification, the 3rd order spherical and chromatic aberration coefficients. Special cases such as zoom lens (i.e., lenses whose magnification may be changed without losing focus) are considered. Results are obtained as a function of the ratios of the electrode lengths and gaps, and as a function of ratios of the controlling voltages. As a result, it is shown that how a multi-element lens system can be operated with the whole focal properties in a useful mode for using in experimental studies.Comment: 20 pages, 15 figure

A 4-D dataset for validation of crystal growth in a complex three-phase material, ice cream

Four dimensional (4D, or 3D plus time) X-ray tomographic imaging of phase changes in materials is quickly becoming an accepted tool for quantifying the development of microstructures to both inform and validate models. However, most of the systems studied have been relatively simple binary compositions with only two phases. In this study we present a quantitative dataset of the phase evolution in a complex three-phase material, ice cream. The microstructure of ice cream is an important parameter in terms of sensorial perception, and therefore quantification and modelling of the evolution of the microstructure with time and temperature is key to understanding its fabrication and storage. The microstructure consists of three phases, air cells, ice crystals, and unfrozen matrix. We perform in situ synchrotron X-ray imaging of ice cream samples using in-line phase contrast tomography, housed within a purpose built cold-stage (-40 to +20oC) with finely controlled variation in specimen temperature. The size and distribution of ice crystals and air cells during programmed temperature cycling are determined using 3D quantification. The microstructural evolution of three-phase materials has many other important applications ranging from biological to structural and functional material, hence this dataset can act as a validation case for numerical investigations on faceted and non-faceted crystal growth in a range of materials

Electrochemical simulation of Solid Oxide Fuel Cell electrodes: an integrated approach to address the microstructure-performance correlation

Understanding the complex interplay between electrode microstructure and electrochemical performance is one of the key aspects for the optimization of Solid Oxide Fuel Cells (SOFC). Physically-based modelling, at different levels of sophistication, can provide a valuable insight in order to help the interpretation of experimental data and provide design indications to improve electrode stability and performance. In this contribution we summarize the different modelling approaches used in our group, ranging from physically-based equivalent circuits, continuum conservation models and 3D models solved within the reconstructed electrode microstructure. When necessary, these models are coupled with percolation theory, packing algorithms and tomographic techniques. Special focus is given to the application of the models to interpret impedance spectra and their thorough validation under different conditions. Examples include the application of the models to electrodes with different microstructures, the study of the degradation mechanisms of Ni-infiltrated anodes as well as impedance simulations in real microstructures (Figure 1). Results reveal that coupling physically-based modelling, impedance spectroscopy and 3D tomography is a promising approach to gain a fundamental understanding of the phenomena occurring at different length scales in SOFC electrodes, allowing for interpreting and planning experiments as well as to design more stable and more efficient electrodes

Acute flaccid paralysis incidence rate and epidemiology in children in Lebanon: a rise in numbers in the post-vaccination and refugee crisis era

Background: Acute flaccid paralysis (AFP) is a clinical syndrome characterized by the acute onset of weakness and paralysis with reduced muscle tone. This study explored the incidence and different aspects of AFP in Lebanese children between 2009 and 2019. Methods: AFP data were collected from the Lebanese Ministry of Public Health. Incidence rate according to year, age groups, clinical data, follow-up, diagnosis, and vaccination status was analyzed in the 11-years period. Results: AFP incidence rates increased importantly from 0.63 per 100,000 in 2009 till 4.96 per 100,000 in 2019. Most of the patients were children under ten years of age, 40.6% of all cases were under five years old, and 37.9% were between 5 and 9 years old. Follow-up revealed that approximately two out of five patients experienced residual weakness. As for the final diagnosis, around 30% of cases were diagnosed as Guillain-Barre Syndrome (GBS). Most cases were children having received between 3 and 5 doses of polio vaccine. Conclusions: The rise in cases coincided with the Syrian refugee crisis in Lebanon and the progressively deteriorating economy in the country; yet, incidence rates were in the lower margin compared with other countries. Keywords: Acute flaccid paralysis; Epidemiology; Guillain-Barré Syndrome; Lebanon; Pediatrics