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In this article, we consider the spatial homogenisation of a multi-phase model for avascular tumour growth and response to chemotherapeutic treatment. The key contribution of this work is the derivation of a system of homogenised partial differential equations describing macroscopic tumour growth, coupled to transport of drug and nutrient, that explicitly incorporates details of the structure and dynamics of the tumour at the microscale. In order to derive these equations, we employ an asymptotic homogenisation of a microscopic description under the assumption of strong interphase drag, periodic microstructure, and strong separation of scales. The resulting macroscale model comprises a Darcy flow coupled to a system of reaction–advection partial differential equations. The coupled growth, response, and transport dynamics on the tissue scale are investigated via numerical experiments for simple academic test cases of microstructural information and tissue geometry, in which we observe drug- and nutrient-regulated growth and response consistent with the anticipated dynamics of the macroscale system. [ABSTRACT FROM AUTHOR]

Adequate drug distribution through tumors is essential for treatment to be effective. Palbociclib is a cyclin-dependent kinase 4/6 inhibitor approved for use in patients with hormone receptor positive, human epidermal growth factor receptor 2 negative metastatic breast cancer. It has unusual physicochemical properties, which may significantly influence its distribution in tumor tissue. We studied the penetration and distribution of palbociclib in vitro, including the use of multicellular three-dimensional models and mathematical modeling. MCF-7 and DLD-1 cell lines were grown as single cell suspensions (SCS) and spheroids; palbociclib uptake and efflux were studied using liquid chromatography-tandem mass spectrometry. Intracellular concentrations of palbociclib for MCF-7 SCS ( C max M) and spheroids ( µ M) and spheroids ( C M) were 32- and 29-fold higher and in DLD-1, 13- and 7-fold higher, respectively, than the media concentration (0.1 max M). Total palbociclib uptake was lower in DLD-1 cells than MCF-7 cells in both SCS and spheroids. Both uptake and efflux of palbociclib were slower in spheroids than SCS. These data were used to develop a mathematical model of palbociclib transport that quantifies key parameters determining drug penetration and distribution. The model reproduced qualitatively most features of the experimental data and distinguished between SCS and spheroids, providing additional support for hypotheses derived from the experimental data. Mathematical modeling has the potential for translating in vitro data into clinically relevant estimates of tumor drug concentrations. SIGNIFICANCE STATEMENT: This study explores palbociclib uptake and efflux in single cell suspension and spheroid models of cancer. Large intracellular concentrations of palbociclib are found after drug exposure. The data from this study may aid understanding of the intratumoural pharmacokinetics of palbociclib, which is useful in understanding how drug distributes within tumor tissue and optimizing drug efficacy. Biomathematical modelling has the potential to derive intratumoural drug concentrations from plasma pharmacokinetics in patients.µ M) were 32- and 29-fold higher and in DLD-1, 13- and 7-fold higher, respectively, than the media concentration (0.1 μ M). Total palbociclib uptake was lower in DLD-1 cells than MCF-7 cells in both SCS and spheroids. Both uptake and efflux of palbociclib were slower in spheroids than SCS. These data were used to develop a mathematical model of palbociclib transport that quantifies key parameters determining drug penetration and distribution. The model reproduced qualitatively most features of the experimental data and distinguished between SCS and spheroids, providing additional support for hypotheses derived from the experimental data. Mathematical modeling has the potential for translating in vitro data into clinically relevant estimates of tumor drug concentrations. SIGNIFICANCE STATEMENT: This study explores palbociclib uptake and efflux in single cell suspension and spheroid models of cancer. Large intracellular concentrations of palbociclib are found after drug exposure. The data from this study may aid understanding of the intratumoural pharmacokinetics of palbociclib, which is useful in understanding how drug distributes within tumor tissue and optimizing drug efficacy. Biomathematical modelling has the potential to derive intratumoural drug concentrations from plasma pharmacokinetics in patients., (Copyright © 2019 by The American Society for Pharmacology and Experimental Therapeutics.)

Measurement of a tissue-specific electrical resistance may offer a discriminatory metric for evaluation of tissue health during cancer surgery. With a move toward minimally-invasive procedures, applicable contact sensing modalities must be scalable, fast and robust. A passive resistance characterisation method utilising a biogalvanic cell as an intrinsic power source has been proposed as a potentially suitable solution. Previous work has evaluated this system with results showing effective discrimination of tissue type and damage (through electroporation). However, aspects of the biogalvanic cell have been found to influence the characterisation performance, and are not currently accounted for within the system model. In particular, the electrode and salt-bridge resistance are not independently determined, leading to over-predictions of tissue resistivity. This paper describes a more comprehensive model and characterisation scheme, with electrode parameters and salt-bridge resistivity being evaluated independently. In a generalised form, the presented model illustrates how the relative resistive contributions from the electrodes and medium relate to the existing characterisation method efficacy. We also describe experiments with physiologically relevant salt solutions (1.71, 17.1, 154 mM), used for validation and comparison. The presented model shows improved performance over the current biogalvanic measurement technique at the median conductivity. Both the proposed and extant system models become unable to predict conductivity accurately at high conductivity due to the dominance of the electrodes. The characterisation techniques have also been applied to data collected on freshly excised human colon tissue (healthy and cancerous). The findings suggest that the resistance of the cell under the test conditions is electrode dominated, leading to erroneous tissue resistance determination. Measurement optimisation strategies and the surgical applicability of the biogalvanic technique are discussed in light of these findings.

In this paper we present a continuum mathematical model of vascular tumour growth which is based on a multiphase framework in which the tissue is decomposed into four distinct phases and the principles of conservation of mass and momentum are applied to the normal/healthy cells, tumour cells, blood vessels and extracellular material. The inclusion of a diffusible nutrient, supplied by the blood vessels, allows the vasculature to have a nonlocal influence on the other phases. Two-dimensional computational simulations are carried out on unstructured, triangular meshes to allow a natural treatment of irregular geometries, and the tumour boundary is captured as a diffuse interface on this mesh, thereby obviating the need to explicitly track the (potentially highly irregular and ill-defined) tumour boundary. A hybrid finite volume/finite element algorithm is used to discretise the continuum model: the application of a conservative, upwind, finite volume scheme to the hyperbolic mass balance equations and a finite element scheme with a stable element pair to the generalised Stokes equations derived from momentum balance, leads to a robust algorithm which does not use any form of artificial stabilisation. The use of a matrix-free Newton iteration with a finite element scheme for the nutrient reaction-diffusion equations allows full nonlinearity in the source terms of the mathematical model. Numerical simulations reveal that this four-phase model reproduces the characteristic pattern of tumour growth in which a necrotic core forms behind an expanding rim of well-vascularised proliferating tumour cells. The simulations consistently predict linear tumour growth rates. The dependence of both the speed with which the tumour grows and the irregularity of the invading tumour front on the model parameters is investigated., (Copyright © 2012 Elsevier Ltd. All rights reserved.)

Published research indicates that regular use of toothpaste containing sodium bicarbonate is effective in reducing volatile sulfur compounds (VSCs) and oral malodor. Gaffar initially reported on the use of sodium bicarbonate as an agent to affect VSCs, indicating that sodium bicarbonate had the potential to alter the VSCs to nonvolatile compounds. Chewing gum would also be suspected of providing benefits in controlling oral malodor through its claimed ability to mechanically aid in the removal of dental plaque. Based on the length of chewing time, the opportunity exists for chewing gum to reach places in the mouth that might be missed during brushing. This activity could contribute to reductions in the amount of viable plaque mass that could produce VSCs.