Cellular Uptake and Efflux of Palbociclib In Vitro in Single Cell and Spheroid Models.

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 3.22 µM) and spheroids (C max 2.91 µM) were 32- and 29-fold higher and in DLD-1, 13- and 7-fold higher, respectively, than the media concentration (0.1 µM). 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.

Drug delivery in a tumour cord model: a computational simulation.

The tumour vasculature and microenvironment is complex and heterogeneous, contributing to reduced delivery of cancer drugs to the tumour. We have developed an in silico model of drug transport in a tumour cord to explore the effect of different drug regimes over a 72 h period and how changes in pharmacokinetic parameters affect tumour exposure to the cytotoxic drug doxorubicin. We used the model to describe the radial and axial distribution of drug in the tumour cord as a function of changes in the transport rate across the cell membrane, blood vessel and intercellular permeability, flow rate, and the binding and unbinding ratio of drug within the cancer cells. We explored how changes in these parameters may affect cellular exposure to drug. The model demonstrates the extent to which distance from the supplying vessel influences drug levels and the effect of dosing schedule in relation to saturation of drug-binding sites. It also shows the likely impact on drug distribution of the aberrant vasculature seen within tumours. The model can be adapted for other drugs and extended to include other parameters. The analysis confirms that computational models can play a role in understanding novel cancer therapies to optimize drug administration and delivery.

Effective equations governing an active poroelastic medium.

In this work, we consider the spatial homogenization of a coupled transport and fluid-structure interaction model, to the end of deriving a system of effective equations describing the flow, elastic deformation and transport in an active poroelastic medium. The 'active' nature of the material results from a morphoelastic response to a chemical stimulant, in which the growth time scale is strongly separated from other elastic time scales. The resulting effective model is broadly relevant to the study of biological tissue growth, geophysical flows (e.g. swelling in coals and clays) and a wide range of industrial applications (e.g. absorbant hygiene products). The key contribution of this work is the derivation of a system of homogenized partial differential equations describing macroscale growth, coupled to transport of solute, that explicitly incorporates details of the structure and dynamics of the microscopic system, and, moreover, admits finite growth and deformation at the pore scale. The resulting macroscale model comprises a Biot-type system, augmented with additional terms pertaining to growth, coupled to an advection-reaction-diffusion equation. The resultant system of effective equations is then compared with other recent models under a selection of appropriate simplifying asymptotic limits.

The impact of electrode resistance on the biogalvanic characterisation technique.

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.

Mathematical and computational models of drug transport in tumours.

The ability to predict how far a drug will penetrate into the tumour microenvironment within its pharmacokinetic (PK) lifespan would provide valuable information about therapeutic response. As the PK profile is directly related to the route and schedule of drug administration, an in silico tool that can predict the drug administration schedule that results in optimal drug delivery to tumours would streamline clinical trial design. This paper investigates the application of mathematical and computational modelling techniques to help improve our understanding of the fundamental mechanisms underlying drug delivery, and compares the performance of a simple model with more complex approaches. Three models of drug transport are developed, all based on the same drug binding model and parametrized by bespoke in vitro experiments. Their predictions, compared for a 'tumour cord' geometry, are qualitatively and quantitatively similar. We assess the effect of varying the PK profile of the supplied drug, and the binding affinity of the drug to tumour cells, on the concentration of drug reaching cells and the accumulated exposure of cells to drug at arbitrary distances from a supplying blood vessel. This is a contribution towards developing a useful drug transport modelling tool for informing strategies for the treatment of tumour cells which are 'pharmacokinetically resistant' to chemotherapeutic strategies.

Multiphase modelling of vascular tumour growth in two spatial dimensions.

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.

Oral malodor control afforded through the use of sodium bicarbonate-containing chewing gum.

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.

Evaluation of the enteric analyzer for identification of Enterobacteriaceae.

The reliability of the Enteric Analyzer for identification of Enterobacteriaceae was evaluated using biochemical results previously obtained for 291 organisms with the conventional, R/B, and Minitek systems. The instrument correctly identified 77.3% of the organisms using conventional system results, 74.2% using R/B results, and 60.5% using Minitek results. The low rate of identification with the conventional system occurs primarily because the instrument is not programmed to consider delayed biochemical reactions. The arbitrary use of 90% and 99% probabilities for test reactions also contributes to a lower percentage of identification. The Enteric Analyzer does not replace the judgment of experienced personnel in the identification of atypical bacteria, but it may prove helpful in speeding up final computer identification of typical microorganisms.

Evaluation of the R/B and Minitek systems for identification of Enterobacteriaceae.

The R/B and Minitek systems for the identification of Enterobacteriaceae were evaluated, and the results were compared with those obtained by conventional methods. Both systems were rapid and allowed correct identification of about 85% of the 294 isolates (23 species) examined. The individual biochemical reactions showed an overall agreement of 92.6% and 93.1% for the R/B and Minitek systems, respectively.