Predicting drug pharmacokinetics and effect in vascularized tumors using computer simulation

In this paper, we investigate the pharmacokinetics and effect of doxorubicin and cisplatin in vascularized tumors through two-dimensional simulations. We take into account especially vascular and morphological heterogeneity as well as cellular and lesion-level pharmacokinetic determinants like P-glycoprotein (Pgp) efflux and cell density. To do this we construct a multi-compartment PKPD model calibrated from published experimental data and simulate 2-h bolus administrations followed by 18-h drug washout. Our results show that lesion-scale drug and nutrient distribution may significantly impact therapeutic efficacy and should be considered as carefully as genetic determinants modulating, for example, the production of multidrug-resistance protein or topoisomerase II. We visualize and rigorously quantify distributions of nutrient, drug, and resulting cell inhibition. A main result is the existence of significant heterogeneity in all three, yielding poor inhibition in a large fraction of the lesion, and commensurately increased serum drug concentration necessary for an average 50% inhibition throughout the lesion (the IC50 concentration). For doxorubicin the effect of hypoxia and hypoglycemia (“nutrient effect”) is isolated and shown to further increase cell inhibition heterogeneity and double the IC50, both undesirable. We also show how the therapeutic effectiveness of doxorubicin penetration therapy depends upon other determinants affecting drug distribution, such as cellular efflux and density, offering some insight into the conditions under which otherwise promising therapies may fail and, more importantly, when they will succeed. Cisplatin is used as a contrast to doxorubicin since both published experimental data and our simulations indicate its lesion distribution is more uniform than that of doxorubicin. Because of this some of the complexity in predicting its therapeutic efficacy is mitigated. Using this advantage, we show results suggesting that in vitro monolayer assays using this drug may more accurately predict in vivo performance than for drugs like doxorubicin. The nonlinear interaction among various determinants representing cell and lesion phenotype as well as therapeutic strategies is a unifying theme of our results. Throughout it can be appreciated that macroscopic environmental conditions, notably drug and nutrient distributions, give rise to considerable variation in lesion response, hence clinical resistance. Moreover, the synergy or antagonism of combined therapeutic strategies depends heavily upon this environment

Tumour dynamics and necrosis: surface tension and stability.

A model is developed for the motion of cells within a multicell spherical tumour. The model allows either for the intercellular forces to be in compression and cells to be compacted to a fixed number density, or for the cell number density to fall and cells to become isolated from each other. The model develops necrotic regions naturally due to force balances rather than being directly attributable to a critical oxygen concentration. These necrotic regions may result in a gradual reduction in local cell density rather than jump to a completely dead region. Numerical and analytical analysis of the spherically symmetric model shows that the long time behaviour of the spheroid depends on any surface tension effects created by cells on the outer surface. For small surface tension the spheroid grows linearly in time developing a large necrotic region, while for larger surface tension the growth can be halted. The linear stability to spherically symmetric perturbations of all the possible resulting steady states is revealed

Planned experiments for mechanical assemblies

For experiments on mechanical products, conventional methods for reducing the experimental effort that is needed to extract information, such as those of Taguchi, can be infeasible because components with the dimensions needed for a standard factorial plan can be prohibitively expensive. Also, many factors for investigation are not directly measurable, as they are derived from the properties of several components and their assembly. Methods are described for finding optimal plans for such experiments from a minimal sample of measured components, and are illustrated through a pilot investigation of a hydraulic pump. Important issues are addressed of the robustness of the plans to possible missing data, for example due to product failure, and the need to ensure that the influences of the various different factors can be clearly extracted from the experimental results. On-going work in the aeronautical industry on products for low-volume manufacturing is also described, where experiments are run on-line so that information can be swiftly obtained without delay in the manufacturing process

Experiments for derived factors with application to hydraulic gear pumps

For experiments on mechanical products composed of several components, such as a hydraulic gear pump, conventional methods of designing and implementing factorial experiments can be impractical because of the prohibitive costs of obtaining certain components with factors set to prespecified values. A further difficulty is that often some of the factors that are believed to influence the product's performance are not features of a single component but are derived as functions of the dimensions of several components arising from the product's assembly. Experiments are proposed which use a sample of measured components to explore the influence of such derived factors. An algorithmic method for obtaining efficient designs is presented and applied to finding plans for studies on the gear pump. An experiment on the pump is described which involved both conventional and derived factors. This experiment led to new knowledge on how to improve the engineering design of the pump and, in particular, on how to improve its robustness to the varying pressures that are experienced in operation

Stochastic modelling of membrane filtration

Membrane fouling during particle filtration occurs through a variety of mechanisms, including internal pore clogging by contaminants, coverage of pore entrances, and deposition on the membrane surface. In this paper we present an efficient method for modelling the behaviour of a filter, which accounts for different retention mechanisms, particle sizes, and membrane geometries. The membrane is assumed to be composed of a series of, possibly interconnected, pores. The central feature is a conductivity function, which describes the blockage of each individual pore as particles arrive, which is coupled with a mechanism to account for the stochastic nature of the arrival times of particles at the pore. The result is a system of ordinary differential equations based on the pore-level interactions. We demonstrate how our model can accurately describe a wide range of filtration scenarios. Specifically, we consider: a case where blocking via multiple mechanisms can occur simultaneously, which have previously required the study through individual models; the filtration of a combination of small and large particles by a track-etched membrane; and particle separation using interconnected pore networks. The model is significantly faster than comparable stochastic simulations for small networks, enabling its use as a tool for efficient future simulations.</p

Stochastic modelling of membrane filtration

Membrane fouling during particle filtration occurs through a variety of mechanisms, including internal pore clogging by contaminants, coverage of pore entrances, and deposition on the membrane surface. In this paper we present an efficient method for modelling the behaviour of a filter, which accounts for different retention mechanisms, particle sizes, and membrane geometries. The membrane is assumed to be composed of a series of, possibly interconnected, pores. The central feature is a conductivity function, which describes the blockage of each individual pore as particles arrive, which is coupled with a mechanism to account for the stochastic nature of the arrival times of particles at the pore. The result is a system of ordinary differential equations based on the pore-level interactions. We demonstrate how our model can accurately describe a wide range of filtration scenarios. Specifically, we consider: a case where blocking via multiple mechanisms can occur simultaneously, which have previously required the study through individual models; the filtration of a combination of small and large particles by a track-etched membrane; and particle separation using interconnected pore networks. The model is significantly faster than comparable stochastic simulations for small networks, enabling its use as a tool for efficient future simulations.</p

Physical modelling of the slow voltage relaxation phenomenon in lithium-ion batteries

In the lithium-ion battery literature, discharges followed by a relaxation to equilibrium are frequently used to validate models and their parametrizations. Good agreement with experiment during discharge is easily attained with a pseudo-two-dimensional model such as the Doyle-Fuller-Newman (DFN) model. The relaxation portion, however, is typically not well-reproduced, with the relaxation in experiments occurring much more slowly than in models. In this study, using a model that includes a size distribution of the active material particles, we give a physical explanation for the slow relaxation phenomenon. This model, the Many-Particle-DFN (MP-DFN), is compared against discharge and relaxation data from the literature, and optimal fits of the size distribution parameters (mean and variance), as well as solid-state diffusivities, are found using numerical optimization. The voltage after relaxation is captured by careful choice of the current cut-off time, allowing a single set of physical parameters to be used for all C-rates, in contrast to previous studies. We find that the MP-DFN can accurately reproduce the slow relaxation, across a range of C-rates, whereas the DFN cannot. Size distributions allow for greater internal heterogeneities, giving a natural origin of slower relaxation timescales that may be relevant in other, as yet explained, battery behavior