A Mathematical Model of Liver Cell Aggregation In Vitro

The behavior of mammalian cells within three-dimensional structures is an area of intense biological research and underpins the efforts of tissue engineers to regenerate human tissues for clinical applications. In the particular case of hepatocytes (liver cells), the formation of spheroidal multicellular aggregates has been shown to improve cell viability and functionality compared to traditional monolayer culture techniques. We propose a simple mathematical model for the early stages of this aggregation process, when cell clusters form on the surface of the extracellular matrix (ECM) layer on which they are seeded. We focus on interactions between the cells and the viscoelastic ECM substrate. Governing equations for the cells, culture medium, and ECM are derived using the principles of mass and momentum balance. The model is then reduced to a system of four partial differential equations, which are investigated analytically and numerically. The model predicts that provided cells are seeded at a suitable density, aggregates with clearly defined boundaries and a spatially uniform cell density on the interior will form. While the mechanical properties of the ECM do not appear to have a significant effect, strong cell-ECM interactions can inhibit, or possibly prevent, the formation of aggregates. The paper concludes with a discussion of our key findings and suggestions for future work

Hyaluronidase induces a transcapillary pressure gradient and improves the distribution and uptake of liposomal doxorubicin (Caelyx™) in human osteosarcoma xenografts

Liposomal drug delivery enhances the tumour selective localisation and may improve the uptake compared to free drug. However, the drug distribution within the tumour tissue may still be heterogeneous. Degradation of the extracellular matrix is assumed to improve the uptake and penetration of drugs. The effect of the ECM-degrading enzyme hyaluronidase on interstitial fluid pressure and microvascular pressure were measured in human osteosarcoma xenografts by the wick-in-needle and micropipette technique, respectively. The tumour uptake and distribution of liposomal doxorubicin were studied on tumour sections by confocal laser scanning microscopy. The drugs were injected i.v. 1 h after the hyaluronidase pretreatment. Intratumoral injection of hyaluronidase reduced interstitial fluid pressure in a nonlinear dose-dependent manner. Maximum interstitial fluid pressure reduction of approximately 50% was found after injection of 1500 U hyaluronidase. Neither intratumoral nor i.v. injection of hyaluronidase induced any changes in the microvascular pressure. Thus, hyaluronidase induced a transcapillary pressure gradient, resulting in a four-fold increase in the tumour uptake and improving the distribution of the liposomal doxorubicin. Hyaluronidase reduces a major barrier for drug delivery by inducing a transcapillary pressure gradient, and administration of hyaluronidase adjuvant with liposomal doxorubicin may thus improve the therapeutic outcome

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