3D simulations of early blood vessel formation

Blood vessel networks form by spontaneous aggregation of individual cells migrating toward vascularization sites (vasculogenesis). A successful theoretical model of two dimensional experimental vasculogenesis has been recently proposed, showing the relevance of percolation concepts and of cell cross-talk (chemotactic autocrine loop) to the understanding of this self-aggregation process. Here we study the natural 3D extension of the computational model proposed earlier, which is relevant for the investigation of the genuinely threedimensional process of vasculogenesis in vertebrate embryos. The computational model is based on a multidimensional Burgers equation coupled with a reaction diffusion equation for a chemotactic factor and a mass conservation law. The numerical approximation of the computational model is obtained by high order relaxed schemes. Space and time discretization are performed by using TVD schemes and, respectively, IMEX schemes. Due to the computational costs of realistic simulations, we have implemented the numerical algorithm on a cluster for parallel computation. Starting from initial conditions mimicking the experimentally observed ones, numerical simulations produce network-like structures qualitatively similar to those observed in the early stages of \emph{in vivo} vasculogenesis. We develop the computation of critical percolative indices as a robust measure of the network geometry as a first step towards the comparison of computational and experimental data.Comment: 25 pages, 9 figures Submitted to: JC

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

A Systems Approach for Tumor Pharmacokinetics

Recent advances in genome inspired target discovery, small molecule screens, development of biological and nanotechnology have led to the introduction of a myriad of new differently sized agents into the clinic. The differences in small and large molecule delivery are becoming increasingly important in combination therapies as well as the use of drugs that modify the physiology of tumors such as anti-angiogenic treatment. The complexity of targeting has led to the development of mathematical models to facilitate understanding, but unfortunately, these studies are often only applicable to a particular molecule, making pharmacokinetic comparisons difficult. Here we develop and describe a framework for categorizing primary pharmacokinetics of drugs in tumors. For modeling purposes, we define drugs not by their mechanism of action but rather their rate-limiting step of delivery. Our simulations account for variations in perfusion, vascularization, interstitial transport, and non-linear local binding and metabolism. Based on a comparison of the fundamental rates determining uptake, drugs were classified into four categories depending on whether uptake is limited by blood flow, extravasation, interstitial diffusion, or local binding and metabolism. Simulations comparing small molecule versus macromolecular drugs show a sharp difference in distribution, which has implications for multi-drug therapies. The tissue-level distribution differs widely in tumors for small molecules versus macromolecular biologic drugs, and this should be considered in the design of agents and treatments. An example using antibodies in mouse xenografts illustrates the different in vivo behavior. This type of transport analysis can be used to aid in model development, experimental data analysis, and imaging and therapeutic agent design.National Institutes of Health (U.S.) (grant T32 CA079443

Identification of Key Processes that Control Tumor Necrosis Factor Availability in a Tuberculosis Granuloma

Tuberculosis (TB) granulomas are organized collections of immune cells comprised of macrophages, lymphocytes and other cells that form in the lung as a result of immune response to Mycobacterium tuberculosis (Mtb) infection. Formation and maintenance of granulomas are essential for control of Mtb infection and are regulated in part by a pro-inflammatory cytokine, tumor necrosis factor-α (TNF). To characterize mechanisms that control TNF availability within a TB granuloma, we developed a multi-scale two compartment partial differential equation model that describes a granuloma as a collection of immune cells forming concentric layers and includes TNF/TNF receptor binding and trafficking processes. We used the results of sensitivity analysis as a tool to identify experiments to measure critical model parameters in an artificial experimental model of a TB granuloma induced in the lungs of mice following injection of mycobacterial antigen-coated beads. Using our model, we then demonstrated that the organization of immune cells within a TB granuloma as well as TNF/TNF receptor binding and intracellular trafficking are two important factors that control TNF availability and may spatially coordinate TNF-induced immunological functions within a granuloma. Further, we showed that the neutralization power of TNF-neutralizing drugs depends on their TNF binding characteristics, including TNF binding kinetics, ability to bind to membrane-bound TNF and TNF binding stoichiometry. To further elucidate the role of TNF in the process of granuloma development, our modeling and experimental findings on TNF-associated molecular scale aspects of the granuloma can be incorporated into larger scale models describing the immune response to TB infection. Ultimately, these modeling and experimental results can help identify new strategies for TB disease control/therapy