Tumor Angiogenesis and Vascular Patterning: A Mathematical Model

Understanding tumor induced angiogenesis is a challenging problem with important consequences for diagnosis and treatment of cancer. Recently, strong evidences suggest the dual role of endothelial cells on the migrating tips and on the proliferating body of blood vessels, in consonance with further events behind lumen formation and vascular patterning. In this paper we present a multi-scale phase-field model that combines the benefits of continuum physics description and the capability of tracking individual cells. The model allows us to discuss the role of the endothelial cells' chemotactic response and proliferation rate as key factors that tailor the neovascular network. Importantly, we also test the predictions of our theoretical model against relevant experimental approaches in mice that displayed distinctive vascular patterns. The model reproduces the in vivo patterns of newly formed vascular networks, providing quantitative and qualitative results for branch density and vessel diameter on the order of the ones measured experimentally in mouse retinas. Our results highlight the ability of mathematical models to suggest relevant hypotheses with respect to the role of different parameters in this process, hence underlining the necessary collaboration between mathematical modeling, in vivo imaging and molecular biology techniques to improve current diagnostic and therapeutic tools

Carboxyl-modified single-wall carbon nanotubes improve bone tissue formation in vitro and repair in an in vivo rat model

Antonio Barrientos-Durán,1,5,* Ellen M Carpenter,2 Nicole I zur Nieden,3 Theodore I Malinin,4 Juan Carlos Rodríguez-Manzaneque,5 Laura P Zanello1,* 1Department of Biochemistry, University of California Riverside, Riverside, CA, USA; 2Department of Psychiatry and Biobehavioral Sciences, UCLA School of Medicine, South Los Angeles, CA, USA; 3Department of Cell Biology and Neuroscience, Stem Cell Center, College of Natural and Agricultural Sciences, University of California Riverside, Riverside, CA, USA; 4Tissue Bank, Department of Orthopedics, University of Miami Miller School of Medicine, Miami, FL, USA; 5Pfizer-University of Granada-Junta de Andalucía Centre for Genomics and Oncological Research (GENYO), Granada, Spain *These authors contributed equally to this workAbstract: The clinical management of bone defects caused by trauma or nonunion fractures remains a challenge in orthopedic practice due to the poor integration and biocompatibility properties of the scaffold or implant material. In the current work, the osteogenic properties of carboxyl-modified single-walled carbon nanotubes (COOH–SWCNTs) were investigated in vivo and in vitro. When human preosteoblasts and murine embryonic stem cells were cultured on coverslips sprayed with COOH–SWCNTs, accelerated osteogenic differentiation was manifested by increased expression of classical bone marker genes and an increase in the secretion of osteocalcin, in addition to prior mineralization of the extracellular matrix. These results predicated COOH–SWCNTs’ use to further promote osteogenic differentiation in vivo. In contrast, both cell lines had difficulties adhering to multi-walled carbon nanotube-based scaffolds, as shown by scanning electron microscopy. While a suspension of SWCNTs caused cytotoxicity in both cell lines at levels >20 µg/mL, these levels were never achieved by release from sprayed SWCNTs, warranting the approach taken. In vivo, human allografts formed by the combination of demineralized bone matrix or cartilage particles with SWCNTs were implanted into nude rats, and ectopic bone formation was analyzed. Histological analysis of both types of implants showed high permeability and pore connectivity of the carbon nanotube-soaked implants. Numerous vascularization channels appeared in the formed tissue, additional progenitor cells were recruited, and areas of de novo ossification were found 4 weeks post-implantation. Induction of the expression of bone-related genes and the presence of secreted osteopontin protein were also confirmed by quantitative polymerase chain reaction analysis and immunofluorescence, respectively. In summary, these results are in line with prior contributions that highlight the suitability of SWCNTs as scaffolds with high bone-inducing capabilities both in vitro and in vivo, confirming them as alternatives to current bone-repair therapies. Keywords: human allografts, demineralized bone matrix, cartilage particles, bone regeneratio