Modeling Three-dimensional Invasive Solid Tumor Growth in Heterogeneous Microenvironment under Chemotherapy

A systematic understanding of the evolution and growth dynamics of invasive solid tumors in response to different chemotherapy strategies is crucial for the development of individually optimized oncotherapy. Here, we develop a hybrid three-dimensional (3D) computational model that integrates pharmacokinetic model, continuum diffusion-reaction model and discrete cell automaton model to investigate 3D invasive solid tumor growth in heterogeneous microenvironment under chemotherapy. Specifically, we consider the effects of heterogeneous environment on drug diffusion, tumor growth, invasion and the drug-tumor interaction on individual cell level. We employ the hybrid model to investigate the evolution and growth dynamics of avascular invasive solid tumors under different chemotherapy strategies. Our simulations reproduce the well-established observation that constant dosing is generally more effective in suppressing primary tumor growth than periodic dosing, due to the resulting continuous high drug concentration. In highly heterogeneous microenvironment, the malignancy of the tumor is significantly enhanced, leading to inefficiency of chemotherapies. The effects of geometrically-confined microenvironment and non-uniform drug dosing are also investigated. Our computational model, when supplemented with sufficient clinical data, could eventually lead to the development of efficient in silico tools for prognosis and treatment strategy optimization.Comment: 41 pages, 8 figure

Multi-scale interaction of flow and the artery wall

We discuss, from the perspective of basic science, the physical and biological processes which underlie atherosclerotic (plaque) initiation at the vascular endothelium, identifying their widely separated spatial and temporal scales which participate. We draw on current, related models of vessel wall evolution, paying particular attention to the role of flow, and proceed to propose, then validate (in practical, qualitative terms, at least) a multiply coupled, multi-scale modeling strategy, which, eventually, aims at a quantitative, patient-specific understanding of the coupling between the flow and the endothelial state

Mathematical modeling of collagen turnover in biological tissue

The final publication is available at Springer via http://dx.doi.org/10.1007/s00285-012-0613-yWe present a theoretical and computational model for collagen turnover in soft biological tissues. Driven by alterations in the mechanical environment, collagen fiber bundles may undergo important chronic changes, characterized primarily by alterations in collagen synthesis and degradation rates. In particular, hypertension triggers an increase in tropocollagen synthesis and a decrease in collagen degradation, which lead to the well-documented overall increase in collagen content. These changes are the result of a cascade of events, initiated mainly by the endothelial and smooth muscle cells. Here, we represent these events collectively in terms of two internal variables, the concentration of growth factor TGF-$\beta$ and tissue inhibitors of metalloproteinases TIMP. The upregulation of TGF-$\beta$ increases the collagen density. The upregulation of TIMP also increases the collagen density through decreasing matrix metalloproteinase MMP. We establish a mathematical theory for mechanically-induced collagen turnover and introduce a computational algorithm for its robust and efficient solution. We demonstrate that our model can accurately predict the experimentally observed collagen increase in response to hypertension reported in literature. Ultimately, the model can serve as a valuable tool to predict the chronic adaptation of collagen content to restore the homeostatic equilibrium state in vessels with arbitrary micro-structure and geometry.Peer ReviewedPostprint (author's final draft

Characterisation of the mechanobiology of stents in vitro

This paper was presented at the 4th Micro and Nano Flows Conference (MNF2014), which was held at University College, London, UK. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute, ASME Press, LCN London Centre for Nanotechnology, UCL University College London, UCL Engineering, the International NanoScience Community, www.nanopaprika.eu.Long-term efficacy of percutaneous coronary intervention (PCI) to treat coronary heart disease is hampered by incidence of in-stent restenosis (ISR). The regrowth of a healthy endothelial layer post-treatment, a key factor in successful vascular repair, has been shown to be affected by the high sensitivity of endothelial cells (EC) to shear stress. Characterisation of stented artery haemodynamics is required to understand the response of EC to complex flow and shear stress patterns induced by stent structure. A device for the in vitro study of coronary stents has been developed and fabricated in polydimethylsiloxane (PDMS). Balloon-mounted cobalt-chromium stents have been successfully deployed, and particle tracking has been employed to obtain streamlines under low flow rate. High-resolution flow-patterns can be imaged, and complemented with in silico analysis from μCT data. The device allows for the seeding of EC, and sustained exposure to shear stress. EC response can be investigated by comparing real-time footage of cellular migration and proliferation to the haemodynamics of the specific region

Microstructured Thin Film Nitinol for a Neurovascular Flow-Diverter

A cerebral aneurysm occurs as a result of a weakened blood vessel, which allows blood to flow into a sac or a ballooned section. Recent advancement shows that a new device, ‘flow-diverter’, can divert blood flow away from the aneurysm sac. People found that a flow-diverter based on thin film nitinol (TFN), works very effectively, however there are no studies proving the mechanical safety in irregular, curved blood vessels. Here, we study the mechanical behaviors and structural safety of a novel microstructured TFN membrane through the computational and experimental studies, which establish the fundamental aspects of stretching and bending mechanics of the structure. The result shows a hyper-elastic behavior of the TFN with a negligible strain change up to 180° in bending and over 500% in radial stretching, which is ideal in the use in neurovascular curved arteries. The simulation determines the optimal joint locations between the TFN and stent frame. In vitro experimental test qualitatively demonstrates the mechanical flexibility of the flow-diverter with multi-modal bending. In vivo micro X-ray and histopathology study demonstrate that the TFN can be conformally deployed in the curved blood vessel of a swine model without any significant complications or abnormalities

Computational modeling of hypertensive growth in the human carotid artery

The final publication is available at Springer via http://dx.doi.org/10.1007/s00466-013-0959-zArterial hypertension is a chronic medical condition associated with an elevated blood pressure. Chronic arterial hypertension initiates a series of events, which are known to collectively initiate arterial wall thickening. However, the correlation between macrostructural mechanical loading, microstructural cellular changes, and macrostructural adaptation remains unclear. Here, we present a microstructurally motivated computational model for chronic arterial hypertension through smooth muscle cell growth. To model growth, we adopt a classical concept based on the multiplicative decomposition of the deformation gradient into an elastic part and a growth part. Motivated by clinical observations, we assume that the driving force for growth is the stretch sensed by the smooth muscle cells. We embed our model into a finite element framework, where growth is stored locally as an internal variable. First, to demonstrate the features of our model, we investigate the effects of hypertensive growth in a real human carotid artery. Our results agree nicely with experimental data reported in the literature both qualitatively and quantitatively.Peer ReviewedPostprint (author's final draft

Replacing vascular corrosion casting by in-vivo micro-CT imaging for building 3D cardiovascular models in mice

The purpose of this study was to investigate if in vivo micro-computed tomography (CT) is a reliable alternative to micro-CT scanning of a vascular corrosion cast. This would allow one to study the early development of cardiovascular diseases. Datasets using both modalities were acquired, segmented, and used to generate a 3D geometrical model from nine mice. As blood pool contrast agent, Fenestra VC-131 was used. Batson's No. 17 was used as casting agent. Computational fluid dynamics simulations were performed on both datasets to quantify the difference in wall shear stress (WSS). Aortic arch diameters show 30% to 40% difference between the Fenestra VC-131 and the casted dataset. The aortic arch bifurcation angles show less than 20% difference between both datasets. Numerically computed WSS showed a 28% difference between both datasets. Our results indicate that in vivo micro-CT imaging can provide an excellent alternative for vascular corrosion casting. This enables follow-up studies

3D modelling of angiogenesis and vascular tumour growth

This paper was presented at the 3rd Micro and Nano Flows Conference (MNF2011), which was held at the Makedonia Palace Hotel, Thessaloniki in Greece. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, Aristotle University of Thessaloniki, University of Thessaly, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute

Computer simulation of glioma growth and morphology

Despite major advances in the study of glioma, the quantitative links between intra-tumor molecular/cellular properties, clinically observable properties such as morphology, and critical tumor behaviors such as growth and invasiveness remain unclear, hampering more effective coupling of tumor physical characteristics with implications for prognosis and therapy. Although molecular biology, histopathology, and radiological imaging are employed in this endeavor, studies are severely challenged by the multitude of different physical scales involved in tumor growth, i.e., from molecular nanoscale to cell microscale and finally to tissue centimeter scale. Consequently, it is often difficult to determine the underlying dynamics across dimensions. New techniques are needed to tackle these issues. Here, we address this multi-scalar problem by employing a novel predictive three-dimensional mathematical and computational model based on first-principle equations (conservation laws of physics) that describe mathematically the diffusion of cell substrates and other processes determining tumor mass growth and invasion. The model uses conserved variables to represent known determinants of glioma behavior, e.g., cell density and oxygen concentration, as well as biological functional relationships and parameters linking phenomena at different scales whose specific forms and values are hypothesized and calculated based on in vitro and in vivo experiments and from histopathology of tissue specimens from human gliomas. This model enables correlation of glioma morphology to tumor growth by quantifying interdependence of tumor mass on the microenvironment (e.g., hypoxia, tissue disruption) and on the cellular phenotypes (e.g., mitosis and apoptosis rates, cell adhesion strength). Once functional relationships between variables and associated parameter values have been informed, e.g., from histopathology or intra-operative analysis, this model can be used for disease diagnosis/prognosis, hypothesis testing, and to guide surgery and therapy. In particular, this tool identifies and quantifies the effects of vascularization and other cell-scale glioma morphological characteristics as predictors of tumor-scale growth and invasion