Mathematical modelling of flow through vascular networks: implications for tumour-induced angiogenesis and chemotherapy strategies

Angiogenesis, the formation of blood vessels from a pre-existing vasculature, is a process whereby capillary sprouts are formed in response to externally supplied chemical stimuli. The sprouts then grow and develop, driven initially by endothelial cell migration, and organize themselves into a branched, connected network structure. Subsequent cell proliferation near the sprout-tip permits further extension of the capillary and ultimately completes the process. Angiogenesis occurs during embryogenesis, wound healing, arthritis and during the growth of solid tumours. In this paper we initially generate theoretical capillary networks (which are morphologically similar to those networks observed in vivo) using the discrete mathematical model of Anderson and Chaplain. This discrete model describes the formation of a capillary sprout network via endothelial cell migratory and proliferative responses to external chemical stimuli (tumour angiogenic factors, TAF) supplied by a nearby solid tumour, and also the endothelial cell interactions with the extracellular matrix. The main aim of this paper is to extend this work to examine fluid flow through these theoretical network structures. In order to achieve this we make use of flow modelling tools and techniques (specifically, flow through interconnected networks) from the field of petroleum engineering. Having modelled the flow of a basic fluid through our network, we then examine the effects of fluid viscosity, blood vessel size (i.e., diameter of the capillaries), and network structure/geometry, upon: (i) the rate of flow through the network; (ii) the amount of fluid present in the complete network at any one time; and (iii) the amount of fluid reaching the tumour. The incorporation of fluid flow through the generated vascular networks has highlighted issues that may have major implications for the study of nutrient supply to the tumour (blood/oxygen supply) and, more importantly, for the delivery of chemotherapeutic drugs to the tumour. Indeed, there are also implications for the delivery of anti-angiogenesis drugs to the network itself. Results clearly highlight the important roles played by the structure and morphology of the network, which is, in turn, linked to the size and geometry of the nearby tumour. The connectedness of the network, as measured by the number of loops formed in the network (the anastomosis density), is also found to be of primary significance. Moreover, under certain conditions, the results of our flow simulations show that an injected chemotherapy drug may bypass the tumour altogether.     

Mathematical modelling of tissue-engineered angiogenesis

We present a mathematical model for the vascularisation of a porous scaffold following implantation in vivo. The model is given as a set of coupled non-linear ordinary differential equations (ODEs) which describe the evolution in time of the amounts of the different tissue constituents inside the scaffold. Bifurcation analyses reveal how the extent of scaffold vascularisation changes as a function of the parameter values. For example, it is shown how the loss of seeded cells arising from slow infiltration of vascular tissue can be overcome using a prevascularisation strategy consisting of seeding the scaffold with vascular cells. Using certain assumptions it is shown how the system can be simplified to one which is partially tractable and for which some analysis is given. Limited comparison is also given of the model solutions with experimental data from the chick chorioallantoic membrane (CAM) assay.     

Emerging insights into mitochondria-specific targeting and drug delivering strategies: Recent milestones and therapeutic implications

Mitochondria are a major intracellular organelle for drug targeting due to its functional roles in cellular metabolism and cell signaling for proliferation and cell death. Mitochondria-targeted treatment strategy could be promising to improve the therapeutic efficacy of cancer while minimizing the adverse side effects. Over the last decades, several studies have explored and focused on mitochondrial functions, which has led to the emergence of mitochondria-specific therapies. Molecules in the mitochondria are considered to be prime targets, and a wide range of molecular strategies have been designed for targeting mitochondria compared with that of the cytosol. In this review, we focused on the molecular mechanisms of mitochondria-specific ligand targeting and selective drug action strategies for targeting mitochondria, including those premised on mitochondrial targeting of signal peptides (MTS), cell-penetrating peptides (CPPs), and use of lipophilic cations. Furthermore, most research has concentrated on specific conjugation of ligands to therapeutic molecules to enhance their effectiveness. There are several variations for the ideal design and development for mitochondrial-targeted drugs, such as selecting a suitable ligand and linker targets. However, some challenges related to drug solubility and selectivity could be resolved using the nanocarrier system. Nanoparticles yield excellent advantages for targeting and transmitting therapeutic drugs, and they offer elegant platforms for mitochondria-specific drug delivery. We explain many of the advanced and proven strategies for multifunctional mitochondria-specific targets, which should contribute to achieving better anticancer therapies in a promising future.     

Mathematical modeling of the onset of capillary formation initiating angiogenesis

It is well accepted that neo-vascular formation can be divided into three main stages (which may be overlapping): (1) changes within the existing vessel, (2) formation of a new channel, (3) maturation of the new vessel. In this paper we present a new approach to angiogenesis, based on the theory of reinforced random walks, coupled with a Michaelis-Menten type mechanism which views the endothelial cell receptors as the catalyst for transforming angiogenic factor into proteolytic enzyme in order to model the first stage. In this model, a single layer of endothelial cells is separated by a vascular wall from an extracellular tissue matrix. A coupled system of ordinary and partial differential equations is derived which, in the presence of an angiogenic agent, predicts the aggregation of the endothelial cells and the collapse of the vascular lamina, opening a passage into the extracellular matrix. We refer to this as the onset of vascular sprouting. Some biological evidence for the correctness of our model is indicated by the formation of teats in utero. Further evidence for the correctness of the model is given by its prediction that endothelial cells will line the nascent capillary at the onset of capillary angiogenesis. Received: 27 May 1999 / Revised version: 28 December 1999 / Published online: 16 February 2001     

Macrophage regulation of tumor angiogenesis: implications for cancer therapy

This article reviews the evidence for macrophages playing an important role in the regulation of tumor angiogenesis. Findings in mouse models show that macrophages promote angiogenesis in tumors both by producing excessive amounts of proangiogenic factors and by physically assisting sprouting blood vessels to augment the complexity of the intra-tumoral vascular network. Recent studies however suggest that macrophages may be dispensable for the initiation of angiogenesis in tumors. Rather, these cells express proangiogenic programs that enhance the complexity of the tumor-associated vasculature, leading to aberrant, plethoric and dysfunctional angiogenesis. Gene expression and cell depletion studies further indicate that tumor-associated macrophages (TAMs) comprise phenotypically and functionally distinct subsets. This may reflect “education” of the macrophage phenotype by signals in some areas of the tumor microenvironment and/or TAM subsets derived from distinct macrophage precursors. Among the better characterized TAM subsets are the proangiogenic (TIE2⁺) and the angiostatic/inflammatory (CD11c⁺) macrophages, which coexist in tumors. Such antagonizing TAM subsets occupy distinct niches in the tumor microenvironment and are present at ratios that vary according to the tumor type and grade. Specifically targeting TAMs or reprogramming them from a proangiogenic to an angiostatic function may “normalize” the tumor vasculature and improve the efficacy of various anticancer therapies, including radiotherapy, chemotherapy and vascular-disrupting agents.     

Screening for therapeutic targets of tumor angiogenesis signatures in 31 cancer types and potential insights

Tumor vessel normalization can increase pericyte coverage, perfusion efficiency and immune infiltration, while reducing hypoxia, vessel leakage, CTC and metastasis. In this study, we systemically presented the expression pattern of tumor angiogenesis gene signatures in 31 cancer types and its association with immune infiltration and cancer metastasis. Specifically, READ, COAD etc. have relatively similar expression patterns with low GPAGs and high PPAGs. Patients with this expression pattern may benefit from tumor vessel normalization. COAD was selected for further investigation and we found GPAG CXCL12 was downregulated while PPAG EPHB3 was overexpressed in COAD, which were further validated using two independent colon cancer dataset. Further study indicated that CXCL12 expression was positively correlated innate inflammation pathways such as NFκB and negatively correlated with metastasis, while EPHB3 had a reverse result. Moreover, CXCL12 was positively correlated with cancer immune infiltration while EPHB3 was negatively correlated with cancer immune infiltration. Besides, the association between CXCL12/EPHB3 and mutation/CNA landscape were also explored. We also discussed the potential application of gut microbiota in cancer treatment. In summary, blood vessel normalization could promote immune infiltration and repress cancer metastasis while immune cell infiltration can promote blood vessel normalization through a positive feedback loop.     

Antimicrobial peptides: clinical relevance and therapeutic implications

Antimicrobial peptides (AMPs) are molecules that provide protection against environmental pathogens, acting against a large number of microorganisms, including bacteria, fungi, yeast, virus and others. Two major groups of antimicrobial peptides are found in humans: cathelicidins and defensins. Recently, several studies have furnished information that besides their role in infection diseases, antimicrobial peptides play a role in diseases as diverse as inflammatory disorders, autoimmunity and cancer. Here, we discuss the role of antimicrobial peptides and vitamin D have in such complex diseases and propose their use should be more explored in the diagnosis and treatment of such conditions.     

Dental stem cells: The role of biomaterials and scaffolds in developing novel therapeutic strategies

Dental stem cells(DSCs) are self-renewable cells that can be obtained easily from dental tissues, and are a desirable source of autologous stem cells. The use of DSCs for stem cell transplantation therapeutic approaches is attractive due to their simple isolation, high plasticity, immunomodulatory properties, and multipotential abilities. Using appropriate scaffolds loaded with favorable biomolecules, such as growth factors, and cytokines, can improve the proliferation, differentiation, migration, and functional capacity of DSCs and can optimize the cellular morphology to build tissue constructs for specific purposes. An enormous variety of scaffolds have been used for tissue engineering with DSCs. Of these, the scaffolds that particularly mimic tissue-specific micromilieu and loaded with biomolecules favorably regulate angiogenesis, cell-matrix interactions, degradation of extracellular matrix, organized matrix formation, and the mineralization abilities of DSCs in both in vitro and in vivo conditions. DSCs represent a promising cell source for tissue engineering, especially for tooth, bone, and neural tissue restoration. The purpose of the present review is to summarize the current developments in the major scaffolding approaches as crucial guidelines for tissue engineering using DSCs and compare their effects in tissue and organ regeneration.     

Xanthohumol-supplemented beer modulates angiogenesis and inflammation in a skin wound healing model. Involvement of local adipocytes

Angiogenesis and inflammation are two intermingled processes that play a role in wound healing. Nevertheless, whenever exacerbated, these processes result in nonhealing wounds. Xanthohumol (XN), a beer‐derived polyphenol, inhibits these processes in many physiopathological situations. This study aimed at examining whether XN ingestion affects wound healing. Wistar rats drinking water, 5% ethanol, stout beer (SB) or stout beer supplemented with 10 mg/L XN (Suppl SB) for 4 weeks, were subjected to a 1.5 cm full skin‐thickness longitudinal incision, and further maintained under the same beverage conditions for another week. No differences in beverage consumption or body weight were found throughout the study but food intake decreased in every group relative to controls. Consumption of Suppl SB resulted in decreased serum VEGF levels (18.42%), N‐acetylglucosaminidase activity (27.77%), IL1β concentration (9.07%), and NO released (77.06%), accompanied by a reduced redox state as observed by increased GSH/GSSG ratio (to 198.80%). Also, the number of blood vessels within the wound granulation tissue seems to reduce in animals drinking Suppl SB (23.08%). Interestingly, SB and primarily Suppl SB showed a tendency to increase adipocyte number (to 194.26% and 156.68%, respectively) and reduce adipocyte size (4.60% and 24.64%, respectively) within the granuloma. Liver function and metabolism did not change among the animal groups as analyzed by plasma biochemical parameters, indicating no beverage toxicity. This study shows that XN intake in its natural beer context reduced inflammation, oxidative stress, and angiogenesis, ameliorating the wound healing process, suggesting that this polyphenol may exert beneficial effect as a nutritional supplement. J. Cell. Biochem. 113: 100–109, 2012. © 2011 Wiley Periodicals, Inc.     

Coupled modelling of tumour angiogenesis, tumour growth and blood perfusion

We propose a mathematical modelling system to investigate the dynamic process of tumour cell proliferation, death and tumour angiogenesis by fully coupling the vessel growth, tumour growth and blood perfusion. Tumour growth and angiogenesis are coupled by the chemical microenvironment and the cell-matrix interaction. The haemodynamic calculation is carried out on the updated vasculature. The domains of intravascular, transcapillary and interstitial fluid flow were coupled in the model to provide a comprehensive solution of blood perfusion variables. An estimation of vessel collapse is made according to the wall shear stress criterion to provide feedback on vasculature remodelling. The simulation can show the process of tumour angiogenesis and the spatial distribution of tumour cells for periods of up to 24 days. It can show the major features of tumour and tumour microvasculature during the period such as the formation of a large necrotic core in the tumour centre with few functional vessels passing through, and a well circulated tumour periphery regions in which the microvascular density is high and associated with more aggressive proliferating cells of the growing tumour which are all consistent with physiological observations. The study also demonstrated that the simulation results are not dependent on the initial tumour and networks, which further confirms the application of the coupled model feedback mechanisms. The model enables us to examine the interactions between angiogenesis and tumour growth, and to study the dynamic response of a solid tumour to the changes in the microenvironment. This simulation framework can be a foundation for further applications such as drug delivery and anti-angiogenic therapies.     

Gene control of synaptic plasticity and memory formation: implications for diseases and therapeutic strategies

There has been nearly a century of interest in the idea that information is stored in the brain as changes in the efficacy of synaptic connections between neurons that are activated during learning. The discovery and detailed report of the phenomenon generally known as long-term potentiation opened a new chapter in the study of synaptic plasticity in the vertebrate brain, and this form of synaptic plasticity has now become the dominant model in the search for the cellular and molecular bases of learning and memory. Accumulating evidence suggests that the rapid activation of the genetic machinery is a key mechanism underlying the enduring modification of neural networks required for the laying down of memory. Here we briefly review these mechanisms and illustrate with a few examples of animal models of neurological disorders how new knowledge about these mechanisms can provide valuable insights into identifying the mechanisms that go awry when memory is deficient, and how, in turn, characterisation of the dysfunctional mechanisms offers prospects to design and evaluate molecular and biobehavioural strategies for therapeutic prevention and rescue.     

Different priming strategies improve distinct therapeutic capabilities of mesenchymal stromal/stem cells: Potential implications for their clinical use

Mesenchymal stromal/stem cells (MSCs) have shown significant therapeutic potential, and have therefore been extensively investigated in preclinical studies of regenerative medicine. However, while MSCs have been shown to be safe as a cellular treatment, they have usually been therapeutically ineffective in human diseases. In fact, in many clinical trials it has been shown that MSCs have moderate or poor efficacy. This inefficacy appears to be ascribable primarily to the heterogeneity of MSCs. Recently, specific priming strategies have been used to improve the therapeutic properties of MSCs. In this review, we explore the literature on the principal priming approaches used to enhance the preclinical inefficacy of MSCs. We found that different priming strategies have been used to direct the therapeutic effects of MSCs toward specific pathological processes. Particularly, while hypoxic priming can be used primarily for the treatment of acute diseases, inflammatory cytokines can be used mainly to prime MSCs in order to treat chronic immune-related disorders. The shift in approach from regeneration to inflammation implies, in MSCs, a shift in the production of functional factors that stimulate regenerative or anti-inflammatory pathways. The opportunity to fine-tune the therapeutic properties of MSCs through different priming strategies could conceivably pave the way for optimizing their therapeutic potential.     

miR-376a inhibits glioma proliferation and angiogenesis by regulating YAP1/VEGF signalling via targeting of SIRT1

BackgroundGlioma is the most common cancer in the central nervous system. Previous studies have revealed that the miR-376 family is crucial in tumour development; however, its detailed mechanism in glioma is not clear.MethodsCellular mRNA or protein levels of miR-376a, SIRT1, VEGF and YAP1 were detected via qRT–PCR or Western blotting. We analysed the proliferation, angiogenesis and migration abilities of glioma cell lines using colony formation, tube formation and Transwell assays. A luciferase assay was performed to determine whether miR-376a could recognize SIRT1 mRNA. Xenograft experiments were performed to analyse the tumorigenesis capacity of glioma cell lines in nude mice. The angiogenesis marker CD31 in xenograft tumours was detected via immunohistochemistry (IHC).ResultsmiR-376a expression was lower in glioma cells than in normal astrocytes. miR-376a mimic inhibited SIRT1, YAP1, and VEGF expression and suppressed the proliferation, migration and angiogenesis abilities of the glioma cell lines LN229 and A172, whereas miR-376a inhibitor exerted the opposite functions. In a luciferase assay, miR-376a inhibited the luciferase activity of WT-SIRT1. SIRT1 overexpression upregulated YAP1 and VEGF in glioma cells and promoted proliferation, migration and angiogenesis. Xenografts with ectopic miR-376a expression exhibited lower volumes and weights and a slower growth curve. Overexpression of miR-376a inhibited YAP1/VEGF signalling and angiogenesis by inhibiting SIRT1 in xenograft tissues.ConclusionmiR-376a directly targets and inhibits SIRT1 in glioma cells. Downregulation of SIRT1 resulted in decreased YAP1 and VEGF signalling, which led to suppression of glioma cell proliferation, migration and angiogenesis.     

No influence of tumor growth by intramuscular injection of hepatocyte growth factor plasmid DNA: safety evaluation of therapeutic angiogenesis gene therapy in mice

Recently, a novel therapeutic treatment for ischemic diseases using angiogenic growth factors to augment collateral artery development has been proposed. As intramuscular injection of naked human hepatocyte growth factor (HGF) plasmid DNA induced therapeutic angiogenesis in several animal test subjects, we have started a clinical trial to treat peripheral arterial disease. However, one might assume that over-expression of angiogenic growth factors could enhance tumor growth. To resolve this issue, we examined the over-expression of HGF in tumor bearing mice. Tumors on their backs were prepared with an intradermal inoculation of A431, human epidermoid cancer cells expressing c-Met. These mice were intramuscularly injected with human HGF plasmid or control plasmid into the femoral muscle. Human HGF concentration was increased only in the femoral muscle, but not in blood. Although recombinant HGF stimulated the growth of A431 cells in vitro, temporally and locally HGF elevation in hindlimb had no effect on tumor growth in mice.     

Tumor-associated macrophages: Effectors of angiogenesis and tumor progression

Tumor-associated macrophages (TAMs) are a prominent inflammatory cell population in many tumor types residing in both perivascular and avascular, hypoxic regions of these tissues. Analysis of TAMs in human tumor biopsies has shown that they express a variety of tumor-promoting factors and evidence from transgenic murine tumor models has provided unequivocal evidence for the importance of these cells in driving angiogenesis, lymphangiogenesis, immunosuppression, and metastasis. This review will summarize the mechanisms by which monocytes are recruited into tumors, their myriad, tumor-promoting functions within tumors, and the influence of the tumor microenvironment in driving these activities. We also discuss recent attempts to both target/destroy TAMs and exploit them as delivery vehicles for anti-cancer gene therapy.     

Impacts of climate change on the vegetation of Africa: an adaptive dynamic vegetation modelling approach

Recent IPCC projections suggest that Africa will be subject to particularly severe changes in atmospheric conditions. How the vegetation of Africa and particularly the grassland–savanna–forest complex will respond to these changes has rarely been investigated. Most studies on global carbon cycles use vegetation models that do not adequately account for the complexity of the interactions that shape the distribution of tropical grasslands, savannas and forests. This casts doubt on their ability to reliably simulate the future vegetation of Africa. We present a new vegetation model, the adaptive dynamic global vegetation model (aDGVM) that was specifically developed for tropical vegetation. The aDGVM combines established components from existing DGVMs with novel process‐based and adaptive modules for phenology, carbon allocation and fire within an individual‐based framework. Thus, the model allows vegetation to adapt phenology, allocation and physiology to changing environmental conditions and disturbances in a way not possible in models based on fixed functional types. We used the model to simulate the current vegetation patterns of Africa and found good agreement between model projections and vegetation maps. We simulated vegetation in absence of fire and found that fire suppression strongly influences tree dominance at the regional scale while at a continental scale fire suppression increases biomass in vegetation by a more modest 13%. Simulations under elevated temperature and atmospheric CO₂ concentrations predicted longer growing periods, higher allocation to roots, higher fecundity, more biomass and a dramatic shift toward tree dominated biomes. Our analyses suggest that the CO₂ fertilization effect is not saturated at ambient CO₂ levels and will strongly increase in response to further increases in CO₂ levels. The model provides a general and flexible framework for describing vegetation response to the interactive effects of climate and disturbances.     

Consequential and attributional environmental assessment of biofuels: implications of modelling choices on climate change mitigation strategies

Purpose

The study aims to assess climate change mitigation potentials when using biomass-based fuels to replace fossil energy under consequential and attributional modelling approaches. The objectives are also to determine policy implications and to recommend the specific contexts suitable for each modelling choice by using specific illustrative cases on biofuels.

Methods

Consequential and attributional modelling approaches are chosen for life cycle greenhouse gas emission assessment of several bioenergy options. The assessed functional unit is 1 MJ of energy from molasses-based ethanol, palm-based biodiesel and electricity production from rice straw. The fossil fuel comparators are gasoline (for molasses-based ethanol), diesel (for palm-based biodiesel) and coal and gas (for rice straw). The substituted and substituting product systems are modelled under the global and national markets depending on the market delimitation of each product.

Results and discussion

The climate change mitigation potentials when using different approaches are dissimilar, because the affected product systems being included in the analysis are not the same. The palm biodiesel could reduce greenhouse gas emissions. The molasses-based ethanol and rice straw-based electricity may or may not mitigate the climate change, since it depends on the methodological choices as well as the baseline situations of the product systems being investigated. The main characteristics of consequential modelling as additionality and the inclusion of only actually affected processes under market-based mechanisms while those of attributional modelling as specification and attribution/allocation have limitations. The limitations lead to potential risks on unintended and undesirable consequences (for the attributional model), unfairness and sub-optimisation (for the consequential model) in policy recommendations.

Conclusions

This research clearly illustrates how certain modelling choices affect the climate change mitigation potentials of biomass-based fuels in comparison with fossil energy. Specific questions and conditions which could be more suitable for each modelling choice are addressed. The attributional modelling is more suitable for national environmental taxation and emission labelling/accounting for import-export, while the consequential modelling is more appropriate for new production development and eco-design. Due to the potential environmental risks arising from the modelling limitations, the consideration of both the widely applied approaches could support decisions more comprehensively.