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Computational and Mathematical Methods in Medicine,Vol. 8, No. 1, March 2007, 1–9
CHRISTOPHER A. HONSTVET† and PAMELA F. JONES‡*
†School of Medicine, University of Leeds, Worsley Building, Clarendon Way, Leeds LS2 9NL, UK
‡Leeds Institute of Molecular Medicine, St James’s University Hospital, Wellcome Trust Brenner Building, Leeds
(Received 21 February 2007; in final form 22 February 2007)
Modelling blood flow and capillary growth in tumours has been the focus of several researchgroups with the aim of generating theoretical models that can be used to predict biologicalbehaviour within these systems. Since dysfunctional angiogenesis is seen in a wide range ofpathological conditions ranging from cardiovascular, to arthritis, to diabetes, it is easy to seehow these models may have a far-reaching influence on future therapeutic strategies.
One major area of anti-cancer treatment is the targeting of the tumour blood vessels.
Paradoxically, different approaches taken in angiogenic therapy have different aims.
Prevention of new vessel growth, or disruption of existing vessels, are both aimed atpreventing sufficient oxygen and nutrients to reach the tumour. However, since drug deliveryto tumours is often very poor, due to the disorganised architecture of the tumour vessels, onesuggested strategy is to improve circulation within a tumour through “normalisation” of thevasculature which results in more effective anti-tumour drug delivery.
There are currently no theoretical models of vessel regression or vascular disruption even
though both are actively targeted by tumour therapies. This article will give an overview ofthe different mechanisms targeted by different anti-angiogenic strategies and highlight areasthat may benefit from the development of predictive theoretical models.
Keywords: Angiogenesis; Anti-angiogenesis; Vessel regression; Vascular disrupting agents;Mathematical modelling
Cancer is a leading cause of death worldwide and it is solid tumours that account for over85% of cancer mortality . For solid tumours to grow and metastasise they must be suppliedwith oxygen and nutrients as well as having an efficient means to remove waste products,and this is achieved through the growth of new blood vessels into the tumour . Thedevelopment of new blood vessels from an existing vasculature is termed angiogenesis and isnormally a highly regulated process. Blood vessels have a continual lining with vascularendothelial cells which in the adult are normally kept quiescent though a controlled balancebetween pro-angiogenic and anti-angiogenic factors (see table 1 and figure 1). However,under certain conditions they can be stimulated to divide through a shift in the balancebetween these factors, leading to the formation of new vasculature. This angiogenic processhas been reviewed elsewhere [3 – 5] and will not be discussed in detail here.
*Corresponding author. Email: firstname.lastname@example.org
Computational and Mathematical Methods in Medicine
ISSN 1748-670X print/ISSN 1748-6718 online q
2007 Taylor & Francis
A few of the known pro-angiogenic factors.
Family of endothelial-specific extracellular ligands that exert robust
angiogenic responses via transmembrane receptor tyrosinekinases, VEGFRs
Family of endothelial-specific extracellular ligands that play subtle
roles in the regulation of angiogenesis via the transmembranereceptor tyrosine kinase. Tie2. Ang-1 acts as maturation/stabilisation factor, where its antagonist, Ang2 can exert eitherinhibitory or pro-angiogenic effect
Family of extracellular ligands that exert induce responses via
transmembrane receptor tyrosine kinases, FGFRs. Not specific
for endothelial cells, but can have strong angiogenic effects.
Receptors found widely across many cell types
Family of extracellular growth factors that act via specfic
transmembrane receptors, the PDGFRs. Plays a role in pericyte
recruitment during capillary growth and maturation
Extracellular ligand bound by specific transmembrane receptor. Not
specific for endothelial cells but evokes strong angiogenic response
Causes pro-angiogenic response through upregulation of endothelial
adhesion molecules as well as induction of VEGF expression
There are over 20 factors identified to date, that have been shown to confer some degree of pro-angiogenic activity in vivo or in vitro.
Some have activities that are specific to endothelial cells; others have a broader range of target cells.
In adults angiogenesis is normally suppressed but becomes active when a tumour starts to
grow. This is known as the angiogenic switch and occurs when a tumour switches to apro-angiogenic phenotype, through an alteration in the balance between pro- and anti-angiogenic factors (figure 1), so inducing the growth of new blood vessels. Factors mostcommonly increased are vascular endothelial growth factor (VEGF) and basic fibroblastgrowth factor (bFGF), that can both induce a robust angiogenic response.
Folkman first proposed that this dependency on vasculature renders tumours susceptible to
anti-angiogenic targeting more than three decades ago . Since then, much time, effort and
The Angiogenic Balance. In the normal adult, angiogenesis is kept quiescent though the expression of
angiogenic inhibitors. In the tumour, the expression of pro-angiogenic factors is increased, while the expression ofangiogenic inhibitors is decreased, resulting in a shift towards the pro-angiogenic state.
Some of the drugs currently in development that aim to target the different components of the angiogenesis
Monoclonal antibody against VEGF. Blocks VEGF binding to receptor
A non-steroidal anti-inflammatory drug (NSAID) that inhibits COX-2, a mediator of VEGF
Synthetic inhibitor of matrix metalloproteinases (MMPs)
A cleavage product of plasminogen, part pof the clotting cascade. Blocks ATP synthase
N-terminal fragment of collagen. Interferes with the actions of bFGF and VEGF
money have been spent on related research and the development of anti-angiogenic therapies,although effective drugs are only now beginning to appear in clinical use. Of the few anti-angiogenic drugs that have so far been approved for use, Bevacizumab (also known asAvastin) as a treatment for colorectal cancer is the most effective [6,7] but many others areshowing success in phases II and III clinical trials (Cancer Research UK 2007)†‡. Inparticular angiogenesis inhibitors seem to be useful in stunting the growth of solid tumoursbefore they have become very large and therefore prevent metastasis . However, theiraction is not suitable for large tumours that have already metastasised. Thus, compounds thatdirectly attack and destroy tumour vasculature vascular disrupting agents (VDAs) are beingresearched as another possible cancer treatment, and again early indications are showingimpressive shutdown of blood supply to tumours resulting in tumour necrosis .
It is clear that angiogenesis inhibitors and VDAs will become increasingly prescribed as
cancer treatments. Thus, an understanding of their action and the assessment of laboratoryand clinical results is important. Also of great interest are possible combination treatmentregimes involving both types of vascular-targeted agents with each other or with traditionalcancer treatments (chemotherapy and radiotherapy). Having assessed the information, futureareas of research and treatment possibilities can be identified.
2. Anti-angiogenic compounds (angiogenesis inhibitors)
Tumour angiogenesis is the result of a complex series of interactions between vascularendothelial cells and various growth factors and other naturally occurring chemicals. It hasbeen shown that without neovasculature a tumour cannot expand past a critical mass .
Thus, targeting angiogenesis to stop tumour growth and metastasis should be a viable cancertherapy. As angiogenesis is such a multi-step process there are many targets where drugs mayexert their effects. Studies have identified a number of possible approaches to targeting anti-angiogenic therapies, which are outlined in table 2.
The inhibition of VEGF has shown the most success in the treatment of cancer by targeting
angiogenesis. Bevacizumab is the only anti-angiogenic treatment currently available: it is arecombinant humanised monoclonal antibody to VEGF  and blocks the VEGF receptorso preventing vascular endothelial cells responding to the angiogenic switch (figure 2).
Success in recent trials in colorectal cancer mean the treatment may soon be available forother types of cancer, and results from breast cancer patients show significant increases in
Mode of Action of VEGF Inhibitors VEGF, a soluble extracellular ligand, (A) binds to a specific
transmembrane receptor tyrosine kinase (B). Bound VEGFR then forms a dimer with another ligand-bound receptor(C), which brings the two cytoplasmic kinase domains close enough to allow cross-phosphorylation(autophosphorylation) and hence activation of both receptors. This activates the subsequent signalling cascadeswhich results in endothelial cell proliferation, migration and differentiation leading to the formation of newcapillaries which sprout towards the angiogenic source (the tumour). Inhibition of VEGF signalling can occur bybinding of an inhibitor to the ligand binding site (D), which then prevents VEGF binding to its receptor.
Alternatively, binding of an antibody, e.g. Bevacizumab, to an epitope in or close to the ligand binding site (E)prevents VEGF binding. In either case, downstream signalling is not activated and hence angiogenesis is not induced.
progression free survival as well as overall survival . Other trials however, have indicatedthat Bevacizumab has little therapeutic value for breast cancer in its later stages .
Prostaglandins play an important role in angiogenesis. In vivo and in vitro tests have
revealed that prostaglandins can induce several growth factors and therefore proliferationof vascular endothelial cells through the stimulation of VEGF [14,15]. Prostaglandinproduction is regulated by COX-2 and studies have shown COX-2 over-expression ismarkedly increased in 85 – 90% of human colorectal carcinoma , as well as in othercancers. Further studies show that patients with elevated COX-2 levels have a poorerprognosis compared to those with low COX-2 levels. Drugs that inhibit COX-2 will thereforeinhibit angiogenesis. Thalidomide is an old drug with a poor reputation but recent studieshave indicated that it suppresses the LPS-mediated induction of COX-2 . As a result, ithas begun to be tested on cancers as a potential anti-angiogenic therapy. So far phase IIclinical trial results have been disappointing. In heavily treated breast cancer a 100 mg dosehad no therapeutic effect but there were marked increases in the patients quality of life .
Ref.  also showed that thalidomide had no effects. However, these trials were basedon patients with cancer that had already been treated and the treatment had failed. Anti-angiogenesis therapy should theoretically be targeted at small tumours before metastasis andso thalidomide is still a potential treatment option.
More recently a novel alternative hypothesis has been presented that predicts that the aim
of treating tumours by targeting angiogenesis should be to normalize tumour vasculature asopposed to destroying it. While current anti-angiogenesis therapies can slow the growth
of tumours they cannot destroy them completely and thus the possibility of remission is high.
Jain suggests that tumour vasculature is highly irregular resulting from the angiogenicimbalance (figure 1). These irregular blood vessels follow tortuous routes that do not supplythe entire growing tumour. The resultant hypoxia of some regions means that conventionaltherapies are not effective and the cancer persists. Normalizing the vasculature by restoringthe angiogenic balance—possibly through the inhibition of VEGF—may result in moresuccessful delivery and action of conventional cancer treatments .
VDAs are low weight molecules that directly attack the blood vessels supplying a tumourresulting in reduction of blood flow and therefore rapid and pronounced tumour necrosis .
One of the most important features of VDAs is that they are selective for the tumour—a drugthat simply attacked all vessels would be disastrous. Tumour vasculature differs in many waysfrom normal vasculature and it is this difference that allows VDAs to exert their actions solelyon tumours . Table 3 summarises some of these differences and how they might be targeted.
The main benefit of VDAs over angiogenesis inhibitors is that they can be effective in fairlyadvanced cancer where solid tumours are large and there are many sites of metastasis.
Combretastatin A-4 phosphate (CA-4-P) is one of the most promising VDAs. It appears to
induce apoptosis in some tumour vascular endothelial cells but the exact mode of action isundefined. It is believed that CA-4-P brings about morphological changes in vessels such as cellretraction, membrane blebbing and the formation of actin stress fibres . Ultimately, all thesechanges result in an increase in vascular permeability thus inducing ischaemia and interstitialtumour pressure and thus the shutdown of blood supply. The morphological changes can alsoresult in the blocking off of blood vessels and haemorrhagic necrosis of the tumour results .
Clinical trials of CA-4-P type drugs are showing promising results. Studies in mice have
shown significant tumour growth delays although tumour growth eventually reached normallevels. Further studies with different doses of CA-4-P showed a 100-fold decrease in blood flowto solid tumours with no significant blood flow loss to the brain and other vital organs . Datafrom early clinical trials are encouraging , showing significant reduction in tumour bloodflow in 3 out of 4 cases, and in one case even a complete response with the patient remaining
Differences between tumour and normal vasculature.
Areas of hypoxia due to Irregular oxygen delivery across
Possibly surface markers unique to tumour endothelium
Targeting disruption of tubulin structures
There are several differences between tumour and normal vasculature that may be potential targets for intervention.
disease free after 33 months . One drawback of such treatment is that long drug exposuretimes are required . As a result there are more possible side effects and more chance ofnormal vasculature being affected. Side effects have included severe tumour pain, dyspnoeaand hypertension. However, most side effects have been controlled with minimal medicalintervention except where pre existing conditions were worsened, such as hypertension.
The tubulin cytoskeleton of vessels is another target for VDAs. By preventing the proper
formation of the cytoskeleton, vessels become more permeable and thus perfuse tumours lesseffectively. ZD6126 is one such agent that is showing success in laboratory trials and intumour models . Excitingly, tumour perfusion was reduced by 70% in just three hours butthe vasculature repaired itself in just 6 hours, again indicating that long drug exposure timesare required. One explanation of this refers back to the angiogenic switch. Hypoxia seems toinduce the pro-angiogenic state. If blood vessels are destroyed rapidly the resulting hypoxiawill strongly select for the pro-angiogenic phenotype. By maintaining a dosage of VDAs anynew vasculature will be destroyed and thus tumour necrosis will occur. Once the tumour isdestroyed there will be no hypoxia and thus no initiation of the pro-angiogenic phenotype.
Another problem encountered when testing VDAs has been a persistent outer ring of
tumour left despite continuing treatment . One explanation of this is that outer tumourcells recruit normal vasculature to supply their needs. As the vasculature is normal the dosesof VDAs being used do not produce any disruptive effects. The vessels are too organised andtoo strong to be broken down by drugs aimed at destroying already weakened vessels.
Unfortunately metastasis can result from these surrounding tumour cells breaking off andmigrating through the blood vessels to other sites. This could provide an explanation as towhy VDAs and anti-angiogenic therapies prevent the growth of tumours but fail to preventthe ultimate spread and mortality of cancer.
While the theoretical basis behind vascular targeted therapy is exciting, clinical results havebeen disappointing, with the early trials showing only limited success as a stand-alonetreatment for cancer. Conventional therapies (chemotherapy and radiotherapy) also havetheir limitations, but targeting vasculature as well as the tumour cells themselves mayproduce a much more toxic environment for cancers and hence combinations of differenttherapies may have greater success.
Combining more then one anti-angiogenic agent is perhaps one way of improving their
effectiveness. There are many regulatory factors involved in angiogenesis and so by targetingseveral different parts of the mechanism more positive effects may be seen. Recent studieshave combined three new angiogenesis inhibitors—marmistat, captopril and fragmin[19,21]. One study investigated the effect these agents had on the release of tumour necrosisfactor alpha (TNFa)—a known pro-angiogenic factor on patients with renal cancer. Cancercells taken from individual patients were stimulated to overproduce TNFa and then treatedwith the cocktail of angiogenesis inhibitors. The patient response was good with manyshowing some improvement or a stabilisation of the cancer. The results were linked to lowerlevels of TNFa in tumour samples . However, this triple combination therapy showed noeffect on plasma levels of VEGF . Furthermore, the cancer still persisted in all patients,which still indicates the limited potential of anti-angiogenic therapy as a treatment by itself.
The idea of combining angiogenesis inhibitors with traditional chemotherapy and
radiotherapy is the next logical step in the progression of vascular targeted cancer agents.
The lack of side effects of anti-angiogenic drugs also makes the combination appealing ascurrent therapies have such dramatic side effects (NCI 2005). Bevacizumab has been licensedfor use only in combination with chemotherapy and radiotherapy. The failure of the targetedaction of chemotherapy and radiotherapy is that tumour cells are able to migrate away fromthe site of action and escape the treatment along new blood vessels formed by angiogenesis.
When VEGF and other pro-angiogenic factors are inhibited new blood vessels are not able toform. Cancer cells are therefore unable to escape from the targeted traditional therapies andso the combination therapy has been shown to have potent anti-tumour effects .
Conventional therapies are often limited by the abnormal vasculature of tumours. There
are often patches within the tumour that are poorly perfused and only just manage to survivethe resulting ischaemia. These areas cannot be targeted by chemotherapy as the drugs haveno means of accessing the area. Similarly radiotherapy is less effective as oxygen levels inthe tumour are low. By using slightly smaller doses of angiogenesis inhibitors it is possiblefor the pro-angiogenic state to remain but vessels will be constructed in a more normal way.
As a result tumour cells are more efficiently perfused and chemotherapy and radiotherapy aremore effective .
It is important to look at combination therapy with angiogenesis inhibitors and
conventional therapies from a negative angle as well. Chemotherapy is limited by poor bloodsupply to the tumour and anti-angiogenesis therapy worsens this blood supply. The newdrugs are not effective enough to completely remove all vasculature and so some tumourcells remain but with relatively poor blood supply thus preventing chemotherapy orradiotherapy from working. This is especially the case in later stage tumours that are largeand have an already fairly established vasculature.
Although some positive clinical trial results have been seen from VDAs the persistent ring
of tumour cells that results after treatment prevents it from being an effective cancertreatment. However, by combining VDAs with other therapies the persistent outer ring maybe able to be destroyed. The outer ring is supplied by a normal vasculature that supplies itwith an efficient blood supply. Thus, chemotherapy agents will be efficiently transported andtransfused into the perimeter cancer cells hopefully resulting in tumour necrosis . In thisway a complete destruction of solid tumours may be possible.
Anti-angiogenesis therapy was first proposed in the 1970s and yet few treatments areavailable to cancer sufferers. Early laboratory work with animals and tumour models showedvery exciting results but these have failed to translate in the clinical setting. The question iswhy. Many of the clinical trials have recruited patients with end stage cancer, which is toolate to target effectively new vessel growth. At this stage the vasculature of a tumour isalready advanced and the best that angiogenesis inhibitors can hope to achieve is to preventfurther growth of the tumour. However, after a while tumour cells seem to continue to growdespite treatment. This could be a result of the complexity of the mechanism ofangiogenesis—if one way is blocked perhaps other methods of vessel growth areup-regulated and new vasculature appears. To assess effectively the possible targets of suchdrugs, trials must be carried out in patients in an early stage of cancer. It is at this stage thattheoretically such treatments will have most success. VDAs are a more recent and perhapsmore promising development based on a concept of targeting and destroying existing tumourvasculature that is viable for use at all stages of cancer.
The possibility of developing predictive mathematical/theoretical models of vascular
disruption and regression offers an exciting alternative to often long-winded and expensiveexperimental and clinical protocols. Combination therapies—vascular targeting combinedwith traditional therapies—need optimising and timing schedules have to be fine-tuned toprovide the most effective treatment for the specific cancer. Experimentally, this takes time andresources. The development of theoretical models, which can both reflect pathological casesand predict treatment outcomes, would have a significant impact in this therapeutic area. Suchmodels could be used to predict the most efficacious combinations of specific targeting agentswith specific chemotherapy, which would then be used as first choice in validation studies.
Similarly, delivery regimes—schedules as well as site of delivery—could be determined usingtheoretical models with the most effective being taken further in the clinical setting.
Although mathematical models exist to study capillary sprouting and growth, as well as
blood flow across tumours, little, if any, attention has been paid to modelling either regressionor disruption of existing blood vessels. Given that clinical diagnosis can only occur when atumour has progressed well beyond the stage at which a blood supply is needed, targetingexisting tumour vasculature is a more viable treatment option than prevention of the initialblood vessel growth. Modelling vascular regression and disruption has the potential to influencetreatment strategies, and hence has huge impact on the clinical management of cancer.
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