Effects of a new anti-tumour drug, fibrinogen E-fragment, in vivo: differential effects on the outer versus the inner areas of tumours

A problem presented at the UK MMSG Nottingham 2000.

Presented by:
Prof Claire Lewis (Medical School, University of Sheffield)
Participants:
J Billingham, CJW Breward, H Byrne, SJ Chapman, E Clark, D Gammack, PD Howell, A King, JR King, P Kramer, C Lewis, J Norbury, M Owen, C Please, MJ Tindall, JAD Wattis, D Wilson

Problem Description

Angiogenesis, the development of new blood vessels from the existing vasculature, is a complex process involving degradation of the matrix round each vessel and then the migration, proliferation and differentiation (rounding up) of endothelial cells to form new vessels. These steps usually occur in response to increased production by local cells of such pro-angiogenic cytokines as VEGF or bFGF (which bind to specific receptors on endothelial cells to activate them). The finding that angiogenesis is critical to the growth of tumours beyond about 2mm3 in size (as well as the progression of such diseases as rheumatoid arthritis, psoriasis and blindness in diabetes) has prompted the widespread hunt for angiogenesis inhibitors. This new class of drug has to be specific for growing blood vessels engaged in angiogenesis, and leave quiescent blood vessels in healthy tissues unaffected. We have developed such a drug: a fragment of the naturally-occurring protein, fibrinogen.

Fibrinogen is a key component of the clotting cascade and can be cleaved into various fragments in vivo by the enzymes thrombin and plasmin. Our results show that a 50kDa polypeptide formed by plasmin cleavage of fibrinogen called fibrinogen E-fragment (FgnE) markedly reduces vascular endothelial growth factor (VEGF) and basic fibroblast growth factor (bFGF) -stimulated migration and differentiation of HuDMECs in vitro. By contrast FgnE had virtually no effect on HuDMECs in the absence of VEGF or bFGF.

FgnE had potent anti-angiogenic effects in vivo in a murine tumour model. Daily injections of FgnE into tumour-bearing mice for 10 days markedly suppressed tumour growth compared to PBS-injected control animals. It also resulted in widespread damage to endothelial cells lining blood vessels, intravascular thrombosis (ie massive clotting in the vessels) and tumour cell necrosis at the centre of the tumours. No such effects were seen at the edge of the tumours (or in the lungs, liver or kidneys) of FgnE-treated mice, suggesting that these anti-angiogenic effects of FgnE were restricted to blood vessels in tumours. The effect at the centre of the tumour was sufficient to cause a reduction in tumour volume over 10 days of treatment as the blood vessels were occluded and the tumour cells around these vessels were starved of nutrients and died. Macrophages then entered these necrotic areas and phagocytosed/removed the cell debris.

However, for the drug to be fully effective in the treatment of human tumours, we need to find out why the blood vessels at the edge of the tumour did not appear to be adversely affected by the drug. There is no evidence, to date, that these outer blood vessels are non-angiogenic (ie quiescent, like blood vessels in healthy tissues) or that they carry blood any less effectively than vessels in the centre of the tumour (so the blood-borne drug should be able to get to/act on all the blood vessels equally within the tumour). We would like to ask the mathematicians present at the study group to help us to look at the possible influence of various putative difference in the outer and inner architecture of tumours on drug access to the vessel surface and anti-angiogenic efficacy in vivo.

Study Group Report

We formulated a model for the mass fractions of dead material, functioning blood vessels and live tumour cells. Our model consisted of three conservation of mass equations (including advection), a condition indicating that our three phases filled space, and a Darcy law relating the speed of motion to the pressure field. We did not explicitly track the oxygen tension, rather, we assumed that it was proportional to the local mass fraction of blood vessels. We assumed that the blood vessels became collapsed if the local pressure exceeded a critical threshold. We imposed conditions of symmetry at the centre of the tumour, and assumed continuity of pressure at the leading edge.

We looked at the limit of our model in which the flow was slow compared to the proliferation timescale, and in which the blood vessel proliferation timescale was small compared to that for tumour cell proliferation. We sought a solution with the spatial structure observed experimentally ( i.e. a central area of dead matter, and an outer proliferating region), and were able to find that the radius of such a tumour grew linearly with time, at least for tumours with large radii. We presented a numerical simulation in such a parameter regime, which highlighted some limitations of the model.

We modified our model to include the effects of FgnE. We assumed that the drug caused some of the blood vessels to be born dysfunctional ( i.e. they didn't supply oxygen, but filled space). We assumed that the number born dysfunctional increased as the drug concentration increased. We found that increasing the drug concentration retarded the growth of the tumour.

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