?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.relation=http%3A%2F%2Fmiis.maths.ox.ac.uk%2Fmiis%2F374%2F&rft.title=Angiogenesis%3A+A+Model+of+Cell+Differentiation&rft.creator=Hinch%2C+R.&rft.subject=Medical+and+pharmaceutical&rft.description=Angiogenesis+is+the+formation+of+blood+vessels%2C+and+is+of+great+importance+in+the+growth+of+tumours.+Attempts+have+been+made+to+desgin+experiments+in+petri-dishes+that+mimic+the+'Conditions+of+tumour+growth.+The+first+of+the+experiments+is+the+'matrigel'+assay.+Matrigel+provides+a+matrix+for+the+endothelial+cells+to+grow+on%2C+and+contains+all+the+nutrients+that+the+cells+need.+It+is+found+that+in+the+matrigel+assay+blood+vessels+didn't+form%2C+although+some+transient+strucutres+formed+at+early+times+in+the+experiment.+The+second+experiment+is+the+'biocure'+assay.+In+this+experiment+the+petri+dish+is+filled+with+both+endothelial+and+fibroblast+cells.+The+fibroblasts+form+a+strucutal+supporting+network+for+the+endothelial+cells.+Tubules+resembling+blood-vessels+formed+after+about+ten+days+in+the+biocure+asssay.+%0D%0A%0D%0AThe+process+of+cell+differentiation+is+thought+to+be+important+in+the+growth+of+blood+vessels.+Cells+can+sense+that+they+are+part+of+a+blood+vessel%2C+and+change+their+shape+to+form+tubules.+Also+it+is+likely+that+they+change+their+chemical+messaging+properties%2C+and+their+abilities+to+bind+to+other+endothelial+cells.+%0D%0A%0D%0AA+model+is+developed+that+describes+cell+differentiation%2C+and+separates+cells+into+different+classes.+For+simplicity+the+spatial+distribution+of+cells+in+different+classes+is+ignored.+Using+simple+population+dynamics%2C+a+set+of+coupled+non-linear+ODEs+is+developed+to+describe+the+dynamics+of+the+system.+The+system+is+found+to+have+two+different+long-time+states%2C+one+corresponding+to+the+formation+of+blood+vessels+and+one+where+vessels+did+not+form.+The+ratio+of+the+cell+proliferation+rate+to+the+cell+maturity+rate+(the+time+it+takes+to+realise+that+it+is+part+of+a+blood+vessel)+is+critical+in+determining+which+is+the+final+state+of+the+system.&rft.date=2000&rft.type=Study+Group+Report&rft.type=NonPeerReviewed&rft.format=application%2Fpdf&rft.language=en&rft.identifier=http%3A%2F%2Fmiis.maths.ox.ac.uk%2Fmiis%2F374%2F1%2FAngiogenesis-a-model-of-cell-differentiation.pdf&rft.identifier=++Hinch%2C+R.++(2000)+Angiogenesis%3A+A+Model+of+Cell+Differentiation.++%5BStudy+Group+Report%5D+++++