  The work analyzes a one-dimensional viscoelastic model of blood vessel growth
under nonlinear friction with surroundings, and provides numerical simulations
for various growing cases. For the nonlinear differential equations, two
sufficient conditions are proven to guarantee the global existence of
biologically meaningful solutions. Examples with breakdown solutions are
captured by numerical approximations. Numerical simulations demonstrate this
model can reproduce angiogenesis experiments under various biological
conditions including blood vessel extension without proliferation and blood
vessel regression.
