  Maintenance of adequate physical and functional pancreatic $\beta$-cell mass
is critical for the prevention or delay of diabetes mellitus. It is well
established that insulin potently activates mitogenic and anti-apoptotic
signaling cascades in cultured $\beta$-cells. Loss of $\beta$-cell insulin
receptors is sufficient to induce type 2 diabetes in mice. However, it remains
unclear whether the {\em in vitro} effect in human islets and the {\em in vivo}
effects in mice can be applied to human physiology. The major obstacle to a
complete understanding of the effects of insulin's feedback in human pancreas
is the absence of technology to measure the concentrations of insulin inside of
pancreas. To contextualize recent {\em in vitro} data, it is essential to know
the local concentration and distribution of insulin in pancreas. To this end,
we continue to estimate the local insulin concentration within pancreas. In
this paper, we investigate the distribution of insulin concentration along the
pancreatic vein through a novel mathematical modeling approach using existing
physiological data and islet imaging data, in contrast to our previous work
focusing on the insulin level within an islet. Our studies suggest that, in
response to an increase in glucose, the insulin concentration along the
pancreatic vein increases nearly linearly in the fashion of increasing quicker
in tail area but slower in head area depending of the initial distribution.
