Lagging Behavior in Biological Systems

The lagging behavior is first exemplified by a rapidly stretched spring and a one-dimensional fin to illustrate the phase-lag concept via the thermal and mechanical properties that most engineers are familiar with. The second-order lagging model is then introduced to correlate with drug delivery in tumors and bioheat transfer that involve multiple carriers in heat/mass transport. Analytical expressions for the phase lags are derived, aiming toward revealing different physical origins for delays in different systems. For drug delivery in tumors involving nonequilibrium mass transport, the lagging behavior results from the finite time required for the rupture of liposome in releasing the antitumor drug and the finite time required for tumor cells to absorb drugs. For bioheat transfer involving nonequilibrium heat transport, on the other hand, the lagging behavior results from the finite time required for exchanging heat between tissue and blood. Pharmacodynamical and biological properties affecting the phase lags, as well as the dominating parameters over the lagging response are identified through the nondimensional analysis. Involvement of the thermal Mach number, which measures the speed of blood flow relative to the conventional thermal wave speed, is a new feature in this extension of the lagging model. The second order effects in lagging are well correlated with the number of carriers involved in nonequilibrium heat and mass transport.