Real-time prediction of heparin concentration in blood extracorporeal circulation by relaxation time distribution (RTD)

Heparin concentration $c$ in a blood extracorporeal circulation has been real-timely predicted based on the relaxation strength ${\Delta \epsilon }_m$ at relaxation frequency $f_m$ extracted by relaxation time distribution (RTD). The simulated extracorporeal circulation was conducted to optimize the number of ${\Delta \epsilon }_m$ for the prediction of c using the porcine whole blood (WB) and low-leukocyte and −platelet blood (LLPB) under the condition of the gradual increment of $c$ from 0 to 8 U/mL with constant flow rate and blood temperature. The experimental results show that among the three relaxation strengths ${\Delta \epsilon }_1$, ${\Delta \epsilon }_2$ and ${\Delta \epsilon }_3$ (in ascending order of frequency), ${\Delta \epsilon }_2$ at $f_2$ = 5.2 ∼ 6.2 MHz and ${\Delta \epsilon }_3$ at $f_3$ = 42 ∼ 50 MHz were correlated to $c$. The ${\Delta \epsilon }_3$ was decreasing with increasing $c$ in both cases, which was influenced by the plasma macromolecular concentrations, while the ${\Delta \epsilon }_2$ was increased with increasing c in WB case but was hardly changed in LLPB case because the ${\Delta \epsilon }_2$ is influenced by the blood cell concentrations and the shape changes of blood cell membranes. Heparin concentration $c$ is estimated by the linear regression formula $c^{PRE}=a_1{(\Delta \epsilon }_2-{\Delta \epsilon }_2^{c=0})+a_2({\Delta \epsilon }_3-{\Delta \epsilon }_3^{c=0})$ ($a_1$ = -0.991, $a_2$ = -0.123) within the mean absolute percentage error (MAPE) of 0.291.