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Non-compartmental pharmacokinetic model was applied to analyze RM plasma and brain levels using Kinetica software (version 2000, Arlington, USA). There are different pharmacokinetic parameters, namely, Cmax (maximum concentration in brain and plasma), Tmax (time to reach maximum concentration), AUC0-∞ (area under the curve), and AUMC0-∞ (area under first moment curve). AUC and AUMC were calculated by the trapezoidal rule; MRT (mean residence time; MRT = AUMC0-∞/AUC0-∞) [45], half-life, and elimination rate constant (k) were calculated for the intranasally administered MST 2 and the intravenous RM solution. In order to ensure the brain-targeting ability of the formulated system, the brain-targeting efficiency (BTE%) which compares the specific delivery of drug to brain after IN administration and IV administration was calculated as per Eq. (3) [46]:

where PIN and BIN are the AUC0-∞ in the plasma (P) and brain (B) after intranasal administration of the optimized system, while PIV and BIV are the AUC0-∞ after IV administration. BTE% values above 100 indicate efficient delivery of the drug to the brain after IN administration [47].

In addition, direct transfer percentage (DTP%) was also calculated to measure the extent of RM reaching the brain directly from the nose relative to the total amount reaching the brain after IN administration. DTP% was calculated following Eqs. (4) and (5) [48]:

where Bx is RM fraction that reached brain through BBB from the systemic circulation after intranasal administration. Positive values for DTP% suggest that the drug passes directly from the nose to the brain after IN administration, while zero or negative values indicate that the drug reaches the brain after being cleared from the nasal cavity to blood stream and then pass through BBB [49]. The pharmacokinetic parameters were analyzed statistically by ANOVA at p value < 0.05 using SPSS (SPSS® statistics program software, IBM, USA).

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