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Mathematical models in drug delivery.pdf
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One of the major challenges to be addressed in the future is the combination of mechanistic theories describing drug release out of the delivery systems with mathematical models quantifying the subsequent drug transport within the human body in a realistic way. Ideally, the effects of the design parameters of the dosage form on the resulting drug concentration time profiles at the site of action and the pharmacodynamic effects will become predictable.
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Mathematical models in drug delivery.pdf
- ((Mathematical models in drug delivery: How modeling has shaped the way we design new drug delivery systems))
- (Interface flux) = km M∞ S.L Flux of mass transfer = Rate of mass mass transfer Area = Mass Time Area = Mass Area. Time = Mt S. t Ci = M∞/SL Ci >> Cb
- One Dimensional Flux Equations for Different Geometries r=R , C=Cs r=0 𝝏𝑪 𝝏𝒓 = 0 B.C: I.C: t=0 , C=C0 ,
- FESEM: ATGD TEM: ATGD 𝐅𝐨𝐫 𝐬𝐡𝐨𝐫𝐭 𝐭𝐢𝐦𝐞: 𝑴𝒕 𝑴∞ ≅ 𝟖 𝑫𝒕 𝝅𝒅𝟐 𝟏 𝟐 − 𝟒𝑫𝒕 𝒅𝟐 = 𝒎𝟏𝒕 𝟏 𝟐 − 𝒎𝟐𝐭 𝑴𝒕 𝑴∞ ≤ 𝟎. 𝟒 𝐅𝐨𝐫 𝐥𝐚𝐧𝐠 𝐭𝐢𝐦𝐞: 𝑴𝒕 𝑴∞ ≅ 𝟏 − 𝟒 𝟐. 𝟒𝟎𝟓𝟐 𝒆 − 𝟐𝟑.𝟏𝟑𝟔𝑫 𝒅𝟐 𝒕 = 𝟏 − 𝒂𝒆−𝒃𝒕 𝑴𝒕 𝑴∞ > 𝟎. 𝟔 𝑴𝒕 𝑴∞ = 𝟏 − 𝟑𝟐 𝝅 𝒏=𝟏 ∞ 𝟏 𝒒𝟐 𝒆𝒙𝒑 − 𝒒𝒏 𝟐 𝑹𝟐 𝑫𝒕 . 𝒑=𝟎 ∞ 𝟏 𝟐𝒑 + 𝟏 𝟐 × 𝒆𝒙𝒑 𝟐𝒑 + 𝟏 𝟐𝝅𝟐 𝑯 𝟐 𝑫𝒕 H
- Low pore interconnectivity causes slower release Higher pore interconnectivity results in increased release
- Divergent method Convergent method