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that are often complicated, cumbersome, and difficult to decode in order to use them in either quality control or product development. |
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A more simplistic, yet comprehensive view of Fig. 15 is given by the Makoid-Banakar Function (Fig. 16). This function simply depicts a model in which there is a zero-order process (B segment of Fig. 16) being shut down by a first-order process. |
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A = Time shift; if A = +ve, the data has a time lag; if A = -ve, the data has a burst effect. |
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B = zero order release rate |
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C = first order shut down rate |
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T: = (TIME-A)×UNIT (TIME-A) |
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where FL and FE are the amount (fraction) released during late and early phases, FM is the maximum amount (fraction) released, F is the cumulative amount (fraction) released. |
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Real time (TIME) is replaced by corrected time (T) to take into consideration the time shift parameter (A). By setting the first derivative of the function to zero, the time (T) to reach the peak is calculated and found to be: |
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By setting the time (T) equal to 1/C, the maximum amount released is found to be: |
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Fmax = B/C×EXP(-1) = B/C×0.36788 |
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If the data exhibits a burst effect, the amount released immediately may be calculated by setting real time (TIME) = 0 in the function. Thus the burst amount would be equal to |
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b. Makoid-Banakar Function Modified for Gradual Early Release (Sigmoid Shape) |
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