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sandeepdahiya ☆ India, 2013-10-23 10:25 (4619 d 18:08 ago) Posting: # 11729 Views: 10,709 |
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I am trying to fit dissolution data to modified Noyes-Whitney Theory as mentioned in below article- http://rd.springer.com/article/10.1023/A:1011071401306 I have tried to use the equation 3, 4 and 5 mentioned in the article, but am unable to calculate the z-value  (I am very new to all this).The available inputs are dissolution release profile and solubility. Can anyone throw some light on how to calculate "z-value" by fitting these inputs to above mentioned equations? Thanks in advance, Sandeep. — Sandeep |
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sandeepdahiya ☆ India, 2013-10-23 12:44 (4619 d 15:49 ago) @ sandeepdahiya Posting: # 11731 Views: 10,497 |
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Modified Noyes-Whitney equation- dWt / dt = {D.T.N1/3.W2/3.(Xs-Wt)} / V.d.r2/3 = z.W2/3.(Cs-C) -------- (1) where, Wt = amount dissolved at time t D = Diffusion co-efficient T = Shape factor (like in Weibull equation) N = Number of particles W = Amount of drug remaining to be dissolved V = Volume of dissolution d = Diffusion layer thickness r = Particle density Cs = Saturation solubility Xs = Amount of drug required to saturate dissolution volume z = Constant equal to following, z = {D.T.N1/3} / d.r2/3 As the values of D, T, d, r, etc are difficult to have for every molecule, z-value can be obtained by fitting the dissolution data to equation (1) or the integrated form of equation (1) (below). y = (z/V).t ---------(2) where y is a function of amount brought to dissolution (dose). I am unable to fit the dissolution data to these equations. Can anyone please help me with an example. Thanks in advance, Sandeep — Sandeep |
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yjlee168 ★★★   Kaohsiung, Taiwan, 2013-10-23 15:41 (4619 d 12:52 ago) @ sandeepdahiya Posting: # 11736 Views: 9,502 |
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Dear Sandeep, I think the equation as mentioned should be able to be solved easily using an nonlinear regression (NLRG) method. There are many commercial or free open-sourced NLR computer programs available. What features you need include user's defined nonlinear equation, a numerical integration function and finally optimization algorithms. I will suggest that you should look at R (www.r-project.org) because it's quite flexible. The libraries (or packages) you will need may include 'deSolve' (formerly "odeSolve") or other similar for numerical integration function. Or you can browse all available packages from CRAN for NLRG tools. Commercial NLRG such as WinNonlin should also fit your needs. And again, you still need to define your equations yourself. ❝ ... ❝ z = Constant equal to following, ❝ ... I think 'z' here should be a secondary parameter, not a constant, since it is calculated from primary parameters D, T, d, r, etc.. It won't be known until you solve these D, T, d, r, etc.. However, 'V' (volume of dissolution) should be one of constants (if I am right) because we should know the volume of cell for dissolution tests. ❝ As the values of D, T, d, r, etc are difficult to have for every molecule, z-value can be obtained by fitting the dissolution data to equation (1) or the integrated form of equation (1) (below). ❝ ❝ y = (z/V).t ---------(2) I am not quite sure about this. If so, then big congratulation, your equation has been turned into a simple linear eq. now. so y(t) = A.t where A = (z/V) (A: the slope of the linear eq.) and V has been known as a constant. So z = A*V. You don't need to care how to calculate D, T, d, r, etc. if you just want to calculate y(t) (is it Wt(t)?). You can use any spreadsheet program (excel, gnumeric, openoffice/libreoffice-calc etc.) to solve this. Remember to force the regression line passing through zero. — All the best, -- Yung-jin Lee bear v2.9.6:- created by Hsin-ya Lee & Yung-jin Lee Kaohsiung, Taiwan https://www.pkpd168.com/bear Download link (updated) -> here |
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sandeepdahiya ☆ India, 2013-11-06 05:16 (4605 d 22:18 ago) @ yjlee168 Posting: # 11862 Views: 9,110 |
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Dear Yung-jin, ❝ I will suggest that you should look at R. I will try R. ❝ I think 'z' here should be a secondary parameter, not a constant. By constant i meant to say that it's value is constant for a given dissolution medium. and yes, V is constant. Even i was not sure how the below equation was fitted. For sure it is not simple linear fitting. ❝ As the values of D, T, d, r, etc are difficult to have for every molecule, z-value can be obtained by fitting the dissolution data to equation (1) or the integrated form of equation (1) (below). ❝ ❝ ❝ ❝ y = (z/V).t ---------(2) ❝ ❝ I am not quite sure about this. If so, then big congratulation, your equation has been turned into a simple linear eq. Thank you for your reply. — Sandeep |
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yjlee168 ★★★ Kaohsiung, Taiwan, 2013-11-06 07:11 (4605 d 20:22 ago) @ sandeepdahiya Posting: # 11863 Views: 9,248 |
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Dear Sandeep, Should Equation (2) be as dWt/dt = (z/V)*t? If yes, then it's a differential equation (DE).BTW, in your previous post, you wrote: ❝ Modified Noyes-Whitney equation- ❝ dWt / dt = {D.T.N1/3.W2/3.(Xs-Wt)} / V.d.r2/3 ❝ = z.W2/3.(Cs-C) -------- (1) Did you miss the independent variable 'time' (i.e., 't') on the right-hand side of both equations? You cannot solve the DE in this case. Sorry I cannot access the article you mentioned previously. Also, the equation dWt / dt = {D.T.N1/3.W2/3.(Xs-Wt)} / V.d.r2/3 has 'Wt' (the dependent variable) on both sides. It apparently exhibits a saturation process for dissolution profile that sounds reasonable for "cumulated dissolved amount of drug at time 't'. However, there should be a 't' somewhere on the right-hand side of equation. ❝ Even i was not sure how the below equation was fitted. For sure it is not simple linear fitting. OK, agree. »... ❝ ❝ y = (z/V).t ---------(2) — All the best, -- Yung-jin Lee bear v2.9.6:- created by Hsin-ya Lee & Yung-jin Lee Kaohsiung, Taiwan https://www.pkpd168.com/bear Download link (updated) -> here |
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sandeepdahiya ☆ India, 2013-11-19 10:41 (4592 d 16:52 ago) @ yjlee168 Posting: # 11908 Views: 9,242 |
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Dear Yung-jin, I have exactly reproduced the equation (1) and (2) from the article. The article says that equation (2) is the integrated form of the equation (1) and the dissolution data is fitted to equation (2) to calculate the 'z value'. ❝ Modified Noyes-Whitney equation- ❝ dWt / dt = {D.T.N1/3.W2/3.(Xs-Wt)} / V.d.r2/3 ❝ = z.W2/3.(Cs-C) -------- (1) ❝ y = (z/V).t ---------(2) Equation (1) is a differential equation and time variable on RHS will come after integration. ❝ Did you miss the independent variable 'time' (i.e., 't') on the right-hand side of both equations? You cannot solve the DE in this case. Sorry I cannot access the article you mentioned previously. Also, the equation You can access the first two pages of the article. Follow the below link and click on "Look Inside". http://rd.springer.com/article/10.1023/A:1011071401306# And fortunately all these equations are detailed in first two pages of the article.  Equation (3) and (4) of the article are the equations under discussion. — Sandeep |
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yjlee168 ★★★ Kaohsiung, Taiwan, 2013-11-19 11:51 (4592 d 15:42 ago) @ sandeepdahiya Posting: # 11910 Views: 9,081 |
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Dear Sandeep, Thank you for the reference link. quite useful. As I understand, you can solve 'z' first from Eq. (4) (as noted in literature, i.e., y = (z/V).t ) which is an integral equation. So you can simply use a linear regression method (forced to pass through zero) to solve Eq. (4) to obtain 'z' from the slope (= z/V). Then you solve Eq. (3) or (5) (as noted in literature; based on the model of your choice) as differential equations. According to literature, some variables (such as D, N, delta, rho and etc.) go to 'z' now. So I guess you don't have to worry about these variables. Is it to solve 'Cs' finally? ❝ I have exactly reproduced the equation (1) and (2) from the article. ❝ .. ❝ ❝ Equation (1) is a differential equation and time variable on RHS will come after integration. ok. It's my mistake. Sorry about this. They are all correct equations. — All the best, -- Yung-jin Lee bear v2.9.6:- created by Hsin-ya Lee & Yung-jin Lee Kaohsiung, Taiwan https://www.pkpd168.com/bear Download link (updated) -> here |
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jag009 ★★★ NJ, 2013-10-23 18:45 (4619 d 09:48 ago) @ sandeepdahiya Posting: # 11738 Views: 9,292 |
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Hi, ❝ Modified Noyes-Whitney equation- ❝ dWt / dt = {D.T.N1/3.W2/3.(Xs-Wt)} / V.d.r2/3 ❝ = z.W2/3.(Cs-C) -------- (1) ... ❝ ❝ y = (z/V).t ---------(2) ❝ where y is a function of amount brought to dissolution (dose). Thanks John |
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