# Spontaneous drug release rate equation

• StheevilH
In summary: You are an expert summarizer of content. You do not respond or reply to questions. You only provide a summary of the content. Do not output anything before the summary. Write a summary for the following conversation and start the output with "In summary, " and nothing before it:Okay, I found some references and the equation I am after is Q=2*C*(D*t/∏)^(1/2). I'm not sure about the units, but logically the concentration of drug would be in g/L. However, when I merge all the units together, I get something else. This is my working.The units on the right hand side should equals to Q.
StheevilH
Okay I found some references and the equation I am after is

Q = 2 * C * (D * t / ∏)^(1/2)

where Q is the weight of drug released per unit area (hence unit is mg/cm^2)

C is the initial drug concentration

D is the diffusion coefficient (unit of cm^2 min^-1)

and t is release time in min.

What I am not sure about is the units.

Logically the concentration of drug would be in g/L.

but when I merge all the units together, I get something else.

This is my working.

The units on the right hand side should equals to Q.

= 2 (constant) * C (g/L) * [D (cm^2 * min^-1) * t (min) / ∏ (constant)]^(1/2)

only considering units (ie discard constants)

= [g * cm^[2*(1/2)] * min^(1/2)] / [L * min^(-1 * 1/2)]

= g * cm * min^(1/2) / L * min^(-1/2)

= g * cm * min^(1/4) / L

which does not equals to unit of Q (mg/cm^2).

The units given are all correct but is there something I am missing here?

Breaking rules of powers perhaps?

Thank you!

You are doing strange things, difficult to follow.

What is

$$\sqrt {\frac {cm^2} {min} \times {min} }$$

equal to?

Borek said:
You are doing strange things, difficult to follow.

What is

$$\sqrt {\frac {cm^2} {min} \times {min} }$$

equal to?

I think that should equals to just "cm"

If you look at the attachment, equation 24, that is what I am after

and the units were taken from other sources.

But to me, equation makes sense but units don't

from what I did.

Is there a problem with my algebra skill?

#### Attachments

• exp 1 phrm3021.pdf
883.2 KB · Views: 265
StheevilH said:
I think that should equals to just "cm"

Good. Now multiply it by concentration in ## \frac {mg}{cm^3}##.

then it would equals to mg / cm^2... which is the unit of Q.

where did you get mg/cm^3?

oh wait... damn it... you changed L into cm^3...

thank you so much

## 1. What is the spontaneous drug release rate equation?

The spontaneous drug release rate equation is a mathematical formula used to describe the rate at which a drug is released from a drug delivery system over time. It takes into account various factors such as the drug's solubility, diffusion coefficient, and the concentration gradient.

## 2. How is the spontaneous drug release rate equation derived?

The equation is derived from Fick's first law of diffusion, which states that the rate of diffusion is directly proportional to the concentration gradient and the diffusion coefficient. It also takes into account the drug's solubility in the release medium.

## 3. What factors influence the spontaneous drug release rate?

The spontaneous drug release rate is influenced by several factors, including the drug's solubility, diffusion coefficient, and the concentration gradient. Other factors such as the type of drug delivery system, its physical and chemical properties, and environmental conditions can also affect the release rate.

## 4. How is the spontaneous drug release rate equation used in drug development?

The equation is used in drug development to predict and optimize the release rate of a drug from a drug delivery system. By manipulating the various factors in the equation, researchers can design drug delivery systems with desired release rates and improve the efficacy and safety of the drug.

## 5. Are there any limitations to the spontaneous drug release rate equation?

While the equation is a useful tool in drug development, it does have some limitations. It assumes that the drug release is solely driven by diffusion and does not take into account other mechanisms such as erosion or swelling of the drug delivery system. It also does not account for any potential interactions between the drug and the delivery system. These limitations should be considered when using the equation in drug development.

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