Compartmental+Models

Compartmental+Models - Compartmental Models Compartmental...

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Compartmental Models
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Compartmental Analysis Useful approach – predictive Conceptual framework to understand drug time courses Body much to complex to truly account for all processes, etc Oversimplification, but predictive and useful No model is right, but many are useful
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Models Amount in Body = Rate In – Rate Out This is a model = + But this isn’t a very convenient way to do it Rate In Amount in body Rate Out
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Body (Distribution?) Mathematically – Compartment: A well mixed unit Transfer occurs between compartments Out Is the body well mixed?? Surprisingly this simple model works! (maybe for ~80% of drugs) Basically if mixing is fast with respect to removal
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The Simplest Model Body k out k out – first order constant, % per min A = amount in body (k out can be k elimination , k elim or K or k dA dt = - kout * A FYI- dA/A = -k*dt = -k dt ln A t 0 = -k t t 0 ln A (t) /A (0) = -k*t – k*0 A (t) /A (0) = e –kt FRACTION REMAINING If first time was not zero- ln A t1 t2 = -k t t1 t2 ln A(t1)/A(t2) = -k*t1 – k*t2 = -k(t1-t2) = k (t2-t1) ln A (t1) /A (t2) = k (t2-t1) A (t1) /A (t2) = e –k(t2-t1)
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The Simplest Model A (t) /A (0) = e –kt FRACTION REMAINING A (t) = A (0) * e –kt What is Amount in body at t=0?? – the dose
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