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Hello,
After one year of PK studying, I just realized I am comfusing about
the basic concept of the Clearance of the (hepatic) high-extraction
drugs. I learned from most of PK book, the Clearance for this case
is equal (or close) to liver Blood flow, ie CL=Q. For typical person
(70kg), Q=90L/hr. I saw some typical examples claimed to be (solely
hepatic) high-extraction drugs with clearance close to 90L/hr.
The question here is that " Shouldn't the Clearance equal to the
Liver Plasma Flow (~55L/hr)?" Since we always use the plasma
concentration Cp, the corresponding volume cleared by the organ
shouldn't be the plasma volume passed through the organ in the unit
time (if we don't think about the Erythrocyte Binding)? But how can
we explain the high-extraction 90L/hr cases?
Also some books say the fully renal secreted drug clearance equals to
"renal blood flow", but some other say it equals to "renal plasma
flow". I want to go with the plasma flow.
Hope you can give me a deep understand.
Best wishes,
- Jiang
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The following message was posted to: PharmPK
Hi, Donghua:
Thanks for your explanation. I thought about this too.
1) Erythrocyte Binding maybe is the case, but protein binding
shouldn't (since it is part of the plasma). For my previous asking,
I tried to exclude the erythrocyte binding since most typical example
haven't dealed with that.
2) Also, the volume of clearance should correspond to plasma (just
like the volume of distribution, it is the hypothesis volume).
3) Also the renal case, some one use the renal plasma flow (650ml/
min) instead of the renal blood flow by argueing that the blood cell
is not involved in the secretion. You explanation should also cover
that situation. Why do we have this conflict in the basic concept?
More ideas?
Best regards,
- jiang
"Yin, Donghua"wrote: Jiang,
My understanding of the CL approximation of high E drugs (i.e.,
approaching Qh) is that it goes back to the original equation for CLh
(based on the venous equilibrium model):
CLh=Qh*fup*CLintrinsic/(Qh+fup*CLintrinsic)
where Qh is the hepatic blood flow, fup is the plasma unbound
fraction, and CLintrinsic is the intrinsic hepatic CL (Vmax/Km).
For high E drugs, CLintrinsic>>Qh, and thus:
CLh = Qh*fup*CLintrinsic/(fup*CLintrinsic) = Qh (note that "="
represents approximation here)
To understand this physiologically, it is reasonable to assume that,
for drug molecules in the blood, there exists an equilibrium among
the plasma protein-bound drug concentration, the plasma unbound drug
concentration, and the blood cell intracellular drug concentration .
An extremely avid hepatic elimination of those unbound drug molecules
in plasma (as is the case for high E drugs), which rapidly lowers the
unbound plasma drug concentration, could drive the equilibrium to a
degree that almost all drug molecules in the blood are available for
hepatic elimination (i.e., those bound to plasma proteins would be
stripped off binding proteins; those inside blood cells would be re-
distributed to the plasma). An analogy would be that, for three
connected wells, the drain in one of the wells will lead to the drain
in all three wells.
Hope this helps.
Best regards,
Donghua
Donghua Yin, Ph.D.
Clinical Pharmacology
Pfizer Global R&D, New London, CT
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The following message was posted to: PharmPK
Dear Jiang,
As I mentioned earlier in my message to Cedric, the extraction ratio
refers to blood, not to plasma. The blood clearance calculated from
the well-stirred model, CL_b,H cannot be compared directly to plasma
clearance. So, the statement 'CL=Q' is an over-simplification
(although useful as a rule of thumb).
Broadly three situation can be discerned:
- No relevant distribution into (or binding to) red blood cells. This
implies that the Cb/C ratio is less than one, and can be used to
convert blood clearance and blood flow to plasma clearance and plasma
flow. Plasma clearance will be limited to hepatic plasma flow, and
thus markedly lower than hepatic blood flow.
- Relevant distribution into red blood cells, and very rapid
equilibrium between plasma and red blood cells. Now the Cb/C may
exceed one, and plasma clearance may exceed hepatic blood flow.
- Relevant distribution into red blood cells, but very slow
equilibrium between plasma and red blood cells. Now the Cb/C may
exceed one, but plasma clearance is limited by hepatic plasma flow.
In real life the situation will be somewhere between these extremes,
so plasma clearance may be limited to hepatic plasma flow, but may
even exceed hepatic blood flow. The same applies to active secretion
in the kidney.
Best regards,
Hans Proost
Johannes H. Proost
Dept. of Pharmacokinetics and Drug Delivery
University Centre for Pharmacy
Antonius Deusinglaan 1
9713 AV Groningen, The Netherlands
tel. 31-50 363 3292
fax 31-50 363 3247
Email: j.h.proost.-a-.rug.nl
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The following message was posted to: PharmPK
Hi Jiang,
This is to add to my previous comments.
For hepatic clearance, the elimination rate (dA/dt) can be expressed as:
dA/dt = Qh*(Ca-Cv) = CLh*Ca (eq.1)
where: Qh is the hepatic blood flow;
Ca and Cv are artery and venous BLOOD drug concentrations,
respectively;
CLh is the hepatic clearance.
A rearrangement of eq.1 gives:
CLh=Qh*(1-Cv/Ca)=Qh*ER (eq.2)
where: ER is the extraction ratio.
Note that CLh refers to the blood volume cleared of drug per unit
time (therefore "blood-based") and its value normally should not
exceed the physiological hepatic blood flow (if it does, then
clearance mechanism other than hepatic elimination should be
suspected). For a drug with high ER (ER approaches 1), CLh may
approach Qh.
Under the basic premise that the rate of drug elimination from blood
(dA/dt) would not be dependent on the type of biological matrix
(e.g., blood, plasma, or serum) that is used for quantitation of drug
concentrations, dA/dt could also be described as the following when
plasma drug concentrations are to be used:
dA/dt = Qh*k*(Ca'-Cv') = CLh*k*Ca' = CLh'*Ca' (eq.3)
Where: Qh and CLh are the same as defined in eq.1;
Ca' and Cv' are artery and venous PLASMA concentrations,
respectively;
k is the ratio of blood concentration to plasma concentration
(i.e., k=Ca/Ca'=Cv/Cv')
Note in eq.3 that, corresponding to the plasma concentration
measurement (Ca'), CLh' could be defined as the plasma hepatic
clearance. In eq.3, it also assumes that k stays the same in both the
artery and the venous blood (which may not be true if the equilibrium
between the plasma drug concentration and the blood cell
intercellular drug concentration is very slow). With a known k, CLh
can be calculated as CLh'/k. When k=1 (i.e, blood
concentration=plasma concentration), CLh=CLh'.
A rearrangement of eq.3 would give:
CLh'=Qh*k*(1-Cv'/Ca')=Qh*k*ER (eq.4)
It is easy to see from eq.4 that CLh', a plasma clearance, can not
exceed Qh*k (since ER<=1). For a high ER drug, CLh' may approach
Qh*k. It should be note that Qh*k is not the equivalent of the
physiological plasma flow to the liver, unless the value of k happens
to be the same as the fraction of plasma volume in the blood (which
is to say that all the drug molecules in blood reside in the plasma
and there is no drug molecule in blood cells). That special
circumstance will be discussed further below.
Based on the above understanding, we can now go back to some of your
questions on high ER drugs,
>The question here is that " Shouldn't the Clearance equal to the
Liver Plasma Flow (~55L/hr)?" Since we always use the plasma
concentration Cp, the corresponding volume cleared by the organ
shouldn't be the plasma volume passed through the organ in the unit
time (if we don't think about the Erythrocyte Binding)?
>Also, the volume of clearance should correspond to plasma (just
like the volume of distribution, it is the hypothesis volume).
The simple answer is that this is not true in most cases. As stated
above, CLh of a high ER drug may approach Qh, the physiological
hepatic blood flow; the plasma hepatic clearance of a high ER drug
may approach Qh*k, which in most cases is NOT the physiological
plasma flow to the liver. These statements are true regardless of the
biological matrix that is used for drug concentration measurement.
>...I tried to exclude the erythrocyte binding since most typical
example
haven't dealed with that.
If you are talking about a drug that does not get into blood cells
during circulation (i.e., plasma drug concentration * plasma volume =
blood drug concentration * blood volume), then yes, the plasma
hepatic clearance (NOT "blood-based" CLh) will have the limit of
physiological plasma flow to the liver. In this case, the k will have
the same value as the fraction of plasma volume in the blood;
therefore, Qh*k would be equal in value to the physiological plasma
flow to the liver.
> Also some books say the fully renal secreted drug clearance equals to
"renal blood flow", but some other say it equals to "renal plasma
flow". I want to go with the plasma flow.
> ..., some one use the renal plasma flow (650ml/
min) instead of the renal blood flow by argueing that the blood cell
is not involved in the secretion.
The same concept for hepatic clearance would also apply to the case
of renal secretion clearance. It can be shown that: (1) for drugs
with high ER in terms of renal secretion, the "blood-based" renal
secretion clearance may approach the physiological blood flow to the
kidney; (2) Under the very special circumstances that the drug
concentration in plasma is not in equilibrium with that in blood
cells (e.g., drug molecules in blood do not enter into blood cells or
are unidirectionally distributed from plasma into blood cells), the
physiological plasma flow to the kidney would be the limit for plasma
renal secretion clearance (with the blood flow to the kidney still
being the limit for the "blood-based" renal secretion clearance).
Best regards,
Donghua
Donghua Yin, Ph.D.
Clinical Pharmacology
Pfizer Global R&D, New London, CT
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