Back to the Top
Dear group,
I have a problem concerning the blood distribution of compounds which are
highly bound to plasma proteins. Let us imagine a compound is 98% bound to
plasma proteins, 1% being bound to cells and 1% being free in plasma water.
The blood to plasma ratio (B/P) could be calculated according to B/P=
(C*H/P) + (1-H) (see Hinderling, 1997, Pharmacological Review ... for
example). C is the concentration in cells, P the concentration in plasma and
H = Hematocrit. For our specific case the calculation gives
B/P=(0.01*0.44/0.99) + (1-0.44) = 0.56.
If we calculate the fraction unbound to blood (fu,blood) using the classical
formula (see Gibaldi & Perrier, 2nd ed., Rev. and Expanded, p. 328) ie
fu,blood = (fu,plasma) / (B/P) we found fu,blood=0.0178 ie 1.8%.
Finally we have the following conclusion : fu,plasma (1%) < fu,blood (1.8%).
Is there anything here that troubles you ? Personally, I can't understand
why fu,blood can be higher than fu,plasma ? Would it be possible that
fraction unbound to blood means (fraction bound to blood cells + fraction in
plasma water). ?
Any thoughts ?
Thanks
Pascal Espié, UCB Pharma, Belgium
Back to the Top
Dear Pascal:
I think that you may have mis-calculated your plasma and blood
concentrations.
Based on your example, consider 1 g of drug in 1 ml of whole blood (0.01 g
free in plasma water, 0.01 g in cells, and 0.98 g bound to plasma proteins).
The cell volume in your example is 0.44 ml, and the plasma volume is 0.56
ml. Let P = plasma concentration, C = concentration in cells, and B = whole
blood concentration.
B = (0.01 g + 0.01 g + 0.99 g) / 1 ml = 1 g/ml
P = (0.01 g + 0.98 g)/ 0.56 ml = 1.7678 g/ml
C = 0.01 g / 0.44 ml = 0.0227 g/ml
fu,p = 0.01 g/0.99 g = 0.0101
fu,b = 0.01 g/1.00 g = 0.01
So, fu,b is less than fu,p.
Based on the Hinderling equation:
B/P = C*H/P + (1-H)
= 0.0227*0.44/1.7678 + (1-0.44) = 0.566
Note that this is in agreement with the expected value from above (i.e., B/P
= 1/1.7678 = 0.566).
Hope this helps,
J. Balthasar
University at Buffalo
Back to the Top
Dear Pascal:
I believe that there may be a typo in the Gibaldi & Perrier equation that
you cited: fu,b = fu,p / (Cb/Cp).
Please consider the following...
Mass free in Blood = Mass free in Plasma
fu,b * Mass in blood = fu,p * Mass in plasma
fu,b * Cb * Volume of blood (Vb) = fu,p * Cp * Volume of plasma
where Volume of plasma = Vb*(1-H)....
fu,b * Cb * Vb = fu,p * Cp * Vb(1-H)
fu,b * Cb = fu,p * Cp * (1-H)
finally,
fu,b = (fu,p*Cp/Cb)*(1-H)
So, I believe that the equation that you cited is incorrect (i.e., missing
the (1-H) term).
J. Balthasar
PharmPK Discussion List Archive Index page
Copyright 1995-2010 David W. A. Bourne (david@boomer.org)