# PharmPK Discussion - Blood distribution for highly protein bound compounds

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• On 1 Jul 2002 at 11:13:10, Espie Pascal (Pascal.Espie.at.UCB-Group.com) sent the message
`Dear group,I have a problem concerning the blood distribution of compounds which arehighly bound to plasma proteins. Let us imagine a compound is 98% bound toplasma 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 ... forexample). C is the concentration in cells, P the concentration in plasma andH = Hematocrit. For our specific case the calculation givesB/P=(0.01*0.44/0.99) + (1-0.44) = 0.56.If we calculate the fraction unbound to blood (fu,blood) using the classicalformula (see Gibaldi & Perrier, 2nd ed., Rev. and Expanded, p. 328) iefu,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 understandwhy fu,blood can be higher than fu,plasma ? Would it be possible thatfraction unbound to blood means (fraction bound to blood cells + fraction inplasma water). ?Any thoughts ?ThanksPascal Espié, UCB Pharma, Belgium`
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• On 1 Jul 2002 at 13:23:47, "Joseph Balthasar" (jb.-a-.acsu.buffalo.edu) sent the message
`Dear Pascal:I think that you may have mis-calculated your plasma and bloodconcentrations.Based on your example, consider 1 g of drug in 1 ml of whole blood (0.01 gfree 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 0.56ml. Let P = plasma concentration, C = concentration in cells, and B = wholeblood concentration.B = (0.01 g + 0.01 g + 0.99 g) / 1 ml = 1 g/mlP = (0.01 g + 0.98 g)/ 0.56 ml = 1.7678 g/mlC = 0.01 g / 0.44 ml = 0.0227 g/mlfu,p = 0.01 g/0.99 g = 0.0101fu,b = 0.01 g/1.00 g = 0.01So, 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) = 0.566Note that this is in agreement with the expected value from above (i.e., B/P= 1/1.7678 = 0.566).Hope this helps,J. BalthasarUniversity at Buffalo`
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• On 1 Jul 2002 at 14:18:24, "Joseph Balthasar" (jb.at.acsu.buffalo.edu) sent the message
`Dear Pascal:I believe that there may be a typo in the Gibaldi & Perrier equation thatyou cited: fu,b = fu,p / (Cb/Cp).Please consider the following...Mass free in Blood = Mass free in Plasmafu,b * Mass in blood = fu,p * Mass in plasmafu,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., missingthe (1-H) term).J. Balthasar`
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