Plasma clearance parameter

[teutonicod]

Dear all,

In the unspecified liver clearance process in PK-Sim, the intrinsic clearance for the liver is calculated using several parameters, one of them being referred to as Plasma clearance. Do you know how this parameter is defined? In a simple model (IV bolus and only unspecified clearance) the value for this Plasma clearance does not coincide with the Total body clearance in the PK-Analysis section, do you have an explanation for the difference of these parameters? Thanks you in advance for your help!

Best regards,

Donato

[msevestre]

Hi @teutonicod,

The plasma clearance is as far as I can tell from your description the input parameter from the clearance process. e.g. this is what the user enters in the system. PK-Sim then calculates, using a well-stirred model, the specific clearance. see here for details

In order to calculate the Plasma clearance in the PK-Analysis section, PK-Sim uses the last 10% of the curve. Please make sure you have simulated long enough. My suggestion would be to increase your simulation time and then check to see if the values are similar

Hope that helps

[teutonicod]

Hi @msevestre ! Thanks for your reply! I tried but I still get two different values. I created a dummy project, so I can share it if needed, for now I have included the screenshots of the parameters.

[msevestre]

@teutonicod Can you try with a 30 min infusion? CL is calculated using AUCInf and most of the AUC comes from the bolus at the beginning.

[Christoph27]

I don't expect that the two plasma clearances are exactly equal. As Michael wrote, the input parameter "plasma clearance" is converted to an intrinsic clearance assuming a well stirred model (cf. e.g. "Yang, J., et al., Drug Metabolism and Disposition 35.3 (2007): 501-502." for the equation used and a discussion of the assumptions). This intrinsic clearance is then used in a PBPK model and the resulting total plasma clearance is different depending on compound properties and if the clearance is high or low.

[teutonicod]

Thank you vary much @Christoph27 and @msevestre for your answers!

[Christoph27]

If I look at the current implementation, there seems to be additionally something else than the above mentioned difference between PBPK and well stirred assumptions: If you add a "Total Hepatic Clearance" process, the clearance rate contains a factor of ~ 1.5 µmol/L corresponding to the concentration of an undefined liver enzyme. However, when CL/[Enzyme] is calculated, an enzyme concentration of 1 µmol/L is assumed. Thus it seems that currently the used CL/[Enzyme] is too high by a factor of ~ 1.5 relative to the given input parameter "plasma clearance" for a "Total Hepatic Clearance" process. It seems that the factor ~1.5 was introduced in order to get the same total plasma clearance with the same specific intrinsic clearance regardless of using a "Total Hepatic Clearance" process or a clearance process with a metabolizing enzyme.

[sfrechen]

The retrograde calculation from plasma clearance to specific clearance corrects for f_cell of the liver(fraction intracellular): CLspec = CL_pls BW (Q_liv+Q_pve) / (fu (Q_liv+Q_pve - CL_pls / B2P BW) V f_cell)

For me, this needs to be corrected as intrinsic clearance would be: CL_int = CLspec (E / f_cell) V * f_cell where E is the hypothetical enzyme concentration of 1 µmol/L (of an unknown enzyme) in mixed liver tissue. Thus, f_cell cancels out and we would obtain:

CLspec = CL_pls BW (Q_liv+Q_pve) / (fu (Q_liv+Q_pve - CL_pls / B2P BW) * V)

With this equation, your PBPK plasma clearance (output) would be approximately equal to your input plasma clearance (at least for compounds where the wll-stirred assumptions hold approximately true).

Work around: set f_cell in the building block of your molecule to 1 in the "total hepatic clearance" process.

[msevestre]

@Yuri05 @sfrechen Anything to change here? If not, please close the issue

[Yuri05]

Anything to change here?

From my point of view: not. @sfrechen please comment

[teutonicod]

Please check with @Christoph27 as well, since in his message he also mention a point which is quite important. Let me know if you need help from my side.

Donato

[sfrechen]

I would say: yes. Do not correct for f_cell in the CLspec equation.

[Christoph27]

I agree, "Total Hepatic Clearance" is currently not doing what I would expect.

[msevestre]

As far as I remember, this was added on purpose a while ago to solve another problem. I don't have access to SVN anymore or youtrack but maybe the reason cab be found?

Was it to ensure that the same value of clspec in a total plasma clearance process vs intrinsic clearance would produce the same results?

[Christoph27]

Might be the reason (I was not involved in that previous discussion) but that is at the cost of an larger deviation of the resulting PBPK clearance from the clearance used as input parameter than needed. Why do we have then the "Total Hepatic Clearance" process at all?

[teutonicod]

I agree with @Christoph27 , I think we need to decide if at all keep this "Plasma clearance" entry in the "Total plasma clearance". Since it can be very misleading. If we think that a back calculation of the clearance with the well stirred model can be useful, I would propose to correct the formula and rename the entry. But I am still unsure on the utility of such a back calculation

[msevestre]

it seems that the factor ~1.5 was introduced in order to get the same total plasma clearance with the same specific intrinsic clearance regardless of using a "Total Hepatic Clearance" process or a clearance process with a metabolizing enzyme.

Yes this is correct If we remove the f_cell, suddenly the same value of CL_Spec would produce two different curves, which is probably more of an issue don't you think?

As to why we have a Total Plasma Clearance process. They are a few reasons

1. This was the input that we had in the old PKSim v4.x
2. The concept of specific clearance is far from trivial and typically hard to understand for new users. Using a plasma clearance as a first step in learning the program was a requested feature
3. If someone has a value for a Total plasma clearance, inputting it in the field can give a rough estimate as to what the CL_spec might be.

If we think that a back calculation of the clearance with the well stirred model can be useful, I would propose to correct the formula and rename the entry.

@teutonicod I don't understand what you mean

[Christoph27]

Just to clarify: I'm fine with having a "Total Hepatic Clearance" process which uses a well stirred model and a total plasma clearance as input. But what is currently implemented is something else (and probably not what we had in the old PKSim v4.x) with an additional factor ~1.5. I don't see the issue with "same value of CL_Spec would produce two different curves" since the enzyme concentration is implicitly different.

[msevestre]

I don't see the issue with "same value of CL_Spec would produce two different curves"

Not really. If you define an enzyme in the individual with a RelExp of 1 in liver and a Ref Conc of 1 (similar to our undefined liver enzyme created), then the same Cl_spec would produce different results, which is definitely weird.

Again, I am happy to revert the changes. I just want to make sure that we understand that the changes were added for a specific reason.

[Yuri05]

As far as I understood @sfrechen : his suggestion was to remove *f_cell in the calculation CLSpec=f(CL_pls,...). Thus, same CLSpec in plasma and in a enzymatic process would still lead to the same clearance rate.

[msevestre]

Even better then :)

[teutonicod]

@msevestre, what I meant was to correct the formula as suggested by @sfrechen , but I was also wandering if we should leave the naming Plasma clearance as it is, since from my point of view, this is not clear at all.

From my understanding, the parameter Plasma clearance is a back calculation, where a total hepatic clearance is used to calculate the intrinsic clearance, according to the equation mentioned by @Christoph27 (Yang, J., et al., Drug Metabolism and Disposition 35.3 (2007): 501-502). Checking this publication, I think that this input parameter would be actually a total liver clearance, so not sure that Plasma clearence is the best way to refer to such parameter.

[msevestre]

From my understanding, the parameter Plasma clearance is a back calculation,

I have the feeling we are not talking about the same parameter lol. the Plasma Clearance is an input. This is not derived in any shape or form from other parameters

I think that this input parameter would be actually a total liver clearance, so not sure that Plasma clearence is the best way to refer to such parameter.

No opinion on that. This was named by our experts so I don't want to open a can of worms here :)

[teutonicod]

@msevestre, I agree, I also had the feeling we were talking about two different parameters (thatś why I clrarly stated the name of the parameter I was referring to ;-)). But this was the parameter my post was originally about, so I was hoping we could also solve this issue :-) (if we think that there is an issue to solve, of course).

Let's see what the other members think about the plasma clearance. I also agree that it does not have any impact, so also wondering on the utility of such parameter.

Also, I would suggest that we mention clearly which equation are we suggesting to change, so that we are all on the same page.

[msevestre]

@teutonicod

This is an INPUT parameter. No backcalculation. If this is the parameterm you mean, then I don't understand what you mean :)

[teutonicod]

Sorry, but I do not have PK-Sim with me, so I may have confused the parameters. I will check that tomorrow.

[sfrechen]

From my point of view, we just need to ajust the formula with regard to back calculation. Naming etc. is fine for me. The process' name tells us that we assume that total plasma clearance equals hepatic plasma clearance.

Maybe a tooltip could be helpful to inform the user about the wll-stirred back calculation and its assumptions (but not necessary...).

[Christoph27]

I agree with Sebastian regarding naming and a possible tooltip

[teutonicod]

The process' name tells us that we assume that total plasma clearance equals hepatic plasma clearance.

From my point of view this was not very clear. But if it is just me, we can leave it as it is. Nevertheless I would strongly suggest updating the tooltip of the parameter Plasma clearence itself, since for now this is what we have :-)

[dzianismr]

Hi Folks,

I was looking into the descrepancy between inputed and calculated CL in PK-Sim, when I came accross this thread. It looks like @sfrechen pinpoint the issue to f_cell in the formula. However PK-Sim 11 still has the same formular. Any thoughts/updates on the topic?

[ReneGeci]

Unfortunately, this bug still persists @Yuri05.

As explained at the beginning of this post (by @sfrechen and @Christoph27), the bug is that when a user creates a "Total Hepatic Clearance"-Process by using a "Plasma Clearance" input value (say 0.5 ml/min/kg) then PK-Sim creates a Clearance process that is +50% too strong (e.g. PK-Analysis would then after simulation show that (Oberved) "Total Plasma clearance" was 0.75 ml/min/kg instead of the desired 0.5 ml/min/kg).

The reason for this is, as outlined before, that PK Sim creates an "undefined" (dummy) liver enzyme in the intracellular space (which has fraction of 0.667). The initial concentration of that "undefined enzyme" in the intracellular space is then ~ 1.5 µmol/L:

... because the relative expression is scaled up by dividing through the fraction intracellular:

This value (here "CP") is then multiplied with the CLspecPerEnzyme...

... which results in a +50% too strong clearance in the model simulation.

As far as I can see there are 3 ways to fix this:

1. Doing what @sfrechen suggested, which is to get rid of the "f_cell" term in the "Specific clearance" formula:

Then Specific Clearance is not divided by 0.667 (so 50% lower) and consequently the observed clearance will be what is expected by the user.

2. Is an idea that @PavelBal suggested, which is to get rid of "CP" in formula 1 (at the top) for the Total Hepatic Clearance process. If the other terms are not multiplied by 1.5, then the user also gets the expected behaviour.

3. Another thing that came to my mind, but I am unsure if that makes sense, is to set the "Enzyme concentration" value that is used to calculate "ClspecPerEnzyme" to 1.5 µmol/L (instead of currently 1):

Then the "ClspecPerEnzyme" would be 50% lower and, again, the user gets the expected behaviour.

I do not understand PK-Sim and the downstream implications of these changes well enough to judge which one is the best fix, but the current behaviour is not what a user would want.

[PavelBal]

@sfrechen @Yuri05 @msevestre

Should we implement the "fix" by removing the CP from the equation? I would actually get rid of the "Unspecific liver" enzyme completely and define the reaction with container criteria.

This will of course be a "breaking change" as old models will behave differently (higher clearance).

[sfrechen]

2. Is an idea that @PavelBal suggested, which is to get rid of "CP" in formula 1 (at the top) for the Total Hepatic Clearance process. If the other terms are not multiplied by 1.5, then the user also gets the expected behaviour.

What do you mean wirh get rid of "CP"? This is the user inout parameter -> how do you want to get rid of it?

Anyway, I believe this tool here allows the user to quickly set-up an hepatic clearance in case a plasma clearance for a compound is known (under the assumption of a well-stirred liver model). I consider this being useful (once the equation is corrected for f_cell as outlined above).

[ReneGeci]

@sfrechen, i will leave it up to @PavelBal to discuss the technicalities of "getting rid of the CP".

just to make sure i am not misunderstood: i also consider this to be a highly useful tool. the reason i am bringing it up again is exactly because i am using it.

[PavelBal]

@sfrechen I think we are suggesting the same, just in the different steps... The liver clearance reaction rate is given as

1. Clearance rate = CP * CLspecPerEnzyme * M * K_water,

with CP being the concentration of the Unspecific liver enzyme, which is refConc * f_cell = 1/f_cell because the reference concentration is always 1. So we get

2. Clearance rate = 1/f_cell * (CLspec / EnzymeConcentration) * M * K_water

where EnzymeConcentration is the input parameter (by default 1 µmol/l)

3.

Clearance rate = 1/f_cell * (
CL_pls * BW * (Q_liv+Q_pve) / (fu  * (Q_liv+Q_pve - CL_pls / B2P* BW) * V * f_cell))
 / EnzymeConcentration(=1)) * M * K_water

I propose to remove CP from 1., you propose to remove f_cell from 3. I favor 1. because then we could remove the Unspecific liver enzyme completely from the model.

To prove that this correction makes sense:

1. I Opened the Alfentanil project and replaced the GFR and enzyme-mediated clearance with Liver plasma clearance. When I enter 3.5 ml/min/kg as input clearance value and simulate, the calculated plasma clearance is 4.6:

1. I corrected the input by dividing by 1.5, the value of CP in the default model 3.5 / 1.49925037481259 = 2.3345. Now the calculated plasma clearance is 3.2 which is much closer to "3.5" what I actually wanted to have.

[sfrechen]

@PavelBal Ok, sorry, my mistake. I just considered CP as "Clearance plasma" without really checking what it actually is. Thanks for clarifying. Indeed, both suggestions are then structurally identifical. I leave it to the developer team to decide :)