Human physiologically based pharmacokinetic model for ACE inhibitors: ramipril and ramiprilat

1472-6904-6-1 1472-6904 Research article Human physiologically based pharmacokinetic model for ACE inhibitors: ramipril and ramiprilat Levitt G David levit001@umn.edu Schoemaker C Rik RSchoemaker@chdr.nl

Department of Physiology, University of Minnesota, 6-125 Jackson Hall, 321 Church St. S. E., Minneapolis, MN 55455, USA

Centre for Human Drug Research Zernikedreef 10, 2333CL Leiden, The Netherlands

BMC Clinical Pharmacology 1472-6904 2006 6 1 1 http://www.biomedcentral.com/1472-6904/6/1 16398929 10.1186/1472-6904-6-1 06 9 2005 06 1 2006 06 1 2006 2006 Levitt and Schoemaker; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Background

The angiotensin-converting enzyme (ACE) inhibitors have complicated and poorly characterized pharmacokinetics. There are two binding sites per ACE (high affinity "C", lower affinity "N") that have sub-nanomolar affinities and dissociation rates of hours. Most inhibitors are given orally in a prodrug form that is systemically converted to the active form. This paper describes the first human physiologically based pharmacokinetic (PBPK) model of this drug class.

Methods

The model was applied to the experimental data of van Griensven et. al for the pharmacokinetics of ramiprilat and its prodrug ramipril. It describes the time course of the inhibition of the N and C ACE sites in plasma and the different tissues. The model includes: 1) two independent ACE binding sites; 2) non-equilibrium time dependent binding; 3) liver and kidney ramipril intracellular uptake, conversion to ramiprilat and extrusion from the cell; 4) intestinal ramipril absorption. The experimental in vitro ramiprilat/ACE binding kinetics at 4°C and 300 mM NaCl were assumed for most of the PBPK calculations. The model was incorporated into the freely distributed PBPK program PKQuest.

Results

The PBPK model provides an accurate description of the individual variation of the plasma ramipril and ramiprilat and the ramiprilat renal clearance following IV ramiprilat and IV and oral ramipril. Summary of model features: Less than 2% of total body ACE is in plasma; 35% of the oral dose is absorbed; 75% of the ramipril metabolism is hepatic and 25% of this is converted to systemic ramiprilat; 100% of renal ramipril metabolism is converted to systemic ramiprilat. The inhibition was long lasting, with 80% of the C site and 33% of the N site inhibited 24 hours following a 2.5 mg oral ramipril dose. The plasma ACE inhibition determined by the standard assay is significantly less than the true in vivo inhibition because of assay dilution.

Conclusion

If the in vitro plasma binding kinetics of the ACE inhibitor for the two binding sites are known, a unique PBPK model description of the Griensven et. al. experimental data can be obtained.

Background

The angiotensin-converting enzyme (ACE) inhibitors are one of the worst characterized drug classes in terms of their quantitative pharmacokinetics and pharmacodynamics. There are a number of factors that complicate the analysis of this drug class:

1) The ACE enzyme in plasma and tissue has a very high affinity (sub nanomolar) for the ACE inhibitors. This produces extremely non-linear kinetics as the concentration falls from high concentrations when most of the drug is free, to low concentrations when most of the drug is bound to ACE.

2) Although it is known that more than 90% of the total ACE is in the tissues, the quantitative distribution of tissue ACE is not well characterized.

3) Although it is known that ACE has two sites with different inhibitor binding constants, the physiological values of these binding constants are not known.

4) The two ACE binding sites have different catalytic substrate selectivity. Predicting the pharmacodynamics of the ACE inhibitors requires knowledge of these substrate activities.

5) The rate of dissociation of the inhibitor from ACE is so slow (hours) that one cannot assume that there is instantaneous equilibrium between the free and bound inhibitor.

6) Assays of the ACE inhibition are unreliable because of uncertainties about the relationship between the in vivo inhibition and the inhibition measured in the standard ACE assay.

7) Most ACE inhibitors are administered orally in the form of a prodrug that is systemically converted to the active inhibitor. Prediction of the pharmacokinetics of the active form requires an understanding of the pharmacokinetics of the prodrug and drug and the details of the conversion of the prodrug to the active form in the liver and kidney.

This paper presents the first attempt to describe a quantitative human physiologically based pharmacokinetic model (PBPK) of the ACE inhibitors. The model describes the pharmacokinetics in terms of realistic human parameters such as the organ blood flows, tissue cellular and extracellular volume and cell membrane permeability. The model incorporates all of the complexities listed above. It is implemented in PKQuest, a general pharmacokinetic software routine that has now been applied to more than 25 different solutes with a wide range of pharmacokinetic properties 12345678. Many of the physiological parameters of the model have been determined previously by application of PKQuest to other drugs and are used directly without modification in this ACE inhibitor model. This includes the tissue blood flows, extracellular volume of distribution of the different tissues, and the tissue albumin concentration (which is important because of non-specific ACE inhibitor albumin binding).

Although it is now generally recognized that rational drug therapy should be based on the quantitative degree on tissue ACE inhibition 9, the dependence of the pharmacodynamic effect on plasma drug levels and ACE activity is still not clear 101112. Huge efforts have been directed at determining optimum dosage with limited results 13. It will be shown that this PBPK model has the potential to provide direct quantitative information about the time and dose dependence of the ACE inhibition in the different tissues.

It has been known for many years that inhibitor binding to ACE was of the "slow tight" class, with dissociation constants in the sub-nanomolar range, and time constants for release from the tight complex of many hours. Because of the non-linear binding curves, it was initially assumed that the binding of the inhibitor (R) to the free enzyme (E) was a two step process:

R + E ↔ R E L ⇄ R E T ( 1 ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqedmvETj2BSbqee0evGueE0jxyaibaieYdOi=BH8vipeYdI8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0lXdbba9pGe9qqFf0dXdHuk9fr=xfr=xfrpiWZqaaeaabiGaaiaacaqabeaabeqacmaaaOqaaiaadkfacqGHRaWkcaWGfbGaeyiLHSQaamOuamaaBaaaleaacaWGfbGaamitaaqabaGccqWIehcGcaWGsbWaaSbaaSqaaiaadweacaWGubaabeaakiaaxMaacaWLjaWaaeWaaeaacaaIXaaacaGLOaGaayzkaaaaaa@3F07@

with rapid formation of a loose complex (R_EL) followed by a slow conversion to the tight form (R_ET) 1415161718. When it was recognized that ACE had two homologous extracellular binding sites (referred to as the "N" and "C" terminal sites), it became apparent that the non-linearity resulted from the presence of these two sites and that the kinetics of each site could be described as a one step process characterized by two equilibrium dissociation constants K_Nand K_C(nM) and unbinding rate constants k_-Nand k_-C(1/min) 19:

R + E C ⇄ k − C k C R E C K C = k − C / k C R + E N ⇄ k − N k N R E N K N = k − N / k N ( 2 ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=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@67E4@

There is conflicting data about the interaction between the two sites (see 20 for recent discussion). In the most detailed experimental measurements of the ACE binding kinetics, Wei et. al. 19 found that the two sites acted independently in the binding of [³H]trandolaprilat. It is assumed here that the N and C site binding of ramiprilat is also independent.

The only quantitative kinetic measurements of K_iand k_-ifor ramiprilat binding to the two sites is at 4°C and 300 mM NaCl 21. Measurements of the rate of substrate hydrolysis indicates that, in going from 25°C and 300 mM Cl^-to 37°C and 120 mM Cl^-, the change in apparent K_iof ramiprilat is small because the temperature and chloride change tend to cancel each other 22. In the following analysis, as a first approximation, it will be assumed that the physiological (37°C and 100 mM Cl) binding constants for the two sites (eq. (2)) are equal to the experimental values at 4°C and 300 mM NaCl.

Although there have been some reports of different binding properties of plasma and tissue ACE 2324252627, the differences are small and could be an artifact of the difficulty of assaying these very high affinity ("tight") enzymes (see below). Since it has been established that the circulating ACE in the plasma is derived from the membrane bound tissue ACE by post-translational proteolytic cleavage 2829, it will be assumed, as a first approximation, that the circulating and tissue ACE are identical. (A major exception is testis ACE which contains only the C terminal domain binding site 21.) This is an important consideration because it allows one to use measurements of the fraction of the circulating plasma ACE that is occupied by bound inhibitor to determine the ACE inhibition in the different tissues – the clinically important factor.

Previous attempts to model the pharmacokinetics and pharmacodynamics of the ACE inhibitors have used compartmental models and were not physiologically based (i.e., using known organ blood flows, etc.) 3031323334. Toutain and colleagues have developed detailed compartment models and used them to accurately describe the non-linear pharmacokinetics/pharmacodynamics of a number of high affinity ACE inhibitors in animals 303132. The most important previous modeling of ramiprilat in humans is that of Brockmeier 3536 who recognized that the renal clearance of ramiprilat provided a direct measurement of the fraction that was free in plasma and used this measurement to estimate the physiological ramiprilat ACE binding constant. All of these earlier models have been limited by the assumption of a single ACE binding site and equilibrium binding and they have not attempted to model the processes involved in the conversion of the prodrug to the drug.

The PBPK model that is applied here to the ACE inhibitors is summarized in fig. 1. It has two features that are implemented for the first time in a PBPK model. The first is the use of a time dependent binding (eq. (2)) in each of the tissues, in place of the usual assumption of equilibrium binding. The second is the physiological model of the cellular uptake and intracellular conversion of ramipril to ramiprilat and the subsequent extrusion to the circulating blood. These features have been implemented in the freely distributed software program PKQuest 37.

Figure 1

PBPK model of the pharmacokinetics of prodrug ramipril (R) and active drug ramiprilat (D)

PBPK model of the pharmacokinetics of prodrug ramipril (R) and active drug ramiprilat (D). The figure schematically illustrates the events in three different tissues (typical "tissue", the liver and the kidney), the intestinal absorption, the renal clearance and enterohepatic recirculation.

The model is applied to the detailed pharmacokinetic analysis of ramipril (prodrug) and ramiprilat (the active dicarboxylic acid ACE inhibitor) previously described by van Griensven et. al38. This is an open, randomized, three-way cross-over study that measured: 1) the plasma ramiprilat following an intravenous (IV) ramiprilat infusion; 2) plasma ramipril and ramiprilat following an IV ramipril infusion; and 3) plasma ramipril and ramiprilat after oral ramipril. In addition, plasma ACE activity and the urinary excretion of ramipril, ramiprilat and the major metabolites were measured in all 3 arms. The requirement that a single PBPK model must be able to describe all these data sets places strong constraints on the model and severely limits the range of the allowed model parameters.

Methods

Notation

R, D – free, unbound, concentration of ramipril and ramiprilat, respectively.

k_N, k_C, k_-N, k_-C– association (1/(nM min)) and dissociation rate (1/min) rate constants for N terminal and C terminal ACE binding site.

K_N, K_C– equilibrium disassociation constant for N terminal and C terminal ACE binding site.

Cl – plasma clearance in terms of total plasma concentration.

Cl_u, Cl_R– free (unbound) and total arterial kidney ramiprilat clearance.

Cl_{int_L}, Cl_{int_K}– intrinsic liver and kidney clearance of ramipril in terms of free, unbound tissue concentration.

f_u, f_{u_cell}– fraction unbound in plasma and in intracellular water.

V_w– intracellular water volume.

P, S, Ps – Cell membrane permeability, surface area, and permeability coefficient (Ps = PS/V_w)

A_D, a, T – gamma function parameters describing intestinal absorption of ramipril (A_D= total amount absorbed.).

A_R, A_slow– amount of intestinal absorption in the form of ramiprilat and the slow ramipril absorption component.

The PBPK model

This section describes the main features of the model. See additional file ACE_supplemental_31oct05.doc (section I) for a detailed mathematical description. The arrangement of the different tissues is shown in fig. 2. The tissue parameters (blood flow, volumes, etc.) are listed in Table 1 and are identical to those used in previous applications of PKQuest 12345678. The connective tissue is divided between two organs: "tendon" with a relatively low blood flow, and "other" with a higher blood flow. The "standard" organ blood flows are assumed and the small changes in peripheral blood flow produced by ramipril 39 are neglected. ACE inhibitors do not produce a significant change in cardiac output 40.

Figure 2

Schematic diagram of the arrangement of the different tissues in the PBPK model

Schematic diagram of the arrangement of the different tissues in the PBPK model. The organ "portal" refers to all the organs drained by the portal vein. The connective tissue is divided between two organs: "tendon" with a relatively low blood flow and "other" with a higher blood flow.

Table 1

Standard human population PBPK organ parameters (not varied).

Organ

Weight (Kg)

ECF water(L)

Flow (L/min)

ACE Tiss/Plasma

Ramiprialat Ps (min^-1)

Ramiprilat fu_cell

Ramipril Ps (min^-1)

Ramipril fu_cell

Blood

5.5

2.68345

0.52

----

liver

1.8

0.2898

0.45

1.37

Adjustable

infinite

0.1

portal

1.5

0.351

1.125

2.0

----

0.05

0.5

muscle

3.042

0.585

1.0

----

0.05

0.5

kidney

0.31

0.04092

1.24

5.62

Adjustable

infinite

0.01

brain

1.4

0.784

0.8

----

0.05

0.5

heart

0.33

0.066

0.264

1.7

----

0.05

0.5

lung

0.536

0.08576

5.6184

----

0.05

0.5

skin

2.6

1.092

0.26

3.51

----

0.05

0.5

tendon

2.55

0.03

7.23

----

0.05

0.5

other

5.524

3.75632

0.1104

5.79

----

0.05

0.5

bone

----

0.5

adipose

17.5

3.5

0.7385

6.81

----

0.05

0.5

Total

17.4572

5.5877

Figure 1 shows a more detailed view of the model that focuses on 3 tissues: the liver, kidney, and one representative "tissue" region. "D" is the free prodrug (ramipril) concentration, and "R" is the free active drug (ramiprilat) concentration. The top square, labeled "tissue" shows the kinetic processes in a typical tissue region. Both the highly water soluble ramiprilat (R) and the tissue ACE binding sites are restricted to the extracellular space (EC). (Exceptions are the liver and kidney which have ramiprilat cell membrane transport systems.) The fraction of tissue volume that is extracellular has been determined previously 6. As described in eq. 2, it is assumed that ACE has two non-interacting binding sites (labeled as "C" and "N" terminal) with different ramiprilat binding constants 1921 (only one binding site is shown in fig. 1). The binding for each site is characterized by the two parameters: k_-ithe unbinding rate constant; and K_ithe dissociation equilibrium constant (k_i= k_-i/K_i). The amount bound is described quantitatively by the differential equations:

d ( R E C ) d t = k C R E C − k − C R E C d ( R E N ) d t = k N R E N − k − N R E N ( 3 ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=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@6516@

There is also a non-specific, non-saturating equilibrium ACE inhibitor binding to the plasma and tissue albumin (A) characterized by the albumin binding constant (B_R):

R + A ↔ B R R A R A = ( B R A ) R ( 4 ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaafaqabeqacaaabaGaemOuaiLaey4kaSIaemyqae0aa4anaSqaaiabdkeacnaaBaaameaacqWGsbGuaeqaaaWcbeGccaGLugcacqWGsbGudaWgaaWcbaGaemyqaeeabeaaaOqaaiabdkfasnaaBaaaleaacqWGbbqqaeqaaOGaeyypa0JaeiikaGIaemOqai0aaSbaaSqaaiabdkfasbqabaGccqWGbbqqcqGGPaqkcaaMc8UaemOuaifaaiaaxMaacaWLjaWaaeWaaeaacqaI0aanaiaawIcacaGLPaaaaaa@4579@

As describe in the additional file 1 ACE_supplemental_31oct05.doc (section I), the amount of albumin binding in the different tissues can be determined from the experimental value for the fraction of albumin bound ramiprilat in plasma (= 0.56 41) and the previously determined "standard human" PKQuest values for the tissue extracellular albumin 6. This supplemental file section also describes in more detail how the above relations for ramiprilat are incorporated into the PKQuest PBPK routine.

Additional File 1

Section I: Detailed derivation of mathematical description of slow tight binding solutes. Section II: Derivation of relationship between 60 minute ACE assay and true in vivo ACE activity. Section III: Analysis of the sensitivity of the model predictions to parameter variations for IV ramiprilat. Section IV: Analysis of the sensitivity of the model predictions to parameter variations for IV and oral ramipril.

Click here for file

The PBPK analysis indicates that ramipril has a finite cell membrane permeability that allows it to enter the intracellular space (IC) (see fig. 1, "tissue"). This is consistent with the relatively high octanol/water partition coefficient at pH 7 of 1.12 of ramipril, one hundred fold greater than that of ramiprilat (0.011) 42. The rate of exchange between the intracellular and extracellular space is determined by two parameters: 1) the cell membrane permeability coefficient (Ps); and 2) the fraction of intracellular solute that is unbound (f_{u_cell}):

d ( D ' ) d t = f u _ c e l l P s ( D − D ' ) P s = P S / V w ( 5 ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaafaqabeqacaaabaWaaSaaaeaacqWGKbazcqGGOaakcqWGebarcqGGNaWjcqGGPaqkaeaacqWGKbazcqWG0baDaaGaeyypa0JaemOzay2aaSbaaSqaaiabdwha1jabc+faFjabdogaJjabdwgaLjabdYgaSjabdYgaSbqabaGccqWGqbaucqWGZbWCcqGGOaakcqWGebarcqGHsislcqWGebarcqGGNaWjcqGGPaqkaeaacqWGqbaucqWGZbWCcqGH9aqpcqWGqbaucqWGtbWucqGGVaWlcqWGwbGvdaWgaaWcbaGaem4DaChabeaaaaGccaWLjaGaaCzcamaabmaabaGaeGynaudacaGLOaGaayzkaaaaaa@54D5@

where D and D' are the free extracellular and intracellular ramipril concentration and Ps is the cellular permeability coefficient (P = permeability, S = surface area, and V_w= intracellular water volume). Extracellular ramipril is also bound to albumin, similar to the binding of ramiprilat (eq. (4)).

The ramiprilat and ramipril kinetics discussed above and illustrated in fig. 1 for the box labeled "tissue" is present in all the tissues, including the liver and kidney and central venous and arterial compartment (binding not shown in fig. 1). Each tissue i is characterized by 3 parameters: 1) total ACE concentration (ACE_i) with two sites per each ACE molecule (Et_Cⁱ= Et_Nⁱ= ACE_i); 2) ramipril cell membrane permeability coefficient (Ps_i) and 3) intracellular ramipril binding (f_{u_cell}). In addition, the ramiprilat liver and kidney Ps and f_{u_cell}must be defined. The ramiprilat ACE binding constants (K_N, K_C, k_-N, k_-C) are assumed to be identical for all tissues.

Both the liver and kidney metabolize the intracellular ramipril (D'). As shown in fig. 1, the liver metabolizes ramipril to ramiprilat (R') and to a number of other metabolites (indicated by M). Three parameters characterize this metabolism: the intrinsic liver (Cl_{int_L}) and kidney (Cl_{int_K}) clearance and the fraction of total liver ramipril metabolism that is converted to ramiprilat (Fr_L). (1- Fr_Lis converted to other metabolites). It is assume that all the ramipril metabolized by the kidney is converted to ramiprilat. The rate that the liver converts intracellular ramipril (free concentration = D') to intracellular ramiprilat (R') is:

Q_R= Cl_{int_L}Fr_LD' (6)

All the intracellular ramiprilat generated by the liver and kidney eventually enters the systemic circulation (see eq. (5)). The intrinsic clearance is in terms of the free concentration. For a flow limited, well stirred tissue, the absolute clearance (Cl) can be approximately related to the intrinsic clearance (Cl_int) in terms of the organ flow (F), and fraction unbound (f_u):

Cl = f_uCl_intF/(F + f_uCl_int) (7)

As illustrated in fig. 1, the extracellular ramiprilat is not metabolized or excreted by the liver. The only excretory pathway removing ramiprilat is the renal excretion (Q_kidney) which is assumed to be proportional to the free, unbound, arterial ramiprilat concentration (R_art):

Q_kidney= Cl_uR_art (8)

Where Cl_uis the unbound renal clearance. The unbound concentration is related to the total arterial plasma concentration (R_{T_art}) by the fraction unbound in arterial plasma (f_u):

Q_kidney= Cl_uR_art= Cl_uf_uR_{T_art}= Cl_RR_{T_art} Cl_R= f_uCl_u (9)

where Cl_Ris the renal total plasma clearance. Because of the highly non-linear ramiprilat binding that results from saturation of the ACE binding sites, the total renal clearance (Cl_R) is non-linear: at high concentrations when most of the ramiprilat is free (f_u→ 1), the clearance is equal to the intrinsic unbound clearance (Cl_R≈ Cl_u≈ 0.4 l/min), while at long times and low concentrations, when most of the ramiprilat is bound, the clearance falls to values less than 0.02 l/min 3536.

The observed delay in the systemic appearance of ramiprilat after either an oral or IV ramipril input depends on the processes involved in the liver and kidney ramipril cellular uptake, intracellular conversion to ramiprilat and then transport to the plasma. These processes have been directly identified in an extensive series of investigations of Pang and colleagues on the behavior of enalapril and enalaprilat in perfused rat liver, kidney and intestine 43444546474849.

Although there was an initial report that the intestinal absorption was carrier mediated 50, Morrison et. al. 51 have clearly shown that the absorption of enalapril is primarily a non-saturable, passive diffusion process. There are three different components for absorption of oral ramipril (fig. 1). The major component is direct absorption of ramipril into the portal circulation where it is subject to first pass metabolism. This component is described by the 3 parameter gamma distribution (A_D, T, a):

I(t) = A_Db^at^a-1exp(-bt)/Γ(a) b = a/T (10)

where A_Dis the total amount absorbed, Γ is the gamma function, a is the dimensionless gamma number and T is a time constant. For most drugs this 3 parameter function provides a good description of the time delay in oral absorption produced by gastric emptying 5. The three parameters A_D, a and T are adjusted for each subject. Pang et. al. 48 have shown in the rat that there is a second component in which some of the oral ramipril can be directly converted to ramiprilat either in the lumen or the intestinal epithelial cells and absorbed into the portal blood. This second component produces a more rapid systemic appearance of ramiprilat than the first component because it bypasses the slower processes involved in the liver and renal production of ramiprilat from ramipril. It is assumed that this ramiprilat absorption has the same time course as the major ramipril component (eq. (10)) with the same values of a and T and a value of A (= A_R) about 10% that of A_D. Finally, in some subjects it was necessary to add a second, much slower rate of ramipril absorption that was described by a constant rate that extended from 200 to 3000 minutes:

I ( t ) = { 0 t < 200 I o 200 < t < 3000 0 t > 3000 } I 0 = A s l o w / ( 3000 − 200 ) ( 11 ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaafaqabeqacaaabaGaemysaKKaeiikaGIaemiDaqNaeiykaKIaeyypa0ZaaiWaaeaafaqabeWacaaabaGaeGimaadabaGaemiDaqNaeyipaWJaeGOmaiJaeGimaaJaeGimaadabaGaemysaK0aaSbaaSqaaiabd+gaVbqabaaakeaacqaIYaGmcqaIWaamcqaIWaamcqGH8aapcqWG0baDcqGH8aapcqaIZaWmcqaIWaamcqaIWaamcqaIWaamaeaacqaIWaamaeaacqWG0baDcqGH+aGpcqaIZaWmcqaIWaamcqaIWaamcqaIWaamaaaacaGL7bGaayzFaaaabaGaemysaK0aaSbaaSqaaiabicdaWaqabaGccqGH9aqpcqWGbbqqdaWgaaWcbaGaem4CamNaemiBaWMaem4Ba8Maem4DaChabeaakiabc+caViabcIcaOiabiodaZiabicdaWiabicdaWiabicdaWiabgkHiTiabikdaYiabicdaWiabicdaWiabcMcaPaaacaWLjaGaaCzcamaabmaabaGaeGymaeJaeGymaedacaGLOaGaayzkaaaaaa@6746@

where A_slowis the total amount absorbed by this component. In summary, the oral absorption is characterized by 5 parameters: A_D, A_R, A_slow, a and T (see Table 4).

Table 4

Intestinal absorption parameters for oral ramipril: 1) the major ramipril absorption component (gamma function, A, a, and T); 2) a slow, long ramipril component (A_slow); and 3) direct intestinal conversion and absorption of ramiprilat (gamma function, A_R, a and T). The total oral dose is 2.5 mg (6010 nanomoles). The total amount absorbed = A + A_slow+ A_R.

Subject

Ramipril- Major component

Slow absorp. Amount A_slow(nmole)

Ramprilat Amount A_R(nmole)

Total Absorption (nmole)

Amount (A) (nmole)

Time const. (T) (min)

Gamma (a)

2500

787

200

3487

1200

367

1627

1600

432

2062

1400

3.2

100

1500

1800

100

1900

800

320

1161

2100

756

200

3056

2200

100

2300

1800

5.5

100

1900

1100

346

100

1546

2700

400

3100

Ave (SD)

1745 (597)

55.1 (20.1)

4.4 (2.3)

273 (301)

130 (105)

2149 (755)

All of these features were incorporated into PKQuest and can be activated using a simple interactive menu. The parameters describing the individual PBPK models of each of the two solutes (ramipril and ramiprilat) are entered first. The two solutes are then coupled by defining the parameters V_max[i,j,m] and K_m[i,j,m] which are the Michaelis-Menten parameters for metabolism of substrate i to product j in tissue m. It is assumed that the ramipril metabolism is liner, so that Km is set to a very large value and V_maxis set equal to K_mCl_int. An arbitrary number of substrates and products are allowed. Most of the figures used in this paper represent standard PKQuest output.

Model parameters

The PBPK model is characterized by a large number of parameters. Most of these parameters are fixed and are identical for all subjects (see Table 1). In addition there are 12 parameters that are adjusted (see below) to fit the data for each subject: 4 characterizing the ramiprilat pharmacokinetics (Table 2); 3 characterizing the ramipril metabolism (Table 3); and 5 characterizing the ramipril intestinal absorption (Table 4). A brief description of these parameters is listed here:

Table 2

Ramiprilat Adjustable PBPK Parameters: Intrinsic renal clearance, ACE plasma concentration, and liver and kidney cell membrane permeability coefficient. The "average weighted residual error" of the PBPK model for the IV ramiprilat input is listed in the last column.

Subject

Renal Clear. Cl_u(l/min)

ACE_plasma(nM)

Membrane Permeability (Ps min^-1)

IV Ramiprilat Ave. Error

Liver

Kidney

0.55

1.5

0.015

0.0003

0.11

0.4

2.35

0.007

0.0015

0.10

0.4

1.65

0.018

0.001

0.17

0.55

1.13

0.01

0.0006

0.16

0.4

1.25

0.015

0.002

0.27

0.7

2.25

0.01

0.0006

0.18

0.4

2.9

0.01

0.0006

0.11

0.37

1.75

0.008

0.0003

0.32

0.45

1.45

0.015

0.002

0.13

0.45

1.4

0.01

0.0003

0.30

0.4

2.25

0.006

0.0003

0.14

Ave (SD)

0.46 (0.10)

1.81 (0.55)

0.011 (0.0039)

0.00086 (0.00067)

0.18 (0.08)

Table 3

Ramipril adjustable PBPK parameters: 1) intrinsic liver clearance (Cl_{int_L}); 2) intrinsic kidney clearance (Cl_{int_K}; 3) the fraction of the liver ramipril clearance that is converted to systemic ramiprilat. The "average weighted residual error'' of the PBPK model plasma ramiprilat following either IV or oral ramipril is listed in the last two columns.

Subject

Cl_{int_L}(l/min)

Cl_{int_K}(l/min)

Fraction to ramiprilat

IV Ramipril Ave. Error

Oral Ramipril Ave. Error

4.8

1.2

0.1

0.2

0.23

1.5

0.32

0.17

0.25

3.6

0.9

0.4

0.23

0.27

0.0

0.17

Poor fit

0.25

0.23

0.28

0.2

0.14

5.5

0.4

0.13

0.22

3.48

0.52

0.2

0.12

0.38

3.5

1.5

0.4

0.30

0.34

2.8

1.2

0.3

0.23

0.14

6.16

0.84

0.2

0.13

0.2

Ave (SD)

3.62 (1.5)

1.06 (0.53)

0.25 (0.13)

0.19 (0.057)

0.24 (0.077)

Ramiprilat ACE binding kinetics

The values determined by Deddish et. al. 21 at 4°C and 300 mM NaCl were used as the default "standard" values for all subjects (see eq. (2)): N site (low affinity): K_N= .276 nM; k_-N= 0.0234/min; C site (high affinity): K_C= 0.039 nM; k_-C= 0.00168/min.

Plasma and tissue ACE concentration

The ACE concentration in normal human plasma determined using a radioimmunoassay varies from 220 to 730 ng/ml 2952. (A single genetic polymorphism accounts for 50% of this normal variation). This corresponds to 1.29 to 4.29 nM, assuming a molecular weight of circulating ACE of 170 kDa 53. The plasma ACE (ACE_plasma) in the PBPK model is a variable parameter, adjusted to optimize the fit to the experimental data. The model values varied from 1.13 to 2.9 nM for the different subject (Table 2). This is the lower end of the experimental range for humans. The tissue ACE is defined by a standard tissue/plasma ratio (listed in Table 1) and is identical for all subjects. The lung, liver, heart, brain and GI tract ratios are in rough agreement with experimental measurements in rats or rabbits 23545556. The skeletal muscle values are based on needle biopsy measurements in humans 5758. Although there are high ACE concentrations in the kidney, most of this activity is in the lumen of the proximal tubule 59, a region that will have limited and slow contact with the circulating ACE inhibitor 56. The total tissue ACE is 68 times the blood ACE. An essential qualitative feature of the PBPK modeling is the requirement for this large total ACE tissue/blood ratio (see Results). High ACE concentrations have been assigned to the loose connective tissue organs ("tendon" and "other") and to "adipose" tissue based on the observation of Sun et. al. 60 that there was high ACE concentration in subcutaneous connective tissue. Especially important is the high adipose tissue/plasma value of 6.8 because adipose tissue makes a large contribution to the pharmacokinetics because of it large weight (Table 1). Although there is no quantitative adipose date in humans, it has been shown that ACE mRNA is expressed in human adipose tissue 61. In rats, the subcutaneous fat/plasma ramiprilat binding ratio at 24 hours after an oral dose was about 5 41.

Ramiprilat renal clearance

The intrinsic renal clearance (Cl_u, eq. (9)) was adjusted to fit the data for each subject (Table 2).

Ramiprilat liver and kidney cell membrane permeability and intracellular binding

The product of the two parameters f_{u_cell}and Ps determines the rate that the intracellular ramiprilat formed from ramipril enters the systemic circulation (eq. (5)). The value of f_{u_cell}for the kidney and liver were assigned arbitrary large values, corresponding to a low binding (Table 1) and the values of Ps were adjusted for each subject (Table 2) to fit the experimental data.

Ramipril liver cell membrane permeability and intracellular binding

The ramipril Ps is finite for all tissues, allowing ramipril to distribute in all the body water. The value of f_{u_cell}determines the equilibrium volume of distribution and Ps determines the time course of this equilibrium. The fixed values listed in Table 1 were assigned to provide optimal fits to the IV ramipril input.

Ramipril metabolic parameters

The intrinsic liver (Cl_{int_L}) and kidney (Cl_{int_K}) clearance and the fraction of the liver clearance that is converted to ramiprilat (Fr_L) were adjusted for each subject to fit the oral and IV ramipril data (Table 3).

Ramipril intestinal absorption parameters

The values of the 5 parameters describing the intestinal ramipril absorption (A_D, a, T, A_R, A_slow, eqs. (10) and (11)) were adjusted to fit the individual subject data (Table 4).

ACE assay

It is well recognized that the standard ACE plasma assay in the presence of inhibitors may give a result that differs significantly from the in vivo plasma activity 356263. The problem arises from the dilution and time dependent effects that become important for the very tight and slow ACE binding. In order to compare the experimental plasma assay measurements with the PBPK model predictions of the fraction of plasma ACE that is complexed with inhibitor, it is necessary to develop a detailed kinetic model of the assay procedure. The following analysis is similar to that of Weisser and Schloos 63, except that they assumed rapid, equilibrium binding, while this analysis use the more general time dependent binding model (eq. (3)).

The ACE assay of the ramipril study used the Vertex kit ACE assay 17 in which a 10 fold dilution of plasma is incubated with 8 mM of the substrate p- [³H]benzoylglycylglycylglycine for 60 minutes at 37°C in 100 mM NaCl. Using the same notation as in eq. (2):

I + E C ⇄ k − C k C I E C S + E C ⇄ K s C S E C → k c a t C P + E C S E C = S E C / K s C I + E N ⇄ k − N k N I E N S + E C ⇄ K s N S E N → k c a t N P + E N S E N = S E N / K s N E t C = E C + I E C + S E C E t N