Quantitative model for the blood pressure‐lowering interaction of valsartan and amlodipine

Abstract

Aims

The objective of this study was to develop a population pharmacokinetic (PK) and pharmacodynamic (PD) model to quantitatively describe the antihypertensive effect of combined therapy with amlodipine and valsartan.

Methods

PK modelling was used with data collected from 48 healthy volunteers receiving a single dose of combined formulation of 10 mg amlodipine and 160 mg valsartan. Systolic (SBP) and diastolic blood pressure (DBP) were recorded during combined administration. SBP and DBP data for each drug alone were gathered from the literature. PKPD models of each drug and for combined administration were built with NONMEM 7.3.

Results

A two‐compartment model with zero order absorption best described the PK data of both drugs. Amlodipine and valsartan monotherapy effects on SBP and DBP were best described by an I _max model with an effect compartment delay. Combined therapy was described using a proportional interaction term as follows: (D₁ + D₂) +ALPHA×(D₁ × D₂). D₁ and D₂ are the predicted drug effects of amlodipine and valsartan monotherapy respectively. ALPHA is the interaction term for combined therapy. Quantitative estimates of ALPHA were −0.171 (95% CI: −0.218, −0.143) for SBP and −0.0312 (95% CI: −0.07739, −0.00283) for DBP. These infra‐additive interaction terms for both SBP and DBP were consistent with literature results for combined administration of drugs in these classes.

Conclusion

PKPD models for SBP and DBP successfully described the time course of the antihypertensive effects of amlodipine and valsartan. An infra‐additive interaction between amlodipine and valsartan when used in combined administration was confirmed and quantified.

What is Already Known about this Subject

• Due to differences in their mechanisms of action, amlodipine (CCB) and valsartan (ARB) are often used in combination to reduce blood pressure.

• Combination therapy is known to be less effective than expected from adding two independent monotherapies (infra‐additive effect).

What this Study Adds

• Predicted bp changes in healthy population from PKPD modelling are consistent with bp changes reported in patient population.

• It is confirmed and quantitatively estimated that the interaction of combined administration leads to an infra‐additive effect.

Tables of Links

TARGETS
G protein‐coupled receptors 2	Voltage‐gated ion channel 3
angiotensin II type 1 receptors http://www.guidetopharmacology.org/GRAC/ObjectDisplayForward?objectId=2534	Calcium channel

LIGANDS
Valsartan http://www.guidetopharmacology.org/GRAC/LigandDisplayForward?ligandId=3726	Amlodipine http://www.guidetopharmacology.org/GRAC/LigandDisplayForward?ligandId=388
angiotensin II http://www.guidetopharmacology.org/GRAC/LigandDisplayForward?ligandId=2352	http://www.guidetopharmacology.org/GRAC/LigandDisplayForward?ligandId=4998

These Tables list key protein targets and ligands in this article that are hyperlinked to corresponding entries in http://www.guidetopharmacology.org, the common portal for data from the IUPHAR/BPS Guide to PHARMACOLOGY 1, and are permanently archived in the Concise Guide to PHARMACOLOGY 2015/16 2, 3

Introduction

The antihypertensive effectiveness of combined therapy with the calcium channel blocker (CCB) amlodipine, and the angiotensin II receptor blocker (ARB) valsartan, has been demonstrated in several large, randomized clinical trials 4. Amlodipine and valsartan are both effective antihypertensive agents 4, 5, 6. Amlodipine is a member of the class of dihydropyridine CCBs that directly blocks calcium influx into vascular smooth muscle and cardiac muscle thereby decreasing peripheral vascular resistance 4, 5, 7. Valsartan, on the other hand, blocks the vasoconstrictor and aldosterone‐secreting effects of angiotensin II by selectively inhibiting the binding of angiotensin II to angiotensin II type 1 receptors 4, 5, 7.

Because amlodipine and valsartan exert their effects through different pharmacological pathways, it is of interest to quantify the combined effects of these drugs. Combination therapy is known to be more effective in reducing blood pressure (BP) than therapy with amlodipine or valsartan given alone 4, 5, 6. But there are no studies that quantitatively describe the combined antihypertensive effect with co‐administration of valsartan and amlodipine in comparison to monotherapy.

With this background, the objectives of this analysis were: first to model the population pharmacokinetics of amlodipine and valsartan, and then to model the antihypertensive population pharmacodynamics (PD) of the two drugs and quantify the drug–drug interaction, based on data collected from a study of the combined administration of the two drugs 7 and the literature data for the single dose administration of each drug.

Methods

Data for combined administration

Combined administration data used in the analysis was derived from 48 healthy subjects enrolled in a comparative pharmacokinetic study to compare the pharmacokinetics of two fixed dose combination (FDC) tablets of valsartan and amlodipine 7.

In that study, the subjects were given a single dose of the FDC tablet of 160 mg valsartan/10 mg amlodipine besylate or a single dose of the FDC tablet of 160 mg valsartan/10 mg amlodipine orotate in a crossover fashion, with a 14‐day washout period. For PK analysis, blood samples were collected at 0 (predose) and 0.5, 1, 1.5, 2, 3, 4, 6, 8, 10, 12, 16, 24, 48, 72, 96, 144, and 192 h. Blood samples up to 48 h were collected for plasma concentration analysis of both amlodipine and valsartan and those sampled from 72 h to 192 h were collected for plasma concentration analysis of amlodipine only. For PD analysis, blood pressure (systolic SBP, diastolic DBP) was measured at 0 (predose) and 2, 4, 8, 12, 16, 24, 48, 72, 96, 144, 192 h after the dose for each tablet. BP was measured while subjects were in the sitting position 7. In this work, for PK analysis all data up to t = 192 h were used, and for PD analysis data only up to t = 24 h were used as blood pressure measurements after 24 h were obtained in the outpatient clinic after discharge and measurement conditions were different.

The study was approved by the Institutional Review Board of Yonsei University Severence Hospital (Seoul, Korea) and performed in accordance with the Declaration of Helsinki and Good Clinical Practice 7. All subjects gave written informed consent before study enrolment.

Data for monotherapy

Previous drug interaction studies for amlodipine and valsartan have shown that there is no clinically relevant pharmacokinetic interaction between the two drugs 4. Therefore, the combined administration PK data 7 was used to develop a PK model for each drug.

In order to develop a model for SBP and DBP time course after monotherapy, a search of the literature was used to obtain results in healthy subjects (Supplementary Table S2). The literature search included the keywords amlodipine, valsartan, healthy volunteers and phase I study. Two studies were considered suitable for further analysis 8, 9 (Supplementary Table S1). The studies for other CCBs and ARBs were similar (Supplementary Table S2). SBP and DBP time courses were obtained from the mean BP values recorded at each measured time point for t ≤ 24 h.

Pharmacokinetic data analysis and modelling

One and two compartment models with first order elimination were tested, allowing for various forms of absorption kinetics. For the two compartment model, the following parameters were estimated; apparent clearance (CL/F), inter‐compartmental clearance (Q/F) and the volume of distribution of central (V₁/F) and peripheral compartment (V₂/F). Each parameter is predicted in a subject whose weight (WT) (in kg) is based on a standard individual CL_STD, Q_STD, V_1STD or V_2STD, whose size is WT_STD. WT_STD was set to 70 kg 10.

Theory based allometric scaling was applied and model parameters were described according to the following equations [10]:

$$\text{FsizeCL}={\left(\frac{\mathrm{WT}}{{\mathrm{WT}}_{\mathrm{STD}}}\right)}^{\frac{3}{4}}$$ (1)

$$\text{FsizeV}={\left(\frac{\mathrm{WT}}{{\mathrm{WT}}_{\mathrm{STD}}}\right)}^1$$ (2)

FsizeCL (Equation (1)) is multiplied by CL_STD and Q_STD to predict CL/F and Q/F and FsizeV (Equation (2)) is multiplied by V_1STD and V_2STD to predict V₁/F and V₂/F.

Covariate analysis for amlodipine and valsartan population PK models included age, serum creatinine, smoking and drinking status. Serum ALT, AST and GGT were also included in the covariate analysis of amlodipine as this drug is extensively metabolized in the liver and hepatic dysfunction may affect the pharmacokinetic characteristics of the drug 11. Stepwise covariate modelling (SCM) was performed using PsN at significance levels of P < 0.05 for forward selection and P < 0.001 for backward elimination 12. The selection procedure was conducted separately for each drug.

Pharmacodynamic modelling

Drug interactions can be labelled as “synergistic”, “additive” or “antagonistic” when the drugs' combined effect exceeds, equals or is less than that of the sum of the effects of the individual drugs, respectively 13. It is preferred to refer to “antagonistic” effects as “infra‐additive” when describing interactions that involve two agonists 14.

A population PKPD model for the time course of SBP and DBP changes in the healthy subject combination treatment study was developed using a sequential PKPD approach (PPP&D 15). The PPP&D method was used, where PD modelling was conducted with the PK data being incorporated in the model‐building process and population parameters of the PK model being fixed at their estimates 15.

A similar approach was used for the PKPD analysis of monotherapy but because only mean concentrations and blood pressures were available, this is a form of naïve pooled analysis. SBP and DBP data were modelled simultaneously.

The time course of blood pressure change from baseline caused by drug was predicted using Equation (3):

$$\mathrm{BP}=\text{Baseline}\times \left(1–\mathrm{PD}\left(\mathrm{Ce}\right)\right)$$ (3)

where BP is blood pressure, Baseline is baseline blood pressure, PD (Ce) represents different types of PD models as a function of drug concentration. Both immediate and delayed response models were tested. An effect compartment model was applied to describe the delayed onset of drug effect. Ce is either the predicted plasma concentration for the immediate effect or the predicted concentration in the effect compartment for the delayed onset PD model.

$$\mathrm{PD}\left(\mathrm{Ce}\right)=\text{Slope}\times \mathrm{Ce}$$ (4)

$$\mathrm{PD}\left(\mathrm{Ce}\right)=\text{Slope}\times log\left(\mathrm{Ce}\right)$$ (5)

$$\mathrm{PD}\left(\mathrm{Ce}\right)=I_{\max }\times \frac{\mathrm{Ce}}{\mathrm{Ce}+\mathrm{IC}50}$$ (6)

$$\mathrm{PD}\left(\mathrm{Ce}\right)=I_{\max }\times \frac{{\mathrm{Ce}}^{\mathrm{\gamma }}}{{\mathrm{Ce}}^{\mathrm{\gamma }}+\mathrm{IC}50}$$ (7)

Several PD models including linear, log‐linear, I _max and Sigmoid I _max models (Equations (4), (5), (6) and (7), respectively) were explored. I _max is the maximum inhibition effect, IC₅₀ is the concentration which produces 50% maximum inhibition and γ refers to the steepness.

An empirical model was used to describe the pharmacodynamic interaction between amlodipine and valsartan. Each drug effect on blood pressure lowering is described using the predicted effect compartment concentration after monotherapy with amlodipine, PD(ACe) or valsartan, PD(VCe). The interaction is described by an empirical additive plus proportional model where the parameter α estimates the global interaction with combined therapy (Equation (8)):

$$\mathrm{BP}=\text{Baseline}\times \left(1–\left(\mathrm{PD}\left(\mathrm{ACe}\right)+\mathrm{PD}\left(\mathrm{VCe}\right)\right)–\mathrm{\alpha }\times \text{Baseline}\times \mathrm{PD}\left(\mathrm{ACe}\right)\times \mathrm{PD}\left(\mathrm{VCe}\right)\right)$$ (8)

Modelling tools

All PK and PD model analyses were done with NONMEM (Version 7.3, ICON, Hanover, MD) and the first order conditional estimation with the interaction option. Visual predictive checks (VPCs) were created using Wings for NONMEM 740 16.

Model selection and evaluation

Model selection was guided by the precision of parameter estimates, objective function value (OFV) and Akaike Information criterion (AIC). To evaluate the final PD models of monotherapies, predicted BP changes were compared to the reported BP changes found in the published literature. To verify that the final population PK and PD models adequately described the central tendency and spread of the data, the models were evaluated using a VPC given 1000 simulated datasets from the final models. Observed concentrations were overlaid with model predictions (mean, 5th and 95th percentiles) to detect the fraction of the data that lay within the model prediction intervals. For the PD interaction term model, VPC of the final model and the model with interaction term of 0 were compared for evaluation purposes. The significance of the interaction parameters were determined using the likelihood ratio test. A total of 200 bootstrap replications were used to estimate parameter imprecision and confidence intervals using a non‐parametric bootstrap approach 17.

Results

Participant demographics and data

Data were available from 48 participants for both amlodipine and valsartan pharmacokinetic analysis. A summary of the demographic characteristics of study subjects is reported in Supplementary Table S3. There were 816 measurements of amlodipine and 624 measurements of valsartan concentrations. For amlodipine, 0.61% of measured concentrations were below the limit of quantitation. For valsartan, there were 6.5% of measured concentrations below the limit of quantitation. There were 336 measurements of SBP and DBP with no missing values. There were no missing values in BP data.

The data from the literature was based on 24 subjects with 12 measurements of mean SBP and DBP for amlodipine and 12 subjects with six measurements of mean SBP and DBP for valsartan for t ≤ 24 h.

Pharmacokinetic model

Population pharmacokinetic analysis for amlodipine and valsartan

The pharmacokinetic data for amlodipine was best described by a two‐compartment model with zero order absorption and first order elimination. The OFV value of −387.497 for zero order absorption compared with −29.849 with first order absorption of amlodipine demonstrated that the zero order absorption model better described the data. This result is in accordance with the bi‐exponential decline seen in the plasma concentration vs. time plot of amlodipine (Supplementary Figure S1). Between‐subject variability for clearance, central volume and duration of zero‐order input for amlodipine were estimated along with correlation between clearance and central volume of distribution. Proportional and additive combined error model best described the residual unidentified variability in the data.

Pharmacokinetic model building for valsartan was conducted in a similar way as for amlodipine, leading to a two‐compartment disposition model with first order elimination based on the bi‐exponential plasma concentration vs. time curve (Supplementary Figure S1) and zero order absorption, which yielded a smaller OFV than first order absorption (7712.434 vs. 7874.858). Correlation between clearance and central volume of distribution was incorporated in the model and the residual unidentified variability was best described by a proportional and additive combined error model.

The estimated pharmacokinetic parameters for amlodipine and valsartan are listed in Supplementary Table S4. Apart from body weight, no other covariate factors were found to be significant (P > 0.001). The apparent clearance (CL/F) for a subject with a body weight of 70 kg was estimated to be 39.4 l h⁻¹ for amlodipine and 6.18 l h⁻¹ for valsartan.

The amlodipine and valsartan PK models were evaluated using VPC (Supplementary Figure S2 and Figure S3). The median peak concentration of both drugs was somewhat underpredicted but subsequently the median predictions adequately follow the median observations. Overall, the variability of the predictions was consistent with the variability of the observations. Therefore, we consider the PK models are acceptable to predict concentrations for the pharmacodynamic models of amlodipine and valsartan.

Pharmacodynamic model

bp lowering effect of amlodipine monotherapy

Plotting the SBP and DBP responses as a function of the measured plasma concentration curve for amlodipine provided some evidence of delayed effect (Figure 1). Therefore, both delayed and immediate response PD models were investigated. The data was best described with an effect compartment delay and an E _max model for both SBP and DBP. The fit from an empirical linear pharmacodynamics model was similar to a pharmacodynamic theory‐based E _max model. Therefore the theory‐based model was selected because of its better extrapolation properties. Estimated I _max from valsartan monotherapy (0.164) was used as a fixed I _max for amlodipine monotherapy, assuming that the amlodipine and valsartan monotherapy show similar efficacy.

Figure 1.

Literature data of mean concentration vs. mean blood pressure response plot after single dose of 10 mg amlodipine was given. SBP is shown on the left‐hand side and DBP is shown on the right‐hand side. Arrows indicate increasing time

A delayed response E _max model with delay parameters for SBP and DBP decreased the OFV by 11.5 compared with an immediate response model. SBP and DBP were plotted as a function of the predicted amlodipine concentrations in the effect compartment. The hysteresis shown in Figure 1 is clearly reduced for both SBP and DBP (Figure 2).

Figure 2.

Predicted concentration in effect compartment vs. mean blood pressure response plot after a single dose of 10 mg amlodipine was given. The concentrations were predicted with an effect compartment delay and an I _max pharmacodynamic model. SBP is shown on the left‐hand side and DBP is shown on the right‐hand side. Arrows indicate increasing time

The estimated PD parameters for amlodipine are listed in Table 1. SBP and DBP responses to amlodipine concentration are described according to the following equations where CE is the predicted effect compartment concentration of amlodipine:

$$\mathrm{SBP}=119\times \left(1-0.164\times \left(\frac{\mathrm{CE}}{\left(\mathrm{CE}+8.27\right)}\right)\right)$$ (9)

$$\mathrm{DBP}=71.3\times \left(1-0.164\times \left(\frac{\mathrm{CE}}{\left(\mathrm{CE}+2.97\right)}\right)\right)$$ (10)

Table 1.

PD estimates from mean healthy subject data of amlodipine monotherapy

	Amlodipine
PD model	Delayed I max
No. of parameters	8
Parameter	Estimate (RSE%)	Bootstrap estimate	95% CI
SBP BSL (mmHg)	119(1.03)	115.32	113–118
DBP BSL (mmHg)	71.3 (2.04)	65.79	63.29–68.9
I max	0.164 FIX	0.164 FIX
SBP IC 50 (ng ml −1 )	8.27 (32.2)	10.80	0–13
DBP IC 50 (ng ml −1 )	2.97 (36.8)	4.79	0–6
SBP Keq (/h)	0.211 (Teq = 3.3 h) (38.3)	0.133	0.1–0.211
DBP Keq (/h)	0.821 (Teq = 0.84 h) (104.7)	0.316	0.1–0.821

Residual variability	Estimate (RSE%)	Bootstrap estimate	95% CI
σ SBP additive (mmHg)	2.01 (17.4)	2.92	0.91–3.65
σ DBP additive (mmHg)	1.36 (22.5)	2.74	0.96–3.59

BSL, estimated baseline; DBP, diastolic blood pressure; SBP, systolic blood pressure; σ, sqrt(NONMEM SIGMA)

The PD models of amlodipine monotherapy were evaluated using VPCs and the predicted maximum BP changes from the PD models compared to reported maximum BP changes found in the literature. The confidence intervals of the SBP and DBP predictions were consistent with the median observations (Supplementary Figure S4). Predicted maximum BP changes of SBP and DBP are in accordance with the reported maximum BP changes from the literature 9 (Supplementary Table S5). Overall, we consider the PD models are acceptable to describe both SBP and DBP after monotherapy.

bp lowering effect analysis for valsartan monotherapy

Plotting the SBP and DBP responses as a function of the measured plasma concentrations of valsartan provided evidence of a delayed onset of effect as shown in Figure 3. Both delayed and immediate response PD models were investigated and the data was best described with an effect compartment delay and an I _max model for both SBP and DBP. With one parameter increase, the OFV of the delayed response model was reduced by 8.4 compared to the immediate response model. The hysteresis shown in Figure 3 is reduced with SBP and disappeared with DBP (Figure 4). The estimated PD parameters for valsartan from the selected model are listed in Table 2. SBP and DBP response to valsartan administration was described according to the following equations where CE is the predicted effect compartment concentration of valsartan:

$$\mathrm{SBP}=126\times \left(1-0.164\times \left(\frac{\mathrm{CE}}{\left(\mathrm{CE}+1200\right)}\right)\right)$$ (11)

$$\mathrm{DBP}=71.3\times \left(1-0.164\times \left(\frac{\mathrm{CE}}{\left(\mathrm{CE}+1200\right)}\right)\right)$$ (12)

Figure 3.

Literature data of mean concentration vs. mean blood pressure response plot after single dose of 160 mg valsartan was given. SBP is shown on the left‐hand side and DBP is shown on the right‐hand side. Arrows indicate increasing time

Figure 4.

Predicted concentration in effect compartment vs. mean blood pressure response plot after single dose of 160 mg valsartan was given. The concentrations were predicted with the chosen final model, an effect compartment delay and an I _max model. SBP is shown on the left‐hand side and DBP is shown on the right‐hand side. Arrows indicate increasing time

Table 2.

PD estimates from mean healthy subject data of valsartan monotherapy

	Valsartan
PD model	Delayed I max
No. of parameters	7
Parameter	Estimate (RSE%)	Bootstrap estimate	95% CI
SBP BSL(mmHg)	126 (1.58)	119.6	117–125
DBP BSL (mmHg)	71.3 (2.52)	67.52	65.1–71.8
I max	0.164 (102)	0.228	0.0623–1
IC 50 (ng ml −1 )	1200 (53.3)	1823.05	1020–4000
Keq (/h)	0.542 (teq = 1.3 h) (59.5)	0.403	0.1–0.777

Residual variability	Estimate (RSE%)	Bootstrap estimate	95% CI
σ SBP additive (mmHg)	3.18 (33.0)	2.82	0.228–4
σ DBP additive (mmHg)	0.41 (35.8)	2.26	0–3.406

DBP, diastolic blood pressure; SBP, systolic blood pressure; σ, sqrt(NONMEM SIGMA)

I _max (0.164) for both SBP and DBP was estimated relative to the BP baseline. When expressed in terms BP units, the I _max for SBP is 20.7 mmHg (= 126 × 0.164) and for DBP 11.7 mmHg (= 71.3 × 0.164). SBP and DBP changes after monotherapy were plotted as a function of the predicted valsartan concentrations in the effect compartment (Figure 4).

The PD models of valsartan monotherapy were evaluated by VPCs and the predicted maximum BP changes from the PD models compared to the reported maximum BP changes found in the literature. The confidence intervals of the SBP and DBP predictions were consistent with the median observations (Supplementary Figure S5). Predicted maximum BP changes of SBP and DBP are in accordance with the reported maximum BP changes from the literature (Supplementary Table S6). Overall, the PD models are acceptable to predict both SBP and DBP and the estimated parameters to be used for the pharmacodynamic models of amlodipine and valsartan combined therapy.

Interaction term of bp lowering effect between amlodipine and valsartan

The interaction between amlodipine and valsartan was best described with a proportional term (Equation (8)). A second interaction model was also investigated to describe the interaction between amlodipine and valsartan (Supplementary Drug interaction models). The core assumption of this second model is that the two drugs compete with each other for occupancy of the same receptor which is not the case for amlodipine and valsartan. This common receptor model led to implausible parameter estimates (e.g. I _max of 0.03 which is seven times smaller than expected) and was not investigated further. The estimated PD parameters for the proportional interaction model are reported in Table 3. The proportional interaction term for SBP was −0.171 and for DBP was −0.0312.

Table 3.

Population PD estimates and interaction term (ALPHA) of amlodipine and valsartan combined administration in healthy subjects

	SBP
Interaction type	Proportional
No. of parameters	8
Parameter	Estimate (RSE%)	Bootstrap estimate	95% CI
BSL (mmHg)	117 (1.10)	116.8	114–119.0
ALPHA	−0.171 (11.6)	−0.178	−0.218–−0.143
PPV	Estimate (RSE%)	Bootstrap estimate	95% CI
BSL	0.059 (18.8)	0.055	0.035–0.074
ALPHA	0 FIX
IC 501	0.468 (84.3)	0.341	0–0.872
IC 502	1.732 (43.4)	1.671	0–3.127
AML Keq a	1.319 (46.5)	1.336	0–2.403
VAL Keq a	0.376 (37.9)	0.371	0–0.613
Residual variability	Estimate (RSE%)	Bootstrap estimate	95% CI
σ additive (mmHg)	7.84 (6.36)	7.84	6.86–8.73

	DBP
Interaction type	Proportional
No. of parameters	6
Parameter	Estimate (RSE%)	Bootstrap estimate	95% CI
BSL (mmHg)	72.8 (1.33)	72.9	71.2–74.7
ALPHA	−0.0312 (57.8)	−0.0336	−0.0774–−0.00283
PPV	Estimate (RSE%)	Bootstrap estimate	95% CI
BSL	0.071 (15.9)	0.07	0.046–0.092
ALPHA	0 FIX
ω IC 501	1.612 (33.1)	1.674	0.907–2.819
ω IC 502	1.131 (32.8)	1.042	0.004–1.622
Residual variability	Estimate (RSE%)	Bootstrap estimate	95% CI
σ additive (mmHg)	4.46 (5.22)	4.45	3.95–4.90

ALPHA, interaction term for co‐administration of amlodipine and valsartan; BSL, estimated baseline; other parameters (I _max, etc.) fixed to values estimated from combined administration PK models and single drug PD models. PPV value calculated from sqrt(NONMEM OMEGA estimate)

The SBP and DBP PD models of amlodipine and valsartan combined administration were evaluated by VPC. To evaluate the appropriateness of the interaction term in the model, the final interaction models for SBP and DBP were compared to models without interaction (Figures 5 and 6). A VPC using a model with the interaction term fixed to 0 for SBP showed a very poor fit between the predictions and the observations, with predicted SBP lower than the observations at all times,. In contrast, the proportional interaction model successfully described the time course of systolic blood lowering effect of the amlodipine and valsartan combined administration.

Figure 5.

VPC plots of SBP without an interaction term model of combined therapy (left) and the same model with the interaction term (right). Observations and predictions are illustrated in red lines and black lines respectively. Solid lines represent median, lower and upper dashed lines represent 5th percentile and 95th percentile respectively. Shaded areas describe 95% confidence interval of the predictions

Figure 6.

VPC plots of DBP without an interaction term model of combined therapy (left) and the same model with the interaction term (right). Observations and predictions are illustrated in red lines and black lines respectively. Solid lines represent median, lower and upper dashed lines represent 5th percentile and 95th percentile respectively. Shaded areas describe 95% confidence interval of the predictions

For DBP, the median predictions adequately follow the median observations. The discrepancy between the predictions and the observations were evident when the interaction term was fixed to 0 as shown in Figure 6. The model without interaction was not so markedly different for DBP but nevertheless the proportional interaction model for the combined therapy was better.

Discussion

In previous population PK studies of amlodipine, the absorption phase was often well described with first order absorption 18, 19, 20. Reported CL/F for amlodipine from other studies varied between 32 and 39 l h⁻¹ 20, 21, 22. The mean or median weight in these studies was near 70 kg. Estimated CL/F of amlodipine in this study for a 70 kg subject was 39.4 l h⁻¹, which is in accordance with findings from previously reported clearance from both quantitative PK modelling and NCA analysis 20, 21, 22.

The population PK model of valsartan is in accordance with findings from a previously published population PK model for valsartan. Lim et al. reported estimates of CL/F, Q, Vc and Vp of 6.07 l h⁻¹, 2.02 l h⁻¹, 13.8 l and 14.2 l, respectively 23, and the mean weight for the study was near 70 kg.

Empirical effect compartment models adequately describe the observed hysteresis between the time course of plasma concentrations and time course of blood lowering effect. Figures 2 and 4 show that the hysteresis either shrinks or completely collapses when the blood lowering effect is plotted as a function of predicted concentration in the effect compartment. Pharmacodynamic effect often lags behind plasma concentration for various reasons such as drug distribution, slow equilibration with the target or changes in a physiological mediator.

It has been reported that amlodipine and valsartan show similar BP reduction in hypertensive patients 24, 25, 26, thus I _max is fixed to the estimated value from valsartan monotherapy as the data is not informative about amlodipine. For amlodipine, estimated C₅₀ of the SBP is about three times bigger than the C₅₀ of DBP (Table 1).

In this work, the mechanism of the interaction could not be determined, so the interaction was described empirically. As a result, a proportional interaction term best described the blood pressure lowering effect of combined administration of amlodipine and valsartan. The interaction term (α) can be described in three categories; infra‐additive if α is less than 0, additive if α is equal to 0 and synergistic if α is greater than 0. We have demonstrated that the combined drug response of amlodipine and valsartan for both SBP and DBP is infra‐additive. Combined administration of amlodipine with valsartan exerts greater antihypertensive effects than that of either drug given alone but less than the sum of the two drugs as monotherapy. This outcome was in an accordance with other publications where the antihypertensive effect of the two drugs in hypertensive patients are greater than the either monotherapy given alone but the drug interaction is infra‐additive 4, 5.

One of the limitations of this study is that the interaction model was quantitatively analysed from healthy subject data, assuming that PK and PD parameters estimated in healthy subjects would be the same in hypertensive patients, with the only difference between these two groups being baseline SBP and DBP. However, as antihypertensive medications are given to patients with hypertension, this assumption was validated by testing if the healthy subject predictions were consistent with blood pressure changes in treated patients.

To this end, blood pressure changes relative to baseline were predicted for healthy subjects and compared with the mean observed changes in five patient studies (Supplementary Table S7). Both amlodipine and valsartan I _max PD models gave similar predictions to changes reported in patients (Table 4), which supported the validity of our assumption.

Table 4.

Comparison between the calculated ratios of mean reported bp changes of patients and predictions from I _max bp models of amlodipine and valsartan at steady state

	Amlodipine patients’ mean	Amlodipine healthy predicted	Valsartan patients’ mean	Valsartan healthy predicted
RSBP (%)	12	9	11	8
RDBP (%)	13	13	11	8

RSBP, RDBP; relative BP changes to SBP and DBP baseline respectively

The PD models are empirically developed to describe the time course of antihypertensive effects of combined therapy. The pharmacology of amlodipine and valsartan and their mechanisms of actions are widely known 4, 6, 25, 27, 28, 29. It would be valuable to develop mechanistic PD models to understand and describe the interaction observed with combined therapy.

Conclusion

An I _max model with effect compartment delay adequately described the SBP and DBP data with both amlodipine and valsartan monotherapy. The quantitatively estimated interaction term of combined administration, defined on the basis of a model developed from monotherapy, is consistent with previous descriptions of an infra‐additive effect.

Competing Interests

All authors have completed the Unified Competing Interest form at http://www.icmje.org/coi_disclosure.pdf (available on request from the corresponding author) and declare: no support from any organization for the submitted work; no financial relationships with any organizations that might have an interest in the submitted work in the previous 3 years; no other relationships or activities that could appear to have influenced the submitted work.

This work was supported by a grant from the Brain Korea 21 PLUS Project for Medical Science, Yonsei University.

Contributors

Y. A. H contributed to data interpretation, literature search, figure creation and writing, N. H. contributed to data interpretation and writing, Y. K. and M. S. contributed to study design, study conduct and data collection, and K. P. coordinated the entire study.

Supporting information

Table S1 Clinical trials used in the analysis of amlodipine and valsartan pharmacokinetics and pharmacodynamics analysis

Table S2 Summary of maximum BP changes after a single dose of calcium channel blockers or angiotensin II receptor blockers (ARBs) in normotensive subjects

Table S3 Demographic characteristics of study subjects for population PK analysis

Table S4 Final population PK estimates of amlodipine and valsartan

Table S5 Comparison between the predicted and the reported maximum BP changes with the final BP models and the literature of amlodipine monotherapy

Table S6 Comparison between the predicted and the reported maximum BP changes with the final BP models and the literature of valsartan monotherapy

Table S7 Summary of maximum BP changes after amlodipine or valsartan were given to patients with hypertension

Figure S1 Spaghetti plot of individual time concentration curves for amlodipine (A, left) and valsartan (B, right), superimposed with median (red dashed line)

Figure S2 VPC plot of population PK model of amlodipine. Inset shows the first 24 h after the dose. Observations and predictions are illustrated in red lines and black lines respectively. Solid lines represent median; lower and upper dashed lines represent 5th percentile and 95th percentile respectively. Shaded areas describe 95% confidence interval of predictions

Figure S3 VPC plot of final population PK model of valsartan. Inset shows the first 24 h after the dose. Observations and predictions are illustrated in red lines and black lines respectively. Solid lines represent median; lower and upper dashed lines represent 5th percentile and 95th percentile respectively. Shaded areas describe 95% confidence interval of predictions

Figure S4 VPC plots of SBP (left) and DBP (right) model of amlodipine monotherapy. Observations and predictions are illustrated in red and black line respectively

Figure S5 VPC plots of SBP (left) and DBP (right) model of valsartan monotherapy. Observations and predictions are illustrated in red and black line respectively

Supporting info item

Heo, Y. ‐A. , Holford, N. , Kim, Y. , Son, M. , and Park, K. (2016) Quantitative model for the blood pressure‐lowering interaction of valsartan and amlodipine. Br J Clin Pharmacol, 82: 1557–1567. doi: 10.1111/bcp.13082.