Chemicals and Reagents

Amlodipine was purchased from Alfa Asear (Haverhill, MA). Glyburide was from Frontier Scientific (Logan, UT). Digoxin was obtained from Tocris (Ellisville, MO). Glyburide-d3 and digoxin-d3 were purchased from Cayman Chemical (Ann Arbor, MI). Amlodipine-d4 was obtained from Toronto Research Chemicals (North York, Canada). Sprague Dawley rat plasma was purchased from Equitech Biotech Inc (Kerrville, TX). Polyethylene glycol 400 (PEG-400) and methylcellulose (viscosity, 400 cP) were from Sigma-Aldrich (St. Louis, MO). 1-Methyl-2-pyrrolidinone (NMP) is from J.T.Baker (Allentown, PA).

Animals

Male Sprague-Dawley single jugular cannulated rats weighing 239–250 g were ordered from Charles River (Wilmington, MA). All rats were singly housed under a reverse 12-hour light/dark cycle. Rats were acclimated for at least four days in the Temple University Health Sciences Campus animal housing facility and 30 minutes in the procedure room prior to the start of the study. Food (standard rodent chow) and water were available ad libitum for fed groups. Food was removed from the cages of fasted groups 12 hours before the beginning of the study. All animal studies were performed with strict adherence to protocols approved by the Temple University IACUC. The total number of animals used was minimized by using the same animal for intestinal measurements after the completion of pharmacokinetic studies.

Rat Intestinal Measurements

Dosing and Sampling of Amlodipine and Glyburide

Rats (n = 3) were intravenously administered a solution containing 2 mg/kg AML and 4 mg/kg GLY prepared in 50%–55% NMP, 20% PEG-400, and 25%–30% Milli-Q water via the jugular cannula. Blood samples (∼0.2 mL) were collected via the jugular cannula into heparinized tubes at 0.08, 0.25, 0.5, 1, 2, 4, 6, 8, 10, and 12 hours postdose. Rats (n = 3) were intravenously administered a solution containing 0.25 mg/kg DIG prepared in 15% NMP with saline via the jugular cannula. Blood samples (∼0.2 mL) were collected via the jugular cannula into heparinized tubes at 0.08, 0.25, 0.5, 0.75, 1, 2, 4, 6, and 8 hours postdose. After each sampling, the loss of blood volume was supplemented with an equal volume of saline containing 100 U/mL heparin. Blood samples were centrifuged at 5000 g for 15 minutes for AML and GLY or 10 000 g for 10 minutes for DIG at 4°C to obtain plasma and kept at −20°C until analysis.

Rats (n = 13) were orally administered a solution containing 5 mg/kg AML and 5 mg/kg GLY in 50%–55% NMP, 20% PEG-400, and 25%–30% Milli-Q water via oral gavage. Although AML is not reported to be a transporter substrate, GLY absorption may be impacted by both uptake and efflux transporters. It is important to note that the use of 20% PEG-400 may alter efflux transporter activity toward GLY (Mudra and Borchardt, 2010), and this caveat was not further explored in the study. Rats were either fed (fed, n = 6), fasted 12 hours and then fed 1-hour postdose [fasted 1 hour feeding time (FT), n = 4], or fasted 12 hours and then fed 2 hours postdose (fasted 2 hours FT, n = 3). Blood samples (∼0.2 mL) were collected via the jugular cannula into heparinized tubes at 0.17, 0.5, 1, 1.5, 2.5, 4, 6, 8, 10, and 24 hours postdose. Blood loss supplementation and plasma sample preparation were the same as that of the AML and GLY intravenous administration study.

Rats (n = 14) were orally administered a solution containing 0.75 mg/kg DIG in 15% NMP in saline via oral gavage. Rats were either fed (fed, n = 5), fasted 12 hours and then fed 0.5 hours postdose (fasted 0.5 hours FT, n = 4), or fasted 12 hours and then fed 1-hour postdose (fasted 1 h FT, n = 5). Blood samples (∼0.2 mL) were collected via the jugular cannula into heparinized tubes at 0.08, 0.25, 0.5, 0.75, 1, 2, 4, 6, 8, and 24 hours postdose. Blood loss supplementation and plasma sample preparation were the same as that of the DIG intravenous administration study.

Plasma samples for AML and GLY were mixed with two and a half times the volume of amlodipine-d4 (25 ng/mL) and glyburide-d3 (150 ng/mL) in acetonitrile as respective internal standards. Samples were vortexed and centrifuged at 15 000 g for 10 minutes at 4°C. Ten microliters supernatant was injected into the liquid chromatography and tandem mass spectrometry (LC-MS/MS) system for analysis. DIG plasma samples were mixed with two times the volume of digoxin-d3 in acetonitrile (ACN). Samples were vortexed and centrifuged at 15 000 g for 10 minutes at 4°C. Twenty microliters supernatant was injected into the LC-MS/MS system for analysis.

Liquid Chromatography Tandem Mass Spectrometry

Analysis was performed using an Agilent series 1100 high-performance liquid chromatography system coupled to an ABSciex API 4000 triple-quadrupole tandem mass spectrometer with an electrospray ionization source. The mass spectrometer was operated in positive ion mode. All LC-MS/MS data were acquired and processed using Analyst software version 1.6.

Chromatographic separation for AML and GLY was performed on a Kinetex C8 column (2.1 mm × 50 mm, 5 µm) protected by a Phenomenex Security Guard C18 (2.0 × 4 mm) guard column. The mobile phase for AML and GLY consisted of water with 0.1% formic acid (FA) as the aqueous phase (A) and ACN with 0.1% FA as the organic phase. The gradient started at 95% A and maintained for 1.3 minutes, ramped down to 0% over 30 seconds and held for 5.7 minutes, and then ramped back to 95% over 10 seconds and maintained until 9 minutes. The flow rate was 500 µL/min. The retention time for AML and AML-d4 was ∼3.00 minutes, whereas the retention time for GLY and GLY-d3 was ∼3.27 minutes. The precursor → product ion transitions observed for AML, AML-d4, GLY, and GLY-d3 were 409.2 → 237.3, 413.2 → 237.3, 494.5 → 369.2, and 497.5 → 372.2, respectively.

For DIG, a Phenomenex Gemini C18 column (100 mm × 4.6 mm, 3 μm) with a Phenomenex Security Guard C18 (2.0 × 4 mm) guard column was used. The mobile phase for DIG consisted of 10 mM ammonium formate in water (pH to 4 with FA) as A and ACN with 0.1% FA as organic phase. The gradient used for DIG elution started at 70% A and maintained for 1 minute, ramped down to 5% over 1.5 minutes and maintained for 2.5 minutes, and increased back to 70% over 0.1 minutes for a total of 7 minutes. The flow rate was 600 μL/min. The retention time for DIG and DIG-d was ∼4.54 minutes. The precursor → product ion transitions analyzed for DIG and DIGd3 were 798.5 → 651.5 and 801.5 → 654.5, respectively.

The dwell time for each ion transition was 200 milliseconds. The operating parameters were optimized as follows: curtain gas, 20 psi; ion source gas 1, 60 psi; ion source gas 2, 40 psi; ion spray voltage, 5000 V; temperature, 500°C. The declustering potential (DP), collision energy (CE), and collision cell exit potential (CXP) for AML are 71V, 17V, and 18V, respectively. The DP, CE, and CXP for GLY are 96V, 21V, and 19V, respectively. The DP, CE, and CXP for DIG are 70V, 20V, and 15V, respectively.

The combined method for AML and GLY was satisfactory for quantification over the range of 1.5–90 ng/mL and 25–1500 ng/mL for AML and GLY in rat plasma, respectively. The method for DIG was suitable for quantification from 0.75–96 ng/mL. The lower limits of quantitation for AML, DIG, and GLY were 1.5 ng/mL, 0.75 ng/mL, and 25 ng/mL, respectively. The inter- and intraday percent accuracy and percent precision were within ± 15% for all three drugs.

Compartmental Modeling of Intravenous Datasets

Individual rat concentration-time profiles as well as naive-pooled averages in each group upon intravenous dosing were used as inputs for compartmental modeling. Assuming linear pharmacokinetics at the doses used, standard compartmental models were used to fit the intravenous datasets. Modeling was conducted with Mathematica version 12.3.1 with 1/y weighting. Model selection was based on corrected Akaike information criterion values, and the compartmental model fitted intravenous concentration-time profiles were used as disposition functions for the absorption model subsequently used for the oral datasets.

Intestinal Model Development

We have previously published in detail a human continuous absorption model (Nagar et al., 2017). The rat model described below used a similar framework, with key anatomic differences modeled as described below. This model predicts the fraction of drug absorbed and can predict bioavailability if first-pass metabolism data are available. The code for this model is provided in Supplemental Materials. The continuous absorption model is based on the basic convection-diffusion equation (Ni et al., 1980):

where drug concentration (C) varies as a function of both x and t, D is the drug molecule diffusion coefficient, Q is the bulk fluid flow rate, r is the radius of the intestinal lumen, and k_i is the first-order rate constant for the ith radial transfer process. The first term describes axial diffusion, the spread of the drug pulse due to intestinal drug mixing; the second term describes convection, the axial bulk movement of the pulse; and the last term describes radial diffusion. This approach also includes relevant physiological and physicochemical factors.

For this model, the intestine is described as a continuous, concentric set of cylinders (Fig. 1). In the axial direction, the drug enters as a plug from the stomach into the duodenum (10 cm), moves along the gut through the jejunum (106 cm), ileum (3 cm), and colon (16 cm) and stops at the terminal colon (Fig. 1A). The model is velocity-based, ensuring that the plug is at the experimentally determined position over time. The small intestine is considered to have a radius of 0.79 cm in the duodenum, 0.92 cm in the jejunum, 0.89 cm in the ileum, and 1.17 cm in the colon.

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Fig. 1.

Rat continuous intestinal absorption model. (A) Depiction of the rat intestine as a continuous cylinder.. (B) Depiction of the radial compartments comprising the concentric cylinders of the rat intestine. Diffusional clearances into (CL_i) and out of (CL_o) membranes are as defined in Materials and Methods. Duo, duodenum; Jej, jejunum; Ile, ileum; r1, radius of Duo; r2, radius of Jej; r3, radius of Ile; r4, radius of the colon.

In the radial direction, this model includes an explicit enterocyte apical membrane, cytosol, and intercellular lipid compartments (Fig. 1B). For absorption, the drug reversibly moves from the lumen (C1), through the apical enterocyte membrane (C2), and into the enterocyte cytosol (C3), where it has the option to go into intracellular lipids (C4). In the final step, the drug irreversibly moves across the basolateral membrane into the portal blood (C5).

Velocity, vel(x)

As the bulk pulse travels along the axial direction, it does so with a fluctuating velocity. Experimental time versus position data collected in-house were used to calculate experimental velocities as a function of x. The following expression for vel(x) was built using these velocities. Due to the absorption of luminal water and change in intestinal diameter, the velocity decreases along the small intestine, with the slowest velocity occurring in the colon. Eq. 2 was used, and the profile and experimental velocity data are shown in Fig. 2A.

where a1 is the cross-sectional area at radius r₁ and a(x) is the cross-sectional area as a function of x.

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Fig. 2.

Physiologic functions describing the intestine. Functions along x are shown for (A) velocity, vel(x); (B) effective diffusion, dif(x); (C) cross-sectional area, a(x); (D) surface area with villi and microvilli, sa_lumen(x); (E) microvilli expansion factor, mf(x); (F) fasted intestinal pH, pH_fast(x); (G) fed intestinal pH, pH_fed(x); (H) P-gp pmol/mg tissue, P-gp(x); and (I) Oatb2b1 normalized pmol/mg tissue, Oatp2b1(x). Experimental data when collected in-house are depicted by filled circles.

Effective Diffusion, dif(x)

Along with bulk axial movement, the drug pulse experiences effective axial diffusion. This axial spreading of the plug is greater than that expected by molecular diffusion and is likely due to peristalsis. Similar to the human model (Nagar et al., 2017), effective axial diffusion is a function of velocity, as shown in eq. 3 and Fig. 2B.

Cross-Sectional Area, a(x)

The cross-sectional area is determined by the radii of each intestinal segment. The radii of the duodenum, jejunum, ileum, and colon are r₁, r₂, r₃, and r₄, respectively. Eq. 4 was used, and the profile and experimental velocity data are shown in Fig. 2C:

where a₁ = πr₁², a₂ = πr₂², a₃ = πr₃², a₄ = πr₄², jej5 = 1.16 m, and ile = 1.19 m were used for distance to the end of the jejunum and ileum, respectively.

Surface Area, sa(x)

The expressions for surface area per unit length (circumference) was based on experimental data collected in-house. The surface areas were determined by the radii and multiplication factors for villi and microvilli. The total surface area including microvilli and villi, sa_lumen(x), is described in eq. 6, and the profile is shown in Fig. 2D. where duo = 0.10 m, jej4 = 0.95 m, jej5 = 1.16 m, and ile = 1.19 m were used for distance to the end of the duodenum, fourth jejunal segment, the entire jejunum, and ileum, respectively.

The expansion factor for the increase in surface area due to microvilli alone, mf(x), is described in eq. 5, and the profile is shown in Fig. 2E.

where duo = 0.10 m, jej3 = 0.74 m, and ile = 1.19 m were used for distance to the end of the duodenum, third jejunal segment, and ileum, respectively. The surface area without microvilli can then be calculated by sa_lumen(x)/mf(x).

Cross-Sectional Area for the Enterocyte Apical Membrane, a_mem(x); Cytosol, a_cyt(x); and Cytosolic Lipid, a_lip(x)

The equations used to describe the cross-sectional area along the intestine for the enterocyte apical membrane, cytosol, and cytosolic lipids are described in more detail previously (Nagar et al., 2017) and are listed below.

Where sa_villi(x) equals sa_lumen(x)/mf(x).

pH of the Intestines, pH(x)

Fasted and fed pH data along the intestine was collected experimentally. The pH along the intestine under fasted conditions was described as a combination of logistic functions expressed in eq. 10 and shown in Fig. 2F. The pH along the intestine under fed conditions was described in eq. 11 and shown in Fig. 2G.

Drug-specific functions:

Apparent Permeability, P_app(x)

For the current model, apparent permeability is based on Caco-2 cell permeability data and is modified by pH as described previously (Nagar et al., 2017). To account for species differences and the transition from in vitro to in vivo, a Caco-2 scaling factor of 1.2 was used. The equations for acids and bases were used were used for P_app(x), respectively.

where P_app(x) is the apparent permeability along the intestine, P_app,scaled is the scaled Caco-2 permeability of a specific drug, ma is the slope of permeability versus pH for acids, mb is the slope of permeability versus pH for bases, pH_C is the pH at which the Caco-2 experiments were conducted, pK_a is the pK_a for the drug, and pH(x) is the pH of the intestine at x. The pH(x) used was either pH_fast(x) or pH_fed(x), depending on the feeding condition of the animals.

Membrane Diffusional Clearances, CL_i(x) and CL_o(x)

The movement of drug between compartments is described by diffusional clearances CL_i(x) and CL_o(x). Movement of drug into the membrane is the product of permeability and surface area:

where CL_i,2(x) is the diffusional clearance when radial diffusion is the rate-limiting step, and CL_i,3(x) is the diffusional clearance for the intracellular lipid compartment by accounting for the difference in the surface area between the plasma membrane and intracellular lipids (1% plasma membrane). P_app2 is the modified apparent permeability when radial diffusion is the rate-limiting step and is modified by a radial diffusion function (eq. 18) to slow radial diffusion as the pulse approaches the end of the colon:

The diffusional clearance out of membranes, CL_o(x), is dependent on membrane partitioning (Korzekwa et al., 2012). Therefore, radial diffusion out of the membranes (eq. 19) and membrane partitioning (eq. 20) can be explained by the following equations:

where f_um is the fraction unbound in microsomes.

Transporter Expression for P-gp and Oatp2b1, P-gp(x) and Oatp(x)

To simulate the impact of transporters P-gp and Oatp2b1, reported transporter levels were used (MacLean et al., 2010; Mai et al., 2021). Transporter expression use and normalization was performed in the same manner as that described previously (Nagar et al., 2017). The P-gp and normalized Oatp2b1 expression functions are shown in Fig. 2, H and I, respectively. This led to the development of Michaelis-Menten saturation functions:

where

To make radial diffusion rate limiting for luminal uptake in the descending colon, the radial diffusion function, f_raddif(x) was used. F_Oatp and F_P-gp are the factors to convert transporter per mg mucosal tissue to mg drug transported per hour per unit volume of lumen for Oatp and apical membrane for P-gp, respectively.

DIG is known to be a P-gp substrate, whereas GLY relies on both Oatp and P-gp (El-Kattan and Varma, 2012; Estudante et al., 2013; Suzuki et al., 2014). Presence of food is reported to inhibit Oatp2b1, leading to PK differences between fasted and fed groups (Lee et al., 2020). The following empirical values, based upon preliminary optimization steps using the observed data, were used for transporter functions for DIG (P-gp) and GLY (P-gp and Oatp).

For DIG, K_m,P-gp = 9000 µM, and F_P-gp = 150 for all groups. For GLY, K_m,P-gp = 50 µM, and F_P-gp = 5000 for all groups. GLY fasted 2 hours FT and fasted 1 hour FT groups used a K_m,Oatp = 5 µM, whereas the fed group used a K_m,Oatp = 50 µM. Fasted 2 hours FT group used F_Oatp = 3.5, whereas the fasted 1 hour FT and fed group used a F_Oatp = 0.2. Thus, Oatp activity had to be reduced for GLY datasets when food was present.

Solution dosing input and disposition equations:

From in vivo data with different feeding times postdose, it is apparent that 1) some of the oral dose is immediately available for absorption, 2) feeding results in delayed release into the intestine, and 3) the longer the time before feeding, the less of the dose is retained. Therefore, drug input from the stomach was modeled by three unit pulse functions with a lag time (Fig. 3). The first pulse represents 10% of the dose that immediately enters the intestine, the second pulse represents the drug that is released into the intestine in the fasted state postdose, and the third pulse is the remaining dose released over a 20-hour period in the presence of food. The unit pulse functions for the three pulses are:

where lag = 0.1 hour, PL_t1 = 0.1 hour, PL_t2 = FT, and PL_t3 = 20 hours; FT is the time food was reintroduced to animals after dosing drug. For fed animals, PL_t2 = 0.001 hour was used.

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Fig. 3.

Feeding times and input functions. (A) Experimental design for fasting and feeding schedule in rats. (B) Schematic for design of input functions. Of the total dose, 10% was input as an immediate pulse, and the remaining 90% was input as a fast + slow pulse: fast pulse under fasted conditions + slow pulse from addition of food for 22 hours. Green, fasted 0.5 hours FT with 18% fast + 72% slow pulse; brown, fasted 1 hour FT with 36% fast + 54% slow pulse; and red, fasted 2 hours FT with 72% fast + 18% slow pulse. (C) Input function used for the fasted 2 hours FT group is depicted as an example. Note the broken X- and Y-axes depicted as such for visual clarity.

The appropriate initial concentration and velocity in the duodenum was achieved by multiplying the upulse functions by the dosing concentration and a volume correction factor:

where C₀ = dose/V_s,o mg/mL, and V_s,o is the volume of water introduced into the stomach with the drug (1 ml/kg). The V_corr term is the volume correction factor for each pulse necessary to achieve the correct velocity entering the intestine:

where Vel0 is the velocity at x = 0.

Drug solution disposition in the rat intestine was modeled for drug concentrations in the lumen, C1(x,t); apical membrane, C2(x,t); enterocyte cytosol, C3(x,t); and optional partitioning into intracellular lipids, C4(x,t), with the following PDEs:

with initial conditions, C1(t, 0) = pulse₁(t) + pulse₂(t) + pulse₃(t),

C1(0, x) = C_1,0 (where C_1,0 is defined as the concentration of pulse₁(t) at t = 0),

C1(t, 1.45) = 0, C2(0, x) = 0, C2(t, 0) = 0, C2(t, 1.45) = 0, C3(0, x) = 0, C3(t, 0) = 0, C3(t, 1.45) = 0, C4(t, 0) = 0, C4(0, x) = 0, C4(t, 1.45) = 0.

Systemic PK and disposition functions:

The movement of drug from the enterocyte cytosol into the systemic PK model was modeled by the input function:

Experimentally collected intravenous data were modeled with two-compartmental PK models, and were used to generate systemic disposition functions. The systemic disposition functions were combined with the input function (eq. 32) to simulate oral PK profiles.

Methods for numerical solutions:

All models were developed using Mathematica 12.3.1. Intravenous data were fit using a NonLinearModelFit with a PrecisionGoal → Infinity and 1/Y weighting. ODEs and PDEs were simulated using the NDSolve function. PDEs were solved using the method of lines with default step sizes, SpatialDiscretization → TensorProductGrid, DifferenceOrder →2, and grid x-coordinates defined as follows:

Input and experimental data:

Permeability data from Caco-2 cells were obtained from the literature (Table 1). An exposure overlap coefficient (EOC) (Holt et al., 2019) was calculated to compare the simulated C-t profiles to the experimental oral PK profiles. An interpolation function was generated from the experimental oral C-t data (Interpolation function in Mathematica with Method → Spline and InterpolationOrder → 1). Since experimental clearances were used, the simulated C-t profile was normalized to have the same area under the curve (AUC) as the experimental profile. The overlap AUC was obtained by integrating the minimum of the two C-t functions. Lastly, the EOC was calculated as the overlap AUC/experimental AUC. The value of the EOC ranges between zero, no overlap, and one, complete overlap.