4.5.1.1 Estimation of Fraction of Drug Absorbed Using Experimental Intestinal Permeability In Vivo

An in vivo method has been successfully established to measure human intestinal permeability by in situ intestinal perfusion (Lennernas et al., 1997; Sun et al., 2002, 2002; Cao et al., 2006). A perfusion tube, as illustrated in Fig. 4.8, is placed in the human jejunum to allow drug passage through a 10-cm intestinal segment. The drug concentration is measured at the inlet and outlet of the perfusion tube. The drug permeability is then calculated with the following equation

where Peff, human is drug permeability in the human intestine, Q is the perfusion flow rate (2 min ml-1), Cin is inlet drug concentration of the perfusion tube, Cout is outlet drug concentration of the perfusion tube, R is human small intestine radius (2 cm), and L is the 10-cm perfusion segment. When the permeability is plotted against the fraction of drug absorbed, the relationship can be established (4.18) (Fig. 4.9) (Amidon et al., 1988, 1995; Oh et al., 1993)

Fa = 1 - exp(-2An) = 1 - exp(-2Peff, human^es/R), (4.18)

where Fa is the fraction of drug absorbed, Peff, human is drug permeability in human intestine, Tres is transit time in human small intestine (3 h), R is the radius of human small intestine (2 cm).

Human jejunum permeability (x 10 cm/s)

Figure 4.9. Prediction of the fraction of drug absorbed using human jejunum permeability. Drugs are labeled with different symbols. Closed symbols are drugs absorbed through carrier-mediated process, while open symbols are drugs absorbed through passive diffusion (Sun et al., 2002)

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Human jejunum permeability (x 10 cm/s) Figure 4.9. Prediction of the fraction of drug absorbed using human jejunum permeability. Drugs are labeled with different symbols. Closed symbols are drugs absorbed through carrier-mediated process, while open symbols are drugs absorbed through passive diffusion (Sun et al., 2002) However, when in situ intestinal perfusion is performed, low drug concentrations are used for permeability measurements. In this case, the drug concentration is always below its solubility limit. Since the fraction of drug absorbed is a function of its solubility and permeability, (4.18) is not suitable for predicting the fraction of drug absorbed when high drug concentration above in vivo solubility limit is used in the experiment. This model has been further modified to overcome this problem by utilizing different calculation methods according to the drug's solubility (Yu et al., 1996; Yu and Amidon, 1999) Fa = 1 — exp(-2An), when Cin < S, Cout < S, (4.19) Fa = 1 — 1 /[ D0 exp(—2An + D0 — 1)], when Cin > S, Cout < S, where Fa is the fraction of drug absorbed, An = if, human x Tres/R, Cin is inlet drug concentration of the perfusion tube, Cout is outlet drug concentration of the perfusion tube, Pef human is drug intestinal permeability in human, Tres is transit time in human small intestine (3h), D0 is dose number [D0 = (dose/volume)/S], and S is drug solubility. The challenge for this method is that drug intestinal permeability has to be obtained in vivo in human, which is very difficult and not available during early stages of drug discovery and development. Meanwhile the relationship between Cout (or Cin) and solubility is also difficult to determine in vivo. 4.5.1.2 Estimation of Maximum Absorbable Dose Using In Vivo Absorption Rate Constant and Drug Solubility Another method has been proposed to estimate maximum absorbable dose (MAD) based on the in vivo absorption rate constant (Curatolo, 1987) with the following equation where S is drug solubility, Ka is absorption rate constant, V is intake water volume (250 ml), and T is transit time in small intestine (3 h). For instance, MAD could be estimated using different Ka values (Table 4.1). However, Ka has to be obtained from in vivo pharmacokinetic studies in animals or humans, which are usually not available during early stages of drug discovery and development. Alternatively Ka can be estimated by in vivo drug permeability if it is available by (4.23) Ka = Peff, human (A/ V) = Peff, human(2n RL/n R2 L) = Peff, human(2/R), (4.23) where A is the surface area, V is the volume, R is the radius, and L is the length of small intestine. However, it is also difficult to estimate the appropriate volume for the calculation in this method. Although standard water intake is 250 ml, the daily gastric secretion volume is 2,000 ml; intestine secretion volume is in the range of 1,500-2,000 ml; and bile and pancreatic secretion is 500-1,500 ml (Dressman etal., 1998).
4.5.1.3 Estimation of MAD from Drug In Vivo Permeability in Humans and Drug Solubility At the steady state of in situ human intestinal perfusion, drug flux J is a function of permeability, drug concentration, and absorption surface area (Amidon et al., 1988, 1995; Oh et al, 1993), Then, where J is drug flux, Peff, human is drug permeability in human intestine, S is drug solubility, A is absorption surface area, T is transit time in small intestine (3 h), R is the radius of small intestine (2 cm), and L is the length of small intestine (6 m). It is worth noting that the small intestine surface area for drug absorption should include surface area of villi and microvilli, but the surface area calculated in (4.24) is only the intestinal tube surface area without such consideration. However, since the permeability obtained in the in situ perfusion is calculated by (4.17), where the surface area also does not include villi and microvilli, the error is cancelled in the MAD calculation in (4.25), and it does not affect the MAD estimation if human intestinal permeability is used. The examples for estimation of MAD using permeability with (4.25), or using calculated Ka from human permeability with (4.22) and (4.23) are summarized in Table 4.2. In comparison of the examples in Tables 4.1 and 4.2, it seems that MAD might be underestimated using the absorption rate constant in (4.22) due to the assumption of 250 ml of volume in the calculation. MAD might be overestimated using permeability in (4.9) due to the assumption that the drug is absorbed at the maximum concentration (at its solubility) in the whole small intestinal region (6 m) Table 4.2. Estimation of MAD using drug intestinal permeability in human with following equation: MAD = Peff humanS2nRLT, MAD = Peff humanSAegT, or with calculated absorption rate constant (Ka) with following equations: Ka = Peff human(2/R) and MAD = SKaVT_ Peff , human Solubility MAD (mg) Peff , human MAD (mg) calculated from effective absorption surface area Calculated K a from Peff , human (min-1 ) MAD (mg) from calculated Ka Peff , human MAD (mg) calculated from effective absorption surface area Calculated K a from Peff , human (min-1 ) MAD (mg) from calculated Ka
with maximum surface area over the entire 3 h absorption period, while in reality only partial small intestine is used at a given time. Therefore, the effective absorption surface area of 800 cm2 is proposed to calculate MAD (Curatolo, 1987). The examples for estimation of MAD using this effective surface area are also summarized in Table 4.2. MAD using the effective absorption surface area seems more appropriate. If the MAD based on permeability and solubility is below the required clinical dose, formulation development, and delivery would be very challenging. |

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