Model perfusion rate-limited

In perfusion models, as depicted in Fig. 3, it is assumed that distribution into and out of the organ is perfusion rate limited such that drug in the organ is in equilibrium with drug concentration in the emergent blood... 

Fig. 17.5 Schematic representation of a physiological based model. Left figure shows the physiological structure, upper right figure shows a model for a perfusion rate limited tissue, and lower right figure shows a model for a permeability rate-limited tissue. Q denotes the blood flow, CL the excretion rate, KP the tissuerplasma distribution coefficient, and PS the permeability surface area coefficient.

Figure 9.6 The dependence of salicylic acid absorption on the net water flux (positive sign flow directed from the lumen and towards the blood) in the rat jejunal loop perfused with hypo-, iso- and hypertonic solutions at pH 6.2 and 2.2. The lines, mean values with 95% confidence limits (shaded areas), were calculated by means of the parameters determined by a kinetic model with the following constants concentration of salicylic acid in the perfusion solution 32.3 /

Despite the limitations of the Pennes bioheat equation, reasonable agreement between theory and experiment has been obtained for the measured temperature profiles in perfused tissue subject to various heating protocols. This equation is relatively easy to use, and it allows the manipulation of two blood-related parameters, the volumetric perfusion rate and the local arterial temperature, to modify the results. Pennes performed a series of experimental studies to validate his model. Over the years, the validity of the Pennes bioheat equation has been largely based on macroscopic thermal clearance measurements in which the adjustable free parameter in the theory, the blood perfusion rate [Xu and Anderson, 1999] was chosen to provide reasonable agreement with experiments for the temperature decay in the vicinity of the thermistor bead probe. Indeed, if the limitation of Pennes bioheat equation is an inaccurate estimation of the strength of the perfusion source term, an adjustable blood perfusion rate will overcome its limitations and provide reasonable agreement between experiment and theory. 

The main limitations of the Weinbaum-Jiji equation are associated with the importance of the countercurrent heat exchange. It was derived to describe heat transfer in peripheral tissue only, where its fundamental assumptions are most applicable. In tissue area containing a big blood vessel (>200 /rm in diameter), the assumption that most of the heat leaving the artery is recaptured by its countercurrent vein could be violated, thus, it is not an accurate model to predict the temperature field. In addition, this theory was primarily developed for closely paired microvessels in muscle tissue, which may not always be the main vascular structure in other tissues, such as the renal cortex. Furthermore, unlike the Pennes equation, which requires only the value of blood perfusion, the estimation of the enhancement in thermal conductivity requires that detailed anatomical studies be performed to estimate the vessel number density, size, and artery-vein spacing for each vessel generation, as well as the blood perfusion rate (Zhu et al., 1995). These anatomic data are normally not available for most blood vessels in the thermally significant range. 

As flow rates decrease, the perfusion medium in the probe approaches equilibrium with the ECF (Wages et al., 1986). Therefore, the dialysate concentration of an analyte sampled at very lowflow rates more closely approximates the concentration in the extracellular environment (Menacherry et al., 1992). Like no net flux and the zero flow models, this is another steady-state analysis with limited application to transient changes based on behavior or pharmacological manipulations. However, the advent of new techniques in analytical chemistry requiring only small sample volumes from short sampling intervals may signal a potential return to the low flow method. 

When experiments are performed in vivo, previously independent components of the model, the sampling, and the analytical method become interdependent. The conditions that were optimal for each independent component must now be considered in relationship to the other components. For example, if the method requires a large sample volume the flow rate of the perfusate must be increased. If the flow rate is increased, the extraction efficiency will be decreased. The result is that the analytical method will require better limits of detection. On the other hand, if the flow rate is decreased to increase the extraction efficiency, the temporal resolution will be compromised [5]. The increased recovery can also deplete compounds of low molecular mass in the tissue near the probe, thereby perturbing the experimental conditions. 

The tissue compartments included in the Shyr model are as follows respiratory tract liver gastrointestinal tract fat and a group of richly perfused tissues including kidney, bone marrow, and heart. Muscle and skin were separated into individual compartments to allow for the simulation of dermal exposure. The distribution of 2-butoxyethanol among compartments was assumed to be limited only by blood flow rate because the lipid solubility of 2-butoxyethanol allowed it to penetrate cell membranes rapidly. Liver was a major site of metabolism in the Shyr model with a minor amount of 2-butoxyethanol-glucuronide formed in the skin at the site of application for dermal exposure. 

Figure 7.6 Flow-limited organ model. The three-compartment model of an individual organ (Figure 7.1c) can be reduced to this simpler two-compartment model if the rate of perfusion is slower than the rate of exchange across membranes in the organ.

If the organ is reasonably well perfused (i.e., the flow-limited conditions are not satisfied), the full physiological pharmacokinetic treatment may be reduced by assuming the organ is membrane limited. Here, the limitation on transport is assumed to occur at either the capillary membrane separating the vascular and interstitial compartments or the plasma membranes separating the interstitial and intracellular compartments. For example, when the net flux between the interstitial and intracellular compartments is much slower than the net flux between the vascular and interstitial compartments and the plasma flow rate, the three-compartment model can be reduced to a two-compartment model ... 

Figure 1. PBPK model for dX -trans-veimoic acid and its metabolites. Abbreviations are Dy intravenous dose (mg) Q or P or C, flow rate or partition coefficient or concentration (mg/1) subscripts c (cardiac), f (fat), g (gut), 1 (liver), pi (placenta), r (richly perfused tissues muscle, bone), s (slowly perfused tissues mammary gland, uterus), sk (skin) Dsc diffusivity in stratum comeum (cm%r) k rate constant subscripts b (biliary clearance), CO2 (side chain oxidation to carbon dioxide/hr), ct (cis/trans isomerization), tc (trans/cis isomerization) e (diffusion limited transfer between placenta and embryo, 1/hr) f (fecal excretion/hr) h (hydrolysis of glucuronide/hr) o (oral absorption) r (intestinal absorption) v (intravenous injection) K or V (affinity constant or maximum velocity where mg = apparent Michaelis-Menten glucuronidation constant and mx = apparent Michaelis-Menten oxidation constant). Rounded box indicates the submodels as diagrammed in Figures 2-5. (Reproduced with permission of Mosby-Year Book, Inc. from the American Academy of Dermatology. Clewell, [29].)...

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