Modeling/simulation blood flow

Trebotich D, Chang W, Lippmarm D (2001) Modelling of blood flow in simple Microsystems, hr Modeling and simulation of rrricrosystems 2001, ISBN 0-9708275-0 ... 

PBPK and classical pharmacokinetic models both have valid applications in lead risk assessment. Both approaches can incorporate capacity-limited or nonlinear kinetic behavior in parameter estimates. An advantage of classical pharmacokinetic models is that, because the kinetic characteristics of the compartments of which they are composed are not constrained, a best possible fit to empirical data can be arrived at by varying the values of the parameters (O Flaherty 1987). However, such models are not readily extrapolated to other species because the parameters do not have precise physiological correlates. Compartmental models developed to date also do not simulate changes in bone metabolism, tissue volumes, blood flow rates, and enzyme activities associated with pregnancy, adverse nutritional states, aging, or osteoporotic diseases. Therefore, extrapolation of classical compartmental model simulations... 

While these models simulate the transfer of lead between many of the same physiological compartments, they use different methodologies to quantify lead exposure as well as the kinetics of lead transfer among the compartments. As described earlier, in contrast to PBPK models, classical pharmacokinetic models are calibrated to experimental data using transfer coefficients that may not have any physiological correlates. Examples of lead models that use PBPK and classical pharmacokinetic approaches are discussed in the following section, with a focus on the basis for model parameters, including age-specific blood flow rates and volumes for multiple body compartments, kinetic rate constants, tissue dosimetry,... 

The original proposal of the approach, supported by a Monte Carlo simulation study [36], has been further validated with both pre-clinical [38, 39] and clinical studies [40]. It has been shown to be robust and accurate, and is not highly dependent on the models used to fit the data. The method can give poor estimates of absorption or bioavailability in two sets of circumstances (i) when the compound shows nonlinear pharmacokinetics, which may happen when the plasma protein binding is nonlinear, or when the compound has cardiovascular activity that changes blood flow in a concentration-dependent manner or (ii) when the rate of absorption is slow, and hence flip-flop kinetics are observed, i.e., when the apparent terminal half-life is governed by the rate of drug input. 

Figure 13.5. Model of Boddy, adapted from reference [7] (Section 13.3.3). The drug-carrier conjugate (DC) is administered at a rate i c(DC) into the central compartment, which is characterized by a volume of distribution To DC is transported by blood flow Qcr to and from the response (target) compartment, characterized by a volume of distribution Vr, and by blood flow Qct to and from the toxicity compartment, characterized by a volume of distribution VV- DC is eliminated from only the central compartment with a clearance CLc(DC). The active drug (D) is released from DC in the central, response and toxicity compartments with first-order rate constants kc, k and fcr> respectively. The D is distributed over these compartments in a manner similar to the DC. The D is eliminated from these compartments with a clearance of CLc(D), CLr(D) and CLt(D), respectively. Conventional drug administration can be simulated by the input of D at a rate i c(D) into the central compartment.

As with classic compartment pharmacokinetic models, PBPK models can be used to simulate drug plasma concentration versus time profiles. However, PBPK models differ from classic PK models in that they include separate compartments for tissues involved in absorption, distribution, metabolism and elimination connected by physiologically based descriptions of blood flow (Figure 10.1). 

Several models have been developed to simulate the absorption, distribution, metabolism and excretion of butadiene, some of its metabolites and its adducts to haemoglobin in mouse, rat and man. Critical aspects are discussed in Csanady et al. (1996) and in Himmelstein et al. (1997). Basically, the models consist of a number of compartments representing diverse tissues and organs, several of which are grouped together. These compartments are linked by blood flow. The main differences between models are the number of metabolizing and nonmetabolizing compartments, the mechanisms of metabolism, the metabolites taken into consideration, and the values of the biochemical. 

The models were developed to simulate the physiology (e.g., blood flows and body composition) of adult rats (Table 3-6). These parameter values were then extrapolated to juvenile rats to accommodate calibration and validation data in which juvenile rats were the test organisms. The extrapolation was achieved by scaling blood flows, metabolic constants, and adipose volumes to various functions of body weight (e.g., allometric scaling). 

A physiologically based pharmacokinetics (PBPK) model based on the ventilation rate, cardiac output, tissue blood flow rates, and volumes as well as measured tissue/air and blood/air partition coefficients has been developed (Medinsky et al. 1989a Travis et al. 1990). Experimentally determined data and model simulations indicated that during and after 6 hours of inhalation exposure to benzene, mice metabolized benzene more efficiently than rats (Medinsky et al. 1989a). After oral exposure, mice and rats appeared to metabolize benzene similarly up to oral doses of 50 mg/kg, above which rats metabolized more benzene than did mice on a per kg body weight basis (Medinsky et al. 1989b). This model may be able to predict the human response based on animal data. Benzene metabolism followed Michaelis-Menton kinetics in vivo primarily in the liver, and to a lesser extent in the bone marrow. Additional information on PBPK modeling is presented in Section 2.3.5. 

Figure 30.6 shows a prediction of the plasma concentration of ARA-C and total radioactivity (ARA-C plus ARA-U) following administration of two separate bolus intravenous injections of 1.2 mg/kg to a 70-kg woman. All compartment sizes and blood flow rates were estimated a -priori, and all enzyme kinetic parameters were determined from published in vitro studies. None of the parameters was selected specifically for this patient only the dose per body weight was used in the simulation. The prediction has the correct general shape and magnitude. It can be made quantitative by relatively minor changes in model parameters with no requirement to adjust the parameters describing metabolism. 

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. 

---