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1.  Use of partition coefficients in flow-limited physiologically-based pharmacokinetic modeling 
Permeability-limited two-subcompartment and flow-limited, well-stirred tank tissue compartment models are routinely used in physiologically-based pharmacokinetic modeling. Here, the permeability-limited two-subcompartment model is used to derive a general flow-limited case of a two-subcompartment model with the well-stirred tank being a specific case where tissue fractional blood volume approaches zero. The general flow-limited two-subcompartment model provides a clear distinction between two partition coefficients typically used in PBPK: a biophysical partition coefficient and a well-stirred partition coefficient. Case studies using diazepam and cotinine demonstrate that, when the well-stirred tank is used with a priori predicted biophysical partition coefficients, simulations overestimate or underestimate total organ drug concentration relative to flow-limited two-subcompartment model behavior in tissues with higher fractional blood volumes. However, whole-body simulations show predicted drug concentrations in plasma and lower fractional blood volume tissues are relatively unaffected. These findings point to the importance of accurately determining tissue fractional blood volume for flow-limited PBPK modeling. Simulations using biophysical and well-stirred partition coefficients optimized with flow-limited two-subcompartment and well-stirred models, respectively, lead to nearly identical fits to tissue drug distribution data. Therefore, results of whole-body PBPK modeling with diazepam and cotinine indicate both flow-limited models are appropriate PBPK tissue models as long as the correct partition coefficient is used: the biophysical partition coefficient is for use with two-subcompartment models and the well-stirred partition coefficient is for use with the well-stirred tank model.
PMCID: PMC3400708  PMID: 22639356
Physiologically-based pharmacokinetics; Flow-limited; Permeability-limited; Well-stirred tank; Compartmental modeling; Partition coefficient; Biophysical; Diazepam; Cotinine
2.  Physiologically-based pharmacokinetic tissue compartment model selection in drug development and risk assessment 
Journal of Pharmaceutical Sciences  2011;101(1):424-435.
The well-stirred tank (WST) has been the predominant flow-limited tissue compartment model in physiologically-based pharmacokinetic (PBPK) modeling. Recently, we developed a two-region asymptotically reduced (TAR) PBPK tissue compartment model through an asymptotic approximation to a two-region vascular-extravascular system to incorporate more biophysical detail than the WST model. To determine the relevance of the novel flow-limited approach (F-TAR), 75 structurally diverse drugs are evaluated herein using a priori predicted tissue:plasma partition coefficients along with hybrid and whole-body PBPK of eight rat tissues to determine the impact of model selection on simulation and optimization. Simulations show the F-TAR model significantly improves the ability to predict drug exposure, with hybrid and whole-body WST model error approaching 50% for tissues with larger vascular volumes. When optimization is used to fit F-TAR and WST models to pseudo data, WST-optimized drug partition coefficients more appropriately represent curve-fitting parameters rather than biophysically meaningful partition coefficients. Median F-TAR-optimized error ranged from -0.4 to 0.3%, while WST-optimized median error ranged from -22.2 to 1.8%. These studies demonstrate the use of F-TAR represents a more accurate, biophysically realistic PBPK tissue model for predicting tissue exposure to drug and should be considered for use in drug development and regulatory review.
PMCID: PMC3314064  PMID: 21968734
Pharmacokinetics; Physiological model; Well stirred model; Tissue partition; In silico modeling; Physicochemical; Singular perturbation; Asymptotic matching; Flow-limited; Compartmental modeling
3.  Development of appropriate equations for physiologically based pharmacokinetic modeling of permeability-limited and flow-limited transport 
Although the implementation of a flow-limited, well-stirred tank (WST) single-compartment tissue model in pharmacokinetics and toxicokinetics is widespread, its use is not always justified biophysically or physiologically. The WST model introduces a loss of biophysical detail, specifically the vascular space, which is present in the standard permeability-limited two-subcompartment (PLT) tissue model. To address this loss of detail when evaluating the in vivo kinetics of drugs, toxins, nutrients, and endogenous metabolites, a novel set of physiologically based pharmacokinetic tissue compartment equations is developed through application of an asymptotic approximation to a two-region vascular–extravascular system to arrive at a permeability-limited two-region asymptotically reduced (P-TAR) model and a flow-limited (F-TAR) model. Development of the TAR modeling approach illustrates the importance of relative timescales in PBPK tissue compartment model selection and the conditions under which improved biophysical realism is advantageous. In the permeability-limited regime, the TAR model formulations enable drug or toxicant concentration to be modeled in the vascular and extravascular spaces equivalent to the PLT tissue model while invoking only one state variable to represent the vascular and extravascular spaces. In the flow-limited regime, the F-TAR model is more biophysically realistic than the WST model because it maintains the anatomical distinction between the vascular and extravascular spaces, and hence offers greater pharmacological and physiological insight than the WST model, without introducing additional computational complexity.
PMCID: PMC3193163  PMID: 21584718
Physiologically based pharmacokinetics; Flow-limited; Permeability-limited; Well-stirred tank; Compartmental modeling; Singular perturbation
4.  Metformin as an energy restriction mimetic agent for breast cancer prevention 
This study examined whether metformin administration inhibited chemically induced mammary carcinogenesis in rats. In cancer prevention, metformin may act (1) indirectly through reducing systemic risk factors; or (2) directly through AMPK-mediated signaling. To begin to delineate clinically relevant mechanisms for breast cancer prevention, metformin was also studied along with dietary energy restriction.
Materials and Methods:
Mammary cancer was induced in female Sprague--Dawley rats (50 mg/kg MNU, i.p.). Metformin was fed alone (AIN93G + 0.05 to 1.0% w/w metformin) or combined with 40% dietary energy restriction. Plasma analytes (e.g., insulin, glucose, IGF-1) and protein expression (e.g., AMPK, mTOR, Akt) in mammary carcinomas and liver were evaluated. Additional studies included (1) aldehyde dehydrogenase flow cytometry, to gauge potential for cancer-initiated cells in mammary carcinomas to respond to metformin; (2) cell culture, to understand dose response (0.02--20 mM) of different cancer cell line molecular subtypes to metformin; and (3) analysis of a rat mammary epithelial cell microarray database, to examine expression of genes related to metformin pharmacokinetics (e.g., organic cation transporters) and pharmacodynamics (e.g., complex I of electron transport).
While a dosing regimen of 1.0%/0.25% metformin-reduced palpable mammary carcinoma incidence, multiplicity, and tumor burden and prolonged latency, lower doses of metformin failed to inhibit carcinogenesis despite effects on plasma insulin. Human breast cancer cell growth inhibition in response to metformin was only observed at high concentrations. Poor in vivo and in vitro response to metformin may be the result of pharmacokinetic (OCT-1 expression was low in rat mammary cells; OCT-3 was downregulated in mammary carcinoma) and pharmacodynamic (complex I transcripts were higher in mammary epithelial cells from carcinomas versus uninvolved gland) effects. In combination with dietary energy restriction, metformin offered protection against new tumor occurrence following release from combined treatment. Flow cytometry indicated the presence of cancer-initiated cells in mammary carcinomas.
As a single agent, metformin possessed limited cancer inhibitory activity. However, metformin may be an effective component of multiagent interventions that target cancer-initiated cells. There is a clear need to identify the conditions under which metformin is likely to benefit prevention and control of breast cancer.
PMCID: PMC3142764  PMID: 21799661
AMP-activated protein kinase; insulin; mammalian target of rapamycin; mammary carcinogenesis; metformin
5.  A Method for Serial Tissue Processing and Parallel Analysis of Aberrant Crypt Morphology, Mucin Depletion, and Beta-Catenin Staining in an Experimental Model of Colon Carcinogenesis 
Biological Procedures Online  2010;12:118-130.
The use of architectural and morphological characteristics of cells for establishing prognostic indicators by which individual pathologies are assigned grade and stage is a well-accepted practice. Advances in automated micro- and macroscopic image acquisition and digital image analysis have created new opportunities in the field of prognostic assessment; but, one area in experimental pathology, animal models for colon cancer, has not taken advantage of these opportunities. This situation is primarily due to the methods available to evaluate the colon of the rodent for the presence of premalignant and malignant pathologies. We report a new method for the excision and processing of the entire colon of the rat and illustrate how this procedure permitted the quantitative assessment of aberrant crypt foci (ACF), a premalignant colon pathology, for characteristics consistent with progression to malignancy. ACF were detected by methylene blue staining and subjected to quantitative morphometric analysis. Colons were then restained with high iron diamine–alcian blue for assessment of mucin depletion using an image overlay to associate morphometric data with mucin depletion. The subsequent evaluation of ACF for beta-catenin staining is also demonstrated. The methods described are particularly relevant to the screening of compounds for cancer chemopreventive activity.
PMCID: PMC3284111  PMID: 21406072
colon carcinogenesis; aberrant crypt foci; mucin depletion; beta-catenin; image analysis; morphometry

Results 1-5 (5)