Data processing: structural design – modeling – simulation – and em – Modeling by mathematical expression
Reexamination Certificate
1999-05-26
2003-04-01
Brusca, John S. (Department: 1631)
Data processing: structural design, modeling, simulation, and em
Modeling by mathematical expression
C703S011000, C702S019000
Reexamination Certificate
active
06542858
ABSTRACT:
INTRODUCTION
1. Technical Field
The present invention relates to computer-implemented pharmacokinetic simulation models and drug design.
2. Background
A. Pharmacokinetic Modeling
Pharmacodynamics refers to the study of fundamental or molecular interactions between drug and body constituents, which through a subsequent series of events results in a pharmacological response. For most drugs the magnitude of a pharmacological effect depends on time-dependent concentration of drug at the site of action (e.g., target receptor-ligand/drug interaction). Factors that influence rates of delivery and disappearance of drug to or from the site of action over time include absorption, distribution, metabolism, and elimination. The study of factors that influence how drug concentration varies with time is the subject of pharmacokinetics.
In nearly all cases the site of drug action is located on the other side of a membrane from the site of drug administration. For example, an orally administered drug must be absorbed across a membrane barrier at some point or points along the gastrointestinal (GI) tract. Once the drug is absorbed, and thus passes a membrane barrier of the GI tract, it is transported through the portal vein to the liver and then eventually into systemic circulation (i.e., blood and lymph) for delivery to other body parts and tissues by blood flow. Thus how well a drug crosses membranes is of key importance in assessing the rate and extent of absorption and distribution of the drug throughout different body compartments and tissues. In essence, if an otherwise highly potent drug is administered extravascularly (e.g., oral) but is poorly absorbed (e.g., GI tract), a majority of the drug will be excreted or eliminated and thus cannot be distributed to the site of action.
The principle routes by which drugs disappear from the body are by elimination of unchanged drug or by metabolism of the drug to a pharmacologically active or inactive form(s) (i.e., metabolites). The metabolites in turn may be subject to further elimination or metabolism. Elimination of drugs occurs mainly via renal mechanisms into the urine and to some extent via mixing with bile salts for solubilization followed by excretion through the GI tract, exhaled through the lungs, or secreted through sweat or salivary glands etc. Metabolism for most drugs occurs primarily in the liver.
Each step of drug absorption, distribution, metabolism, and elimination can be described mathematically as a rate process. Most of these biochemical processes involve first order or pseudo-first order rate processes. In other words, the rate of reaction is proportional to drug concentration. For instance, pharmacokinetic data analysis is based on empirical observations after administering a known dose of drug and fitting of the data by either descriptive equations or mathematical (compartmental) models. This permits summarization of the experimental measures (plasma/blood level-time profile) and prediction under many experimental conditions. For example after rapid intravenous administration, drug levels often decline mono-exponentially (first-order elimination) with respect to time as described in Equation 1, where Cp(t) is drug concentration as a function of time, Cp(0) is initial drug concentration, and k is the associated rate constant that represents a combination of all factors that influence the drug decay process (e.g., absorption, distribution, metabolism, elimination).
Cp
(
t
)=
Cp
(0)
et
−kt
(Eq. 1)
This example assumes the body is a single “well-mixed” compartment into which drug is administered and from which it also is eliminated (one-compartment open model). If equilibrium between drug in a central (blood) compartment and a (peripheral) tissue compartment(s) is not rapid, then more complex profiles (multi-exponential) and models (two- and three-compartment) are used. Mathematically, these “multi-compartment” models are described as the sum of equations, such as the sum of rate processes each calculated according to Equation 1 (i.e., linear pharmacokinetics).
Experimentally, Equation 1 is applied by first collecting time-concentration data from a subject that has been given a particular dose of a drug followed by plotting the data points on a logarithmic graph of time versus drug concentration to generate one type of time-concentration curve. The slope (k) and the y-intercept (C0) of the plotted “best-fit” curve is obtained and subsequently incorporated into Equation 1 (or sum of equations) to describe the drug's time course for additional subjects and dosing regimes.
When drug concentration throughout the body or a particular location is very high, saturation or nonlinear pharmacokinetics may be applicable. In this situation the capacity of a biochemical and/or physiological process to reduce drug concentration is saturated. Conventional Michaelis-Menten type equations are employed to describe the nonlinear nature of the system, which involve mixtures of zero-order (i.e., saturation:concentration independent) and first-order (i.e., non-saturation:concentration dependent) kinetics. Experimentally, data collection and plotting are similar to that of standard compartment models, with a notable exception being that the data curves are nonlinear. Using a time versus concentration graph to illustrate this point, at very high drug concentration the data line is linear because the drug is being eliminated at a maximal constant rate (i.e., zero-order process). The data line then begins to curve in an asymptotic fashion with time until the drug concentration drops to a point where the rate process becomes proportional to drug concentration (i.e., first-order process). For many drugs, nonlinear pharmacokinetics applies to events such as dissolution of the therapeutic ingredient from a drug formulation, as well as metabolism and elimination. Nonlinear pharmacokinetics also can be applied to toxicological events related to threshold dosing.
Classical one, two and three compartment models used in pharmacokinetics require in vivo blood data to describe time-concentration effects related to the drug decay process, i.e., blood data is relied on to provide values for equation parameters. For instance, while a model may work to describe the decay process for one drug, it is likely to work poorly for others unless blood profile data and associated rate process limitations are generated for each drug in question. Thus, such models are very poor for predicting the in vivo fate of diverse drug sets in the absence of blood data and the like derived from animal and/or human testing.
In contrast to the standard compartment models, physiological-based pharmacokinetic models are designed to integrate basic physiology and anatomy with drug distribution and disposition. Although a compartment approach also is used for physiological models, the compartments correspond to anatomic entities such as the GI tract, liver, lung etc., which are connected by blood flow. Physiological modeling also differs from standard compartment modeling in that a large body of physiological and physicochemical data usually is employed that is not drug-specific. However, as with standard compartment models the conventional physiological models lump rate processes together. Also, conventional physiological models typically fail to incorporate individual kinetic, mechanistic and physiological processes that control drug distribution and disposition in a particular anatomical entity, even though multiple rate processes are represented in vivo. Physiological models that ignore these and other important model parameters contain an underlying bias resulting in poor correlation and predictability across diverse data sets. Such deficiencies inevitably result in unacceptable levels of error when the model is used to describe or predict drug fate in animals or humans. The problem is amplified when the models are employed to extrapolate animal data to humans, and worse, when in vitro data is relied on for prediction in animals or humans.
For instance, the
Grass George M.
Leesman Glen D.
Norris Daniel A.
Sinko Patrick J.
Wehrli John E.
Arent Fox Kintner & Plotkin & Kahn, PLLC
Brusca John S.
Lion Bioscience AG
Moran Marjorie A.
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