Bateman function

After oral dosing, the bi-exponential Bateman function holds true with the absorption rate constant (Ka). 

According to the law of corresponding areas (FH Dost), the area derived from the integrated Bateman function (AUCpo = AUCiv) is the same as the area after-intravenous dosing if the bioavailability (F) is complete. 

Time-dependent absorption using a Bateman function model with or without lag time (Higaki et al., 2001)... 

Inverse Bateman The inverse Bateman function describes transient recovery from a baseline disease severity score, followed by reoccurrence of the disease, and is also useful for describing diseases that exhibit cyclical episodes. The function can also be implemented to describe a transient placebo response when warranted. For example, Holford et al. (25) used the inverse Bateman function to describe the time course of depression in placebo-treated patients. This model was selected for this work in part because of the transient response seen in placebo-treated patients and in part because of the cyclical nature of the disease where patients would be expected to improve and worsen over the course of treatment. Therefore, the first exponential process describes the recovery phase and the second exponential process is used to account for onset of disease in the next episode. 

Cyclical Modification of Inverse Bateman Function A cosine function can be used to describe patterns similar to the exponential and inverse Bateman models and can therefore be used as the function for disease progress. However, this same cosine function can also be used to impose a cyclical modulation on another function. 

A derived time scale (days) is done to improve numerical stabihty and to put the rate constants into more understandable units. The exponential functions for the inverse Bateman function are calculated. 

In this equation, the disease progression model is evaluated at any time t and the cosine function is added to the overall disease progression model to determine the status. Here, SADamp and Phase define the amplitude of the underlying cyclical change in disease severity score and the time to the maximum worsening of that score. A plot of an inverse Bateman function with a cyclical component is provided in Figure 21.11. 

Biexponential Input Function A biexponential (Bateman) function is sometimes useful because it is also capable of producing an input profile similar to the inverse Gaussian function and can describe nonlinear absorption processes. The representation for this input function is given as... 

Figure 2.5 Time dependence of the exposure concentration on the uptake (invasion) and the elimination of a chemical substance according to the Bateman function.

A special case occurs with the entero-hepatic recycling of a drug that can be described by using the sum of two Bateman-like functions. 

Bateman H., Erdelyi A. Higher Transcendental Functions (McGraw-Hill, New York) (1953). 

Guide Bioinformatics, 1998, 18. Attwood, T. K., The quest to deduce protein function from sequence the role of pattern databases, Int. ]. Biochem. Cell Biol., 2000, 32, 139. Bateman, A., Bieney, E., Durbin, R., Eddy, S. R., Howe, K. L., and Sonnhammbe, E. L., The Pfam Protein Families Database, Nucleic Acids Res., 2000, 28, 263. 

S. Fliigge, Practical Quantum Mechanics, Springer-Verlag, New York 1974 A. Erdelyi, Ed., higher Transcendental Functions, Vols. I and 2, Bateman Manuscript Project, McGraw-Hill, New York, 1953 A. Matsumoto, J. Phys. B At. Mol. Opt. Phys. 21, 2863 (1988). 

Various measurements of viscosity as a function of solids in diluted and concentrated milk reveal a curvilinear relationship (Bateman and Sharp 1928 Deysher, et al. 1944 Leighton and Kurtz 1930). Eilers et al. (1947) calculated voluminosity at several solids concentrations (skim milk), showing that the voluminosity of the caseinate particles does not change but that the apparent voluminosity of the total solids decreases as the concentration is raised. This may merely signify that... 

Another resource derived from BLOCKS and PRINTS is IDENTIFY, which, instead of encoding the exact information at each position in an alignment, tolerates alternative residues according to a set of prescribed groupings of related biochemical properties. IDENTIFY and its search software, eMOTIF (Huang and Brutlag, 2001), are accessible for use from the protein function Web server of the Biochemistry Department at Stanford University, http //dna.Stanford.edu/identify/. PANAL (http //mgd.ahc.umn.edu/panal/run panal.html) of Computational Biology Centers at the University of Minnesota is a combined resource for ProSite, BLOCKS, PRINTS, and Pfam (Bateman et al., 2000). 

Donohue JF, van Noord JA, Bateman ED, Langley SJ, Lee A, Witek TJ Jr, Kesten S, Towse L. A 6-month, placebo-controlled study comparing lung function and health status changes in COPD patients treated with tiotropium or salmeterol. Chest 2002 I22(l) 47-55. 

Apweiler, R., T. K. Attwood, A. Bairoch, A. Bateman, E. Birney, M. Biswas, R Bucher, et al. 2000. InterPro—An integrated documentation resource for protein families, domains and functional sites. Bioinformatics 16 1145-50. 

Bateman, H. and Erdelyi, A., Higher Transcendental Functions, Vol. 1, McGraw-Hill Book Corp., New York, 1953. 

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