Logarithm, dose

Buoen et al. (9) reported that the dose-escalation schemes used in FTIH studies could be categorized as linear, logarithmic, modified Fibonacci, or miscellaneous. The latter included dose-escalation regimens in which the three standardized methods are combined. The authors reported that in 12 out of the 105 studies they reviewed a linear escalation method with fixed dose increment was used. A logarithmic dose-escalation scheme in which the relative dose increment was the same (e.g., 100%) was used in 22 studies. Four of the studies used a modified version of the Fibonacci escalation scheme, which is frequently used in cancer Phase 1 trials (6, 12-14). For most of the studies reviewed (i.e., 63.8%, or 67 studies) the dose-escalation schemes used did not seem to follow one particular scheme. In some cases two of the escalation schemes described above were combined (e.g., starting with a logarithmic escalation to convert later into a modified Fibonacci sequence), while for other studies, no escalation scheme was apparent. The doses appeared to have been chosen arbitrarily (11). 

This logarithmic relationship between dose and duration of action is a fundamental one which is unaffected by the functional presence or absence of cholinesterase. That is, individual logarithmic dose-duration curves are parallel straight lines for subjects with different esterase activities. The explanation can only be that the cholinesterase activity chiefly determines the initial loading of the muscle endplate in other words, that it hydrolyzes a substantial portion of succinylcholine immediately after injection into the blood stream, and thereby regulates the fraction available for receptor occupation in the endplate. A more recent... 

Figure 2-1. Graded dose-response and dose-binding graphs. A. Relation between drug dose or concentration and drug effect. When the dose axis is linear, a hyperbolic curve is commonly obtained. B. Same data, logarithmic dose axis, the dose or concentration at which effect is half-maximal Is denoted EC q, while the maximal effect is C. If the percentage of receptors that bind drug is plotted against drug concentration, a similar curve is obtained, and the concentration at which 50% of the receptors are bound is denoted and the maximal number of receptors bound is termed...

The basic criterion of a bioassay is the index of precision (A). This depends on the slope of the logarithmic dose-response graph b) and the standard deviation (s) of the points from the line (obtained by subtracting each value of y from its recorded value yc) ... 

Bioautography vs. Mycobacterium ranae UC16I, Sarcina lutea PCI 1001 or Bacillus subtiUs UC564. Component poteiuaes estimated from satd. curves plotted as zone width vs. logarithmic dose R f (estimated from drawing)... 

Noise. Technical differences exist between personal noise dosimeters and high accuracy sound level meters and these may alter the usual preference for personal monitors. But it is exposure to noise rather than general room noise that must be estimated for comparison with noise exposure criteria, the logarithmic expression and alternative means of summation (3 vs 5 db doubling) compHcate statistics. Exposure criteria for both dose and peak exposure must be evaluated, and space and time variabiUty of noise intensity can be immense. 

Everyone receives small radiation doses every day Figure 8.3-5 illustrates some of the doses received from background and other types of radiation. Note that the scale is logarithmic , and that background and cosmic-ray doses vary over an order of magnitude just with location and elevation. In addition to these natural sources, most people receive some medical and dental doses each year. 

Keeping the composition of copolymerization media constant the total comonomer concentration of which is varied. The absorbed dose was kept constant at 0.14 KGy for the AM-AANa and at 0.35 KGy for the AM-DAEA-HCl systems. The results are shown in Figs. 4 and 5, which show the rate of polymerization, Rp, the degree of polymerization, and the intrinsic viscosity increase with increasing monomer concentration. At comonomer concentration >2.1 M/L, DPn decreases with increasing comonomer concentration. From the logarithmic plots, exponents of the comonomer concentration for the AM-AANa system were determined to be [17,54]. 

Dose-response curves depict the response to an agonist in a cellular or subcellular system as a function of the agonist concentration. Specifically, they plot response as a function of the logarithm of the concentration. They can be defined completely by three parameters namely, location along the concentration axis, slope, and maximal asymptote... 

FIGURE 3.6 Classical model of agonism. Ordinates response as a fraction of the system maximal response. Abscissae logarithms of molar concentrations of agonist, (a) Effect of changing efficacy as defined by Stephenson [24], Stimulus-response coupling defined by hyperbolic function Response = stimulus/(stimulus-F 0.1). (b) Dose-response curves for agonist of e = 1 and various values for Ka. 

FIGURE 5.10 Effects of co-expressed G-protein (G ) on neuropeptide NPY4 receptor responses (NPY-4). (a) Dose-response curves for NPY-4. Ordinates Xenopus laevis melanophore responses (increases light transmission). Ordinates logarithms of molar concentrations of neuropeptide Y peptide agonist PYY. Curves obtained after no co-transfection (labeled 0 jig) and co-transfection with cDNA for Gai6. Numbers next to the curves indicate jig of cDNA of Ga]g used for co-transfection, (b) Maximal response to neuropeptide Y (filled circles) and constitutive activity (open circles) as a function of pg cDNA of co-transfected G g. 

The measured dose ratios are then used to calculate Log (DR-1) ordinates for the corresponding abscissal logarithm of the antagonist concentration that produced the shift in the control curve. A linear equation of the form... 

FIGURE 6.6 Schilcl regression for pirenzepine antagonism of rat tracheal responses to carbachol. (a) Dose-response curves to carbachol in the absence (open circles, n = 20) and presence of pirenzepine 300 nM (filled squares, n = 4), 1 jjM (open diamonds, n=4), 3j.lM (filled inverted triangles, n = 6), and 10j.iM (open triangles, n = 6). Data fit to functions of constant maximum and slope, (b) Schild plot for antagonism shown in panel A. Ordinates Log (DR-1) values. Abscissae logarithms of molar concentrations of pirenzepine. Dotted line shows best line linear plot. Slope = 1.1 + 0.2 95% confidence limits = 0.9 to 1.15. Solid line is the best fit line with linear slope. pKB = 6.92. Redrawn from [5],... 

Dose-response data are obtained and plotted on a semi-logarithmic axis, as shown in Figure 12.3a (data shown in Table 12.3a). 

Log normal distribution, the distribution of a sample that is normal only when plotted on a logarithmic scale. The most prevalent cases in pharmacology refer to drug potencies (agonist and/or antagonist) that are estimated from semilogarithmic dose-response curves. All parametric statistical tests on these must be performed on their logarithmic counterparts, specifically their expression as a value on the p scale (-log values) see Chapter 1.11.2. 

Batch fermentation is the most widely used method of amino add production. Here the fermentation is a dosed culture system which contains an initial, limited amount of nutrient. After the seed inoculum has been introduced the cells start to grow at the expense of the nutrients that are available. A short adaptation time is usually necessary (lag phase) before cells enter the logarithmic growth phase (exponential phase). Nutrients soon become limited and they enter the stationary phase in which growth has (almost) ceased. In amino add fermentations, production of the amino add normally starts in the early logarithmic phase and continues through the stationary phase. 

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