Effective dose curve

TED50= Tl[2 (IM/H) ln(2 + (Cpeak/CE50) AH) TED90 = 7T/2 (IM/H) ln(10+9 (Cpeak/CE50)A//) For single dose monoexponential kinetics and direct effect conditions, the area under the effect time curve (AUEC) can be derived by integration of the Hill equation. 

Figure 9. Effective dose equivalent per hour and per unit radon concentration (A J-B, V J-E), equilibrium factor ( ) and unattached fraction (o, right ordinate) versus the attachment rate. The curves are calculated as in Figure 7.

Endpoint/Concentration/Rationale In the absence of data specifically identifying AEGL-2 endpoints, the AEGL-2 was based upon a 3-fold reduction of the AEGL-3 values for all time periods. Given the steepness of the exposure-dose curve, it is believed that a 3-fold downward adjustment would be protective against serious longterm, irreversible effects, or the inability to escape. 

Figure 2-8 The various types of response vs. log dose curves. ED, effective dose TD, toxic dose LD, lethal dose. For gases, LC (lethal concentration) is used.

If the response to the chemical or agent is minor and reversible (such as minor eye irritation), the response-log dose curve is called the effective dose (ED) curve. Values for ED50, ED10, and so forth are also used. 

Most often, response-dose curves are developed using acute toxicity data. Chronic toxicity data are usually considerably different. Furthermore, the data are complicated by differences in group age, sex, and method of delivery. If several chemicals are involved, the toxicants might interact additively (the combined effect is the sum of the individual effects), synergisti-cally (the combined effect is more than the individual effects), potentiately (presence of one increases the effect of the other), or antagonistically (both counteract each other). 

The lowest value on the response versus dose curve is called the threshold dose. Below this dose the body is able to detoxify and eliminate the agent without any detectable effects. In reality the response is only identically zero when the dose is zero, but for small doses the response is not detectable. 

In vitro clonal tumor cell studies have demonstrated the severe cytotoxicity of a-particles delivered by At single exponential cell survival-dose curves were obtained, with (37% survival) values of 29-48 cGy and 57-73 cGy for Chinese hamster V-79 (5J ) and HEp2 cells, respectively (55). In both studies the oxygen enhancement ratio (OER) was found to be slightly greater than unity, probably resulting from the low-LET components of At decay (see Fig. 5). In biological systems, such a-particle emissions enable comparable cytotoxicities to be effected in both hypoxic and euoxic tumor cell populations. 

ECETOC (1995) recommended a factor of 2 to be used in case the extent of the relevant effect is of minor importance, and the slope of the dose-response curve reasonably justifies the assumption that a halving of the LOAEL would be likely to arrive at the no-effect dose. A factor of 3 was recommended as a default value, which would be used in the majority of cases. Extent and severity of the effect at the LOAEL and/or a very flat dose-response curve may justify the use of a higher factor. 

In the case of dose additivity, the dose-response curve of A is determined on a linear- or log-dose scale, and an equi-effective dose of A (liA.equi) and B d resulting in the same effect is estimated. Using the fixed dose d of chemical B and adding various doses dp - i A.equi) of A, the dose-response curve should shift to the left and reach the same maximum as the maximum for the dose-response curve of A alone when the effect of B is smaller than Amax- However, in case of competitive agonism, the effect of B does not affect the effect of A -f B at higher dose of A. 

Quantal dose-response curves based on all-or-none responses. A. Relationship between the dose of phenobarbital and the protection of groups of rats against convulsions. B. Relationship between the dose of phenobarbital and the drug s lethal effects in groups of rats. ED50, effective dose, 50% LD50, lethal dose, 50%. 

The quantal dose-response curve represents estimates of the frequency with which each dose elicits the desired response in the population. In addition to this information, it also would be useful to have some way to express the average sensitivity of the entire population to phenobarbital. This is done through the calculation of an ED50 (effective dose, 50% i.e., the dose that would protect 50% of the animals). This value can be obtained from the dose-response curve in Figure 22A, as shown by the broken lines. The ED50 for phenobarbital in this population is approximately 4mg/kg. 

Figure 5.9. Dose-response profile in a population. (A) Relationship between responding patients, expressed as percentage of individuals, and plasma drug concentrations. With increasing drug concentration, the proportion of patients who derive therapeutic benefit, without concentration-limited side effect peaks, and then declines. (B) A schematic representation of dose-response curves. Typical therapeutic and lethal responses at indicated doses are evaluated in animal models to estimate therapeutic index, TI. ED50, effective dose needed to produce a therapeutic response in 50% of animals, exhibiting therapeutic response LD50, effective dose needed to produce lethal effects in 50% of animals.

The quantal dose-effect curve is often characterized by stating the median effective dose (ED50), which is the dose at which 50% of individuals exhibit the specified quantal effect. (Note that the abbreviation ED50 has a different meaning in this context... 

The existence of "no-effect doses" for toxic compounds is a controversial point, but it is clear that to measure the exposure sufficiently accurately and to detect the response reliably are major problems (see below for further discussion). Suffice it to say that certain carcinogens are carcinogenic after exposure to concentrations measured in parts per million, and the dose-response curves for some nitrosamines and for ionizing radiation appear to pass through zero when the linear portion is extrapolated. At present, therefore, in some cases no-effect levels cannot be demonstrated for certain types of toxic effect. 

It relates the pharmacologically effective dose to the toxic or lethal dose (Fig. 2.8). The therapeutic index gives some indication of the safety of the compound in use, as the larger the ratio, the greater the relative safety. However, as already indicated, simple comparison of parameters derived from the dose-response curve such as the LD50 and TD50 may be... 

Figure 4 shows that some of the synthetic preparations exhibit lethal toxicity and/or pyrogenicity. Compared to lipid A, however, the effective doses of the synthetic preparations for lethality and pyrogenicity were ca. 1000 and 100 times higher. Obviously, there is a separation of activities Preparation 302 is pyrogenic, but not lethal, while preparations 314 and 315 are lethal, but not pyrogenic. Furthermore, preparation 316, which could be directly solubilized in water, was toxic to galactosamine-treated mice in a dose of 50 pg/mouse. With this dose, a low monophasic fever curve was seen in rabbits. In contrast,... 

Quantal Dose-Response Curves and the Median Effective Dose... 

FIGURE 1-4 Cumulative dose-response curve. The median effective dose CED5tl) is 10 mg, and the median toxic dose (TD50] is 320 mg. The therapeutic index (Tf) for this drug is 32. 

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