Response functions general relationships

LET. Although there is general agreement that high-LET radiation is more carcinogenic, than low-LET radiation, the relation between them has not been satisfactorily quantified and may also vary by tumor site. This relationship, of course, dqiends partly on the respective dose-response functions appropriate for high- and low-LET radiation. 

It is important to recognize the unique relationship that exists between the responses to an impulse and step change in concentration. The derivative of the step response (Eq. 2.14) is identical to the impulse response (Eq. 2.4), and the integral of the impulse response is identical to the step response. This reciprocity is an important property of linear systems in general. The reader should now appreciate that under linear conditions, the time dependence of any concentration profile can be treated by adding the response functions for its component impulses. 

The principal aim in undertaking regression analysis is to develop a suitable mathematical model for descriptive or predictive purposes. The model can be used to confirm some idea or theory regarding the relationship between variables or it can be used to predict some general, continuous response function from discrete and possibly relatively few measurements. 

Logistic function generally yields a sigmoidally shaped line similar to that defined by drug dose-response relationships in biological systems. It is defined by y = (1 + e-(a + bx))-1. 

The high to low dose extrapolation problem is conceptually straight-forward. The probability of a toxic response is modeled by a dose-response function P(D) which represents the probability of a toxic response when exposed to D units of the toxic agent. A general mathematical model is chosen to describe this functional relationship, its unknown parameters are estimated from the available data, and this estimated dose-response function P(D) is then used to either (1) estimate the response measure at a particular low dose level of interest or (2) estimate that dose level corresponding to a desired low level of response (this dose estimate is commonly known as the virtually safe dose, VSD). 

Values for tte internal variabtes in thetmodynamic, internal equilibriwn are generally uniquely defined by the values for the external variables. For instance, in a simple, thermomechanical system (i.e. one that reacts mechanically solely volume-elastically) the equilibrium concentrations of the conformational isomers are uniquely described by temperature and pressure. In this case the conformational isomerism is not explicitly percqitible, but causes only overall effects, for example in the system s enthalpy or entropy. Elastic macroscopic effects may, however, occur when the relationship between internal and external variables is not single-valued. Then the response-functions of the system diverge or show discontinuities. The Systran undergoes a thermodynamic transformation. The best-known example of sudi a transformation based on conformational isomerism is the helix-coil transition displayed by sonte polymers in solution. An example in the scdid state is the crystal-to-condis crystal transition discussed in this paper. The conditions under which such transformations occur are dealt with in more detail in Sect 2.2. 

An outstanding feature of the FPD in the sulphur mode is its non-linear response function. In general, the relationship between peak area. A, and analyte mass, m, is described by an exponential form ... 

Before going further, I think it will be helpful if we examine closely one of the fundamental underlying aspects of the theory which gives rise to many of the important kinetic features I have sketched previously. First, however, the general relationship between distribution functions and experimentally observed response functions must be understood. As an example in this case, I will briefly review the relationship between the distribution of elastic relaxation times H( ) and the experimentally determined stress relaxation modulus E(t). Mathematically these functions are related by the expression... 

Despite the problems in generalizing from animals to humans, both the animal and the human studies show considerable internal consistency in that they both support a continuous dose-response functional relationship between lead and neurotoxic biochemical, morphological, electrophysiological, and behavioural effects. 

The fluctuation-dissipation theorem (FDT) of Callen and Welton states a general relationship between the response of a given system to an external disturbance and the internal fluctuation of the system in the absence of the dismrbance. Such a response is characterized by a response function or equivalently by an admittance or an impedance. For dielectric relaxation, the complex dielectric function, e ( u), is related to the dipole moment correlation function < >( ) via Fourier transformation ... 

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