Quantitative analysis of dose-effect relationships: the combined effects of multiple drugs or enzyme inhibitors

Impulses and Physiological States in Theoretical Models of Nerve Membrane

In recent years, great emphasis has been placed on the role of arterial stiffness in the development of cardiovascular diseases. Indeed, the assessment of arterial stiffness is increasingly used in the clinical assessment of patients. Although several papers have previously addressed the methodological issues concerning the various indices of arterial stiffness currently available, and their clinical applications, clinicians and researchers still report difficulties in selecting the most appropriate methodology for their specific use. This paper summarizes the proceedings of several meetings of the European Network for Non-invasive Investigation of Large Arteries and is aimed at providing an updated and practical overview of the most relevant methodological aspects and clinical applications in this area.

Expert consensus document on arterial stiffness: methodological issues and clinical applications

The hope was recently expressed (Hill 1937, p. 116) that with the development of a more accurate and rapid technique for muscle heat measurement, a much more consistent picture might emerge of the energy relations of muscles shortening (or lengthening) and doing positive (or negative) work. This hope has been realized, and some astonishingly simple and accurate relations have been found, relations, moreover, which (among other things) determine the effect of load on speed of shortening, allow the form of the isometric contraction to be predicted, and are the basis of the so-called “visco-elasticity” of skeletal muscle. This paper is divided into three parts. In Part I further developments of the technique are described: everything has depended on the technique, so no apology is needed for a rather full description of it and of the precautions necessary. In Part II the results themselves are described and discussed. In Part III the “visco-elastic” properties of active muscle are shown to be a consequence of the properties described in Part II.

The heat of shortening and the dynamic constants of muscle

The median-effect equation derived from the mass-action law principle at equilibrium-steady state via mathematical induction and deduction for different reaction sequences and mechanisms and different types of inhibition has been shown to be the unified theory for the Michaelis-Menten equation, Hill equation, Henderson-Hasselbalch equation, and Scatchard equation. It is shown that dose and effect are interchangeable via defined parameters. This general equation for the single drug effect has been extended to the multiple drug effect equation for n drugs. These equations provide the theoretical basis for the combination index (CI)-isobologram equation that allows quantitative determination of drug interactions, where CI 1 indicate synergism, additive effect, and antagonism, respectively. Based on these algorithms, computer software has been developed to allow automated simulation of synergism and antagonism at all dose or effect levels. It displays the dose-effect curve, median-effect plot, combination index plot, isobologram, dose-reduction index plot, and polygonogram for in vitro or in vivo studies. This theoretical development, experimental design, and computerized data analysis have facilitated dose-effect analysis for single drug evaluation or carcinogen and radiation risk assessment, as well as for drug or other entity combinations in a vast field of disciplines of biomedical sciences. In this review, selected examples of applications are given, and step-by-step examples of experimental designs and real data analysis are also illustrated. The merging of the mass-action law principle with mathematical induction-deduction has been proven to be a unique and effective scientific method for general theory development. The median-effect principle and its mass-action law based computer software are gaining increased applications in biomedical sciences, from how to effectively evaluate a single compound or entity to how to beneficially use multiple drugs or modalities in combination therapies.

http://www.protocol-online.org/forums/uploads/monthly_09_2010/post-8165-008503000%201284677034.ipb

Theoretical Basis, Experimental Design, and Computerized Simulation of Synergism and Antagonism in Drug Combination Studies

Muscular Exercise, Lactic Acid, and the Supply and Utilization of Oxygen

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The Combinations of Haemoglobin with Oxygen and with Carbon Monoxide. I.

In an investigation now being carried out by us at Manchester observations are being made, under various conditions, upon the velocity of the pulse wave in man. As a preliminary to this investigation it was thought advisable to study the theory of the transmission of the pulse wave, and the following pages contain the results arrived at, together with an account of experiments upon the velocity of the pulse wave in an isolated human artery.

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The Velocity of the Pulse Wave in Man

The diffusion of dissolved substances through cells and tissues is a determining factor in many vital processes. The slowness of diffusion on the scale of ordinary sensible objects gives to the unaided imagination an imperfect realisation of its speed and importance in systems of the dimensions of the living cell. The diffusion constant k is expressed in terms of the number of unit quantities of substance which diffuse per minute across an area of 1 sq. cm. in a gradient of concentration per cm. of 1 unit quantity per c. c. For aqueous solutions of ordinary substances k is usually of the order of 2 to 10 times 10-4. The diffusion constant is of the dimensions L2T-1, 2 in length, -1 in time. Expressing it in units of 1μ (0·0001 cm.) instead of 1 cm., and of 1σ (0·001 sec.) instead of minutes, k is of the order of unity, instead of multiple of 10-4. Thus the diffusion constant is a fairly large quantity for systems involving distances of the order of 1μ and times of the order of 1σ. A cylinder 1 cm. in diameter composed of material similar to frog's nerve, if suddenly placed in oxygen, would take 185 minutes to attain 90 per cent. of is full saturation with that gas. An actual nerve 0·7 mm. thick would take 54 seconds for the same stage of saturation to be reached. A single nerve fiber 7μ thick would take only 5·4 σ. Again, the rapidity of diffusion attainable in systems of small dimensions is the basis of the capillary circulation, and therewith of the whole design of the larger animals; and the rate at which diffusion an supply oxygen to a fatigued muscle for the removal of lactic acid is an important factor in determining the speed at which recovery can occur.

Archibald Vivian Hill

Papers

The heat of shortening and the dynamic constants of muscle

Muscular Exercise, Lactic Acid, and the Supply and Utilization of Oxygen

The Combinations of Haemoglobin with Oxygen and with Carbon Monoxide. I.

The Velocity of the Pulse Wave in Man

The Diffusion of Oxygen and Lactic Acid through Tissues