Creation of model, its research

5. Check of adequacy of model to real object. The instruction of borders of applicability of model. Thus, the model coordinates real object with the purpose of research:, simplifies object, enables to carry out research, keeps that interests the researcher.

Fig.1.

Physical, biological, mathematical models often apply in biophysics, biology and medicine. Also analog modelling is widespread.

Classification of models:

The physical model has the physical nature, identical with investigated object. For example, current of blood on vessels is modelled by movement of a liquid on pipes (rigid or elastic). At modelling electric processes in heart, it is considered as electric current dipole. The real membrane is replaced artificial (for example, a liposome) for studying processes permeability of ions through biological membranes. Liposome - physical model of a biological membrane. The physical devices temporarily replacing bodies of an alive organism, also it is possible to carry to physical models: an artificial kidney - model of a kidney, cardiostimulator - model of processes in sinus node of heart, the device of artificial breath - model of lungs.

Biological models - represent the biological objects convenient for experimental researches on which properties, laws of biophysical processes in real complex objects are studied. For example, laws of occurrence and distribution of potential of action in nervous fibres have been studied only after a finding of good biological model, it is huge axon оf a squid. Experience of Ussing proving existence of active transport, has been lead on biological model - a leather of a frog which modelled property of a biological membrane to carry out active transport. Laws of contractility a myocardium it is established on the basis of model ling experiments on a capillary muscle.

Mathematical models - the description of processes in real object by means of the mathematical equations, usually differential equations. For realization of mathematical models computers now are widely used. The computer is used at research of pathological processes in cardiology, developments of epidemics, it is possible to change easily scale on time: to accelerate or slow down current of process, to consider process in a stationary mode as it is offered in model of reduction of a muscle, and on space For example, it is possible to enter local spatial heterogeneity of parameters, to change a configuration of a zone of a pathology. Changing factors or entering new members in the differential equations, it is possible to consider various properties of object, or theoretically to create objects with new properties, for example, to receive medical products of more effective action. By means of the computer it is possible to solve the complex equations and to predict behaviour of system: current of disease, efficiency of treatment, action of a pharmaceutical preparation.

If processes in model have other physical nature, than the original, but are described by the same mathematical device (as a rule, the identical differential equations) such model is called analog. Usually in the form of analog model it is used electric schemes. For example, the electric circuit consisting of resistance, capacities and coils of inductance is analog model of vascular system.

The basic requirements to which the model should answer:

1. Adequacy - conformity of model to object, i.e. model should to make laws of the studied phenomena with the set degree of accuracy. The analysis of adequacy should be spent at a choice of model and at comparison of results of modelling by behaviour of object.

2. Borders of applicability of model should be established, i.e. a condition at which the chosen model is adequate to studied object should be precisely specified, because any model does not give the exhaustive description of object. Borders of applicability are defined by assumptions which are provided at drawing up of model. As a rule, the more assumptions, the less border of applicability. So, for example, liposome is adequate model of a biological membrane if permeability lip id double layer of membranes for various substances is studied. If the purpose of research - electrogenesis in cells in this case a liposome not adequate model, borders of its applicability do not satisfy the purpose of research. Nernst’s equation well describes a membrane potential difference for the cell, being in rest that is in an equilibrium condition, it is adequate mathematical model of system in the given condition. If to consider a phase of depolarization of action potential, when the condition of system far from equilibrium condition and goes a stream of ions to a cell, this equation becomes not adequate to process. Model Hodgkin-Haksley is adequate mathematical model of process of formations of potential of action in axon of a squid.

Reception of new data about course of studied process, its properties is result of modelling. The result of modelling, as a rule, does not give exhaustive data on studied object, but it deepens our knowledge of it, allows carrying out further more complex researches. So, in the equation of three-componential model of Hill existence viscous components has been shown at reduction of a muscle.

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